REAL is non empty V35() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V35() V40() V41() Element of bool REAL
bool REAL is non empty V35() set
{} is set
the Relation-like non-empty empty-yielding functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() ext-real non positive non negative V35() V40() V42( {} ) V79() FinSequence-like FinSequence-membered integer set is Relation-like non-empty empty-yielding functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() ext-real non positive non negative V35() V40() V42( {} ) V79() FinSequence-like FinSequence-membered integer set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
{{},1} is set
[:1,1:] is Relation-like non empty set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is Relation-like non empty set
bool [:[:1,1:],1:] is non empty set
omega is non empty epsilon-transitive epsilon-connected ordinal V35() V40() V41() set
bool omega is non empty V35() set
bool NAT is non empty V35() set
COMPLEX is non empty V35() set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
{{}} is non empty trivial V42(1) set
INT is non empty V35() set
the non empty set is non empty set
the Element of the non empty set is Element of the non empty set
[: the non empty set , the non empty set :] is Relation-like non empty set
[:[: the non empty set , the non empty set :], the non empty set :] is Relation-like non empty set
bool [:[: the non empty set , the non empty set :], the non empty set :] is non empty set
the Relation-like Function-like V18([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :] is Relation-like Function-like V18([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :]
[:INT, the non empty set :] is Relation-like non empty V35() set
[:[:INT, the non empty set :], the non empty set :] is Relation-like non empty V35() set
bool [:[:INT, the non empty set :], the non empty set :] is non empty V35() set
the Relation-like Function-like V18([:INT, the non empty set :], the non empty set ) Element of bool [:[:INT, the non empty set :], the non empty set :] is Relation-like Function-like V18([:INT, the non empty set :], the non empty set ) Element of bool [:[:INT, the non empty set :], the non empty set :]
( the non empty set , the Element of the non empty set , the Relation-like Function-like V18([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :], the Relation-like Function-like V18([:INT, the non empty set :], the non empty set ) Element of bool [:[:INT, the non empty set :], the non empty set :]) is () ()
the carrier of ( the non empty set , the Element of the non empty set , the Relation-like Function-like V18([: the non empty set , the non empty set :], the non empty set ) Element of bool [:[: the non empty set , the non empty set :], the non empty set :], the Relation-like Function-like V18([:INT, the non empty set :], the non empty set ) Element of bool [:[:INT, the non empty set :], the non empty set :]) is set
AG is non empty ()
the carrier of AG is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ML is V31() ext-real V79() integer set
ZS is Element of the carrier of AG
the of AG . (ML,ZS) is set
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
the of AG . [ML,ZS] is set
AD is V31() ext-real V79() integer Element of INT
the of AG . (AD,ZS) is Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
the of AG . [AD,ZS] is set
AG is non empty set
[:AG,AG:] is Relation-like non empty set
[:[:AG,AG:],AG:] is Relation-like non empty set
bool [:[:AG,AG:],AG:] is non empty set
[:INT,AG:] is Relation-like non empty V35() set
[:[:INT,AG:],AG:] is Relation-like non empty V35() set
bool [:[:INT,AG:],AG:] is non empty V35() set
ZS is Element of AG
ML is Relation-like Function-like V18([:AG,AG:],AG) Element of bool [:[:AG,AG:],AG:]
AD is Relation-like Function-like V18([:INT,AG:],AG) Element of bool [:[:INT,AG:],AG:]
(AG,ZS,ML,AD) is () ()
op0 is epsilon-transitive epsilon-connected ordinal Element of 1
op2 is Relation-like Function-like V18([:1,1:],1) Element of bool [:[:1,1:],1:]
pr2 (INT,1) is Relation-like Function-like V18([:INT,1:],1) Element of bool [:[:INT,1:],1:]
[:INT,1:] is Relation-like non empty V35() set
[:[:INT,1:],1:] is Relation-like non empty V35() set
bool [:[:INT,1:],1:] is non empty V35() set
(1,op0,op2,(pr2 (INT,1))) is non empty () ()
() is () ()
AG is non empty trivial V50() 1 -element left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () ()
the carrier of AG is non empty trivial V35() V42(1) set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is V31() ext-real V79() integer set
ML is V31() ext-real V79() integer set
ZS + ML is V31() ext-real V79() integer set
(AG,AD,(ZS + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . ((ZS + ML),AD) is set
[(ZS + ML),AD] is set
{(ZS + ML),AD} is set
{(ZS + ML)} is non empty trivial V42(1) set
{{(ZS + ML),AD},{(ZS + ML)}} is set
the of AG . [(ZS + ML),AD] is set
(AG,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,AD) is set
[ZS,AD] is set
{ZS,AD} is set
{ZS} is non empty trivial V42(1) set
{{ZS,AD},{ZS}} is set
the of AG . [ZS,AD] is set
(AG,AD,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,AD) is set
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the of AG . [ML,AD] is set
(AG,AD,ZS) + (AG,AD,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((AG,AD,ZS),(AG,AD,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,AD,ZS),(AG,AD,ML)] is set
{(AG,AD,ZS),(AG,AD,ML)} is set
{(AG,AD,ZS)} is non empty trivial V42(1) set
{{(AG,AD,ZS),(AG,AD,ML)},{(AG,AD,ZS)}} is set
the addF of AG . [(AG,AD,ZS),(AG,AD,ML)] is set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the addF of AG . [ML,AD] is set
ZS is V31() ext-real V79() integer set
(AG,(ML + AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ZS,(ML + AD)) is set
[ZS,(ML + AD)] is set
{ZS,(ML + AD)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(ML + AD)},{ZS}} is set
the of AG . [ZS,(ML + AD)] is set
(AG,ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,ML) is set
[ZS,ML] is set
{ZS,ML} is set
{{ZS,ML},{ZS}} is set
the of AG . [ZS,ML] is set
(AG,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,AD) is set
[ZS,AD] is set
{ZS,AD} is set
{{ZS,AD},{ZS}} is set
the of AG . [ZS,AD] is set
(AG,ML,ZS) + (AG,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,ML,ZS),(AG,AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ML,ZS),(AG,AD,ZS)] is set
{(AG,ML,ZS),(AG,AD,ZS)} is set
{(AG,ML,ZS)} is non empty trivial V42(1) set
{{(AG,ML,ZS),(AG,AD,ZS)},{(AG,ML,ZS)}} is set
the addF of AG . [(AG,ML,ZS),(AG,AD,ZS)] is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is V31() ext-real V79() integer set
ML is V31() ext-real V79() integer set
ZS * ML is V31() ext-real V79() integer set
(AG,AD,(ZS * ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . ((ZS * ML),AD) is set
[(ZS * ML),AD] is set
{(ZS * ML),AD} is set
{(ZS * ML)} is non empty trivial V42(1) set
{{(ZS * ML),AD},{(ZS * ML)}} is set
the of AG . [(ZS * ML),AD] is set
(AG,AD,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,AD) is set
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the of AG . [ML,AD] is set
(AG,(AG,AD,ML),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,(AG,AD,ML)) is set
[ZS,(AG,AD,ML)] is set
{ZS,(AG,AD,ML)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(AG,AD,ML)},{ZS}} is set
the of AG . [ZS,(AG,AD,ML)] is set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (1,ZS) is set
[1,ZS] is set
{1,ZS} is set
{1} is non empty trivial V42(1) set
{{1,ZS},{1}} is set
the of AG . [1,ZS] is set
AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . (AG,ML) is set
[AG,ML] is set
{AG,ML} is set
{AG} is non empty trivial V42(1) set
{{AG,ML},{AG}} is set
the of ZS . [AG,ML] is set
CA is V31() ext-real V79() integer set
(ZS,ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (CA,ML) is set
[CA,ML] is set
{CA,ML} is set
{CA} is non empty trivial V42(1) set
{{CA,ML},{CA}} is set
the of ZS . [CA,ML] is set
ML + (ZS,ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS . (ML,(ZS,ML,CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[ML,(ZS,ML,CA)] is set
{ML,(ZS,ML,CA)} is set
{ML} is non empty trivial V42(1) set
{{ML,(ZS,ML,CA)},{ML}} is set
the addF of ZS . [ML,(ZS,ML,CA)] is set
AD is V31() ext-real V79() integer set
(ZS,ML,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AD,ML) is set
[AD,ML] is set
{AD,ML} is set
{AD} is non empty trivial V42(1) set
{{AD,ML},{AD}} is set
the of ZS . [AD,ML] is set
(ZS,ML,AD) + (ZS,ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . ((ZS,ML,AD),(ZS,ML,CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(ZS,ML,AD),(ZS,ML,CA)] is set
{(ZS,ML,AD),(ZS,ML,CA)} is set
{(ZS,ML,AD)} is non empty trivial V42(1) set
{{(ZS,ML,AD),(ZS,ML,CA)},{(ZS,ML,AD)}} is set
the addF of ZS . [(ZS,ML,AD),(ZS,ML,CA)] is set
AD + CA is V31() ext-real V79() integer set
(ZS,ML,(AD + CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . ((AD + CA),ML) is set
[(AD + CA),ML] is set
{(AD + CA),ML} is set
{(AD + CA)} is non empty trivial V42(1) set
{{(AD + CA),ML},{(AD + CA)}} is set
the of ZS . [(AD + CA),ML] is set
ML + (0. ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . (ML,(0. ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[ML,(0. ZS)] is set
{ML,(0. ZS)} is set
{{ML,(0. ZS)},{ML}} is set
the addF of ZS . [ML,(0. ZS)] is set
(ZS,(0. ZS),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(0. ZS)) is set
[AG,(0. ZS)] is set
{AG,(0. ZS)} is set
{{AG,(0. ZS)},{AG}} is set
the of ZS . [AG,(0. ZS)] is set
(ZS,(0. ZS),AG) + (ZS,(0. ZS),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS . ((ZS,(0. ZS),AG),(ZS,(0. ZS),AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(ZS,(0. ZS),AG),(ZS,(0. ZS),AG)] is set
{(ZS,(0. ZS),AG),(ZS,(0. ZS),AG)} is set
{(ZS,(0. ZS),AG)} is non empty trivial V42(1) set
{{(ZS,(0. ZS),AG),(ZS,(0. ZS),AG)},{(ZS,(0. ZS),AG)}} is set
the addF of ZS . [(ZS,(0. ZS),AG),(ZS,(0. ZS),AG)] is set
(0. ZS) + (0. ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . ((0. ZS),(0. ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(0. ZS),(0. ZS)] is set
{(0. ZS),(0. ZS)} is set
{(0. ZS)} is non empty trivial V42(1) set
{{(0. ZS),(0. ZS)},{(0. ZS)}} is set
the addF of ZS . [(0. ZS),(0. ZS)] is set
(ZS,((0. ZS) + (0. ZS)),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,((0. ZS) + (0. ZS))) is set
[AG,((0. ZS) + (0. ZS))] is set
{AG,((0. ZS) + (0. ZS))} is set
{{AG,((0. ZS) + (0. ZS))},{AG}} is set
the of ZS . [AG,((0. ZS) + (0. ZS))] is set
(ZS,(0. ZS),AG) + (0. ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . ((ZS,(0. ZS),AG),(0. ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(ZS,(0. ZS),AG),(0. ZS)] is set
{(ZS,(0. ZS),AG),(0. ZS)} is set
{{(ZS,(0. ZS),AG),(0. ZS)},{(ZS,(0. ZS),AG)}} is set
the addF of ZS . [(ZS,(0. ZS),AG),(0. ZS)] is set
- 1 is V31() ext-real non positive V79() integer set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . ((- 1),ZS) is set
[(- 1),ZS] is set
{(- 1),ZS} is set
{(- 1)} is non empty trivial V42(1) set
{{(- 1),ZS},{(- 1)}} is set
the of AG . [(- 1),ZS] is set
ZS + (AG,ZS,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(AG,ZS,(- 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(AG,ZS,(- 1))] is set
{ZS,(AG,ZS,(- 1))} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(AG,ZS,(- 1))},{ZS}} is set
the addF of AG . [ZS,(AG,ZS,(- 1))] is set
(AG,ZS,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (1,ZS) is set
[1,ZS] is set
{1,ZS} is set
{1} is non empty trivial V42(1) set
{{1,ZS},{1}} is set
the of AG . [1,ZS] is set
(AG,ZS,1) + (AG,ZS,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,ZS,1),(AG,ZS,(- 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ZS,1),(AG,ZS,(- 1))] is set
{(AG,ZS,1),(AG,ZS,(- 1))} is set
{(AG,ZS,1)} is non empty trivial V42(1) set
{{(AG,ZS,1),(AG,ZS,(- 1))},{(AG,ZS,1)}} is set
the addF of AG . [(AG,ZS,1),(AG,ZS,(- 1))] is set
1 + (- 1) is V31() ext-real V79() integer set
(AG,ZS,(1 + (- 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((1 + (- 1)),ZS) is set
[(1 + (- 1)),ZS] is set
{(1 + (- 1)),ZS} is set
{(1 + (- 1))} is non empty trivial V42(1) set
{{(1 + (- 1)),ZS},{(1 + (- 1))}} is set
the of AG . [(1 + (- 1)),ZS] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(- ZS) + (ZS + (AG,ZS,(- 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ZS),(ZS + (AG,ZS,(- 1)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ZS),(ZS + (AG,ZS,(- 1)))] is set
{(- ZS),(ZS + (AG,ZS,(- 1)))} is set
{(- ZS)} is non empty trivial V42(1) set
{{(- ZS),(ZS + (AG,ZS,(- 1)))},{(- ZS)}} is set
the addF of AG . [(- ZS),(ZS + (AG,ZS,(- 1)))] is set
(- ZS) + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ZS),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ZS),ZS] is set
{(- ZS),ZS} is set
{{(- ZS),ZS},{(- ZS)}} is set
the addF of AG . [(- ZS),ZS] is set
((- ZS) + ZS) + (AG,ZS,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((- ZS) + ZS),(AG,ZS,(- 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((- ZS) + ZS),(AG,ZS,(- 1))] is set
{((- ZS) + ZS),(AG,ZS,(- 1))} is set
{((- ZS) + ZS)} is non empty trivial V42(1) set
{{((- ZS) + ZS),(AG,ZS,(- 1))},{((- ZS) + ZS)}} is set
the addF of AG . [((- ZS) + ZS),(AG,ZS,(- 1))] is set
(0. AG) + (AG,ZS,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),(AG,ZS,(- 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),(AG,ZS,(- 1))] is set
{(0. AG),(AG,ZS,(- 1))} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),(AG,ZS,(- 1))},{(0. AG)}} is set
the addF of AG . [(0. AG),(AG,ZS,(- 1))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,ZS] is set
{ZS,ZS} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ZS},{ZS}} is set
the addF of AG . [ZS,ZS] is set
(AG,ZS,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (1,ZS) is set
[1,ZS] is set
{1,ZS} is set
{1} is non empty trivial V42(1) set
{{1,ZS},{1}} is set
the of AG . [1,ZS] is set
(AG,ZS,1) + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,ZS,1),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ZS,1),ZS] is set
{(AG,ZS,1),ZS} is set
{(AG,ZS,1)} is non empty trivial V42(1) set
{{(AG,ZS,1),ZS},{(AG,ZS,1)}} is set
the addF of AG . [(AG,ZS,1),ZS] is set
(AG,ZS,1) + (AG,ZS,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,ZS,1),(AG,ZS,1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ZS,1),(AG,ZS,1)] is set
{(AG,ZS,1),(AG,ZS,1)} is set
{{(AG,ZS,1),(AG,ZS,1)},{(AG,ZS,1)}} is set
the addF of AG . [(AG,ZS,1),(AG,ZS,1)] is set
1 + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
(AG,ZS,(1 + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((1 + 1),ZS) is set
[(1 + 1),ZS] is set
{(1 + 1),ZS} is set
{(1 + 1)} is non empty trivial V42(1) set
{{(1 + 1),ZS},{(1 + 1)}} is set
the of AG . [(1 + 1),ZS] is set
(AG,ZS,2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (2,ZS) is set
[2,ZS] is set
{2,ZS} is set
{2} is non empty trivial V42(1) set
{{2,ZS},{2}} is set
the of AG . [2,ZS] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,ZS] is set
{ZS,ZS} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ZS},{ZS}} is set
the addF of AG . [ZS,ZS] is set
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is V31() ext-real V79() integer set
- AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(- ML),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . (AG,(- ML)) is set
[AG,(- ML)] is set
{AG,(- ML)} is set
{AG} is non empty trivial V42(1) set
{{AG,(- ML)},{AG}} is set
the of ZS . [AG,(- ML)] is set
(ZS,ML,(- AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . ((- AG),ML) is set
[(- AG),ML] is set
{(- AG),ML} is set
{(- AG)} is non empty trivial V42(1) set
{{(- AG),ML},{(- AG)}} is set
the of ZS . [(- AG),ML] is set
(ZS,ML,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . ((- 1),ML) is set
[(- 1),ML] is set
{(- 1),ML} is set
{(- 1)} is non empty trivial V42(1) set
{{(- 1),ML},{(- 1)}} is set
the of ZS . [(- 1),ML] is set
(ZS,(ZS,ML,(- 1)),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(ZS,ML,(- 1))) is set
[AG,(ZS,ML,(- 1))] is set
{AG,(ZS,ML,(- 1))} is set
{{AG,(ZS,ML,(- 1))},{AG}} is set
the of ZS . [AG,(ZS,ML,(- 1))] is set
AG * (- 1) is V31() ext-real V79() integer set
(ZS,ML,(AG * (- 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . ((AG * (- 1)),ML) is set
[(AG * (- 1)),ML] is set
{(AG * (- 1)),ML} is set
{(AG * (- 1))} is non empty trivial V42(1) set
{{(AG * (- 1)),ML},{(AG * (- 1))}} is set
the of ZS . [(AG * (- 1)),ML] is set
AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(- ML),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . (AG,(- ML)) is set
[AG,(- ML)] is set
{AG,(- ML)} is set
{AG} is non empty trivial V42(1) set
{{AG,(- ML)},{AG}} is set
the of ZS . [AG,(- ML)] is set
(ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,ML) is set
[AG,ML] is set
{AG,ML} is set
{{AG,ML},{AG}} is set
the of ZS . [AG,ML] is set
- (ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
1 * AG is V31() ext-real V79() integer set
- (1 * AG) is V31() ext-real V79() integer set
(ZS,ML,(- (1 * AG))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . ((- (1 * AG)),ML) is set
[(- (1 * AG)),ML] is set
{(- (1 * AG)),ML} is set
{(- (1 * AG))} is non empty trivial V42(1) set
{{(- (1 * AG)),ML},{(- (1 * AG))}} is set
the of ZS . [(- (1 * AG)),ML] is set
(- 1) * AG is V31() ext-real V79() integer set
(ZS,ML,((- 1) * AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (((- 1) * AG),ML) is set
[((- 1) * AG),ML] is set
{((- 1) * AG),ML} is set
{((- 1) * AG)} is non empty trivial V42(1) set
{{((- 1) * AG),ML},{((- 1) * AG)}} is set
the of ZS . [((- 1) * AG),ML] is set
(ZS,(ZS,ML,AG),(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . ((- 1),(ZS,ML,AG)) is set
[(- 1),(ZS,ML,AG)] is set
{(- 1),(ZS,ML,AG)} is set
{(- 1)} is non empty trivial V42(1) set
{{(- 1),(ZS,ML,AG)},{(- 1)}} is set
the of ZS . [(- 1),(ZS,ML,AG)] is set
AG is V31() ext-real V79() integer set
- AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(- ML),(- AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . ((- AG),(- ML)) is set
[(- AG),(- ML)] is set
{(- AG),(- ML)} is set
{(- AG)} is non empty trivial V42(1) set
{{(- AG),(- ML)},{(- AG)}} is set
the of ZS . [(- AG),(- ML)] is set
(ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,ML) is set
[AG,ML] is set
{AG,ML} is set
{AG} is non empty trivial V42(1) set
{{AG,ML},{AG}} is set
the of ZS . [AG,ML] is set
- (- AG) is V31() ext-real V79() integer set
(ZS,ML,(- (- AG))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . ((- (- AG)),ML) is set
[(- (- AG)),ML] is set
{(- (- AG)),ML} is set
{(- (- AG))} is non empty trivial V42(1) set
{{(- (- AG)),ML},{(- (- AG))}} is set
the of ZS . [(- (- AG)),ML] is set
AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . (AG,ML) is set
[AG,ML] is set
{AG,ML} is set
{AG} is non empty trivial V42(1) set
{{AG,ML},{AG}} is set
the of ZS . [AG,ML] is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
ML - AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
ML + (- AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS . (ML,(- AD)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[ML,(- AD)] is set
{ML,(- AD)} is set
{ML} is non empty trivial V42(1) set
{{ML,(- AD)},{ML}} is set
the addF of ZS . [ML,(- AD)] is set
(ZS,(ML - AD),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(ML - AD)) is set
[AG,(ML - AD)] is set
{AG,(ML - AD)} is set
{{AG,(ML - AD)},{AG}} is set
the of ZS . [AG,(ML - AD)] is set
(ZS,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,AD) is set
[AG,AD] is set
{AG,AD} is set
{{AG,AD},{AG}} is set
the of ZS . [AG,AD] is set
(ZS,ML,AG) - (ZS,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- (ZS,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,ML,AG) + (- (ZS,AD,AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . ((ZS,ML,AG),(- (ZS,AD,AG))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(ZS,ML,AG),(- (ZS,AD,AG))] is set
{(ZS,ML,AG),(- (ZS,AD,AG))} is set
{(ZS,ML,AG)} is non empty trivial V42(1) set
{{(ZS,ML,AG),(- (ZS,AD,AG))},{(ZS,ML,AG)}} is set
the addF of ZS . [(ZS,ML,AG),(- (ZS,AD,AG))] is set
(ZS,(- AD),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(- AD)) is set
[AG,(- AD)] is set
{AG,(- AD)} is set
{{AG,(- AD)},{AG}} is set
the of ZS . [AG,(- AD)] is set
(ZS,ML,AG) + (ZS,(- AD),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . ((ZS,ML,AG),(ZS,(- AD),AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(ZS,ML,AG),(ZS,(- AD),AG)] is set
{(ZS,ML,AG),(ZS,(- AD),AG)} is set
{{(ZS,ML,AG),(ZS,(- AD),AG)},{(ZS,ML,AG)}} is set
the addF of ZS . [(ZS,ML,AG),(ZS,(- AD),AG)] is set
AG is V31() ext-real V79() integer set
ZS is V31() ext-real V79() integer set
AG - ZS is V31() ext-real V79() integer set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ML is non empty set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
(ML,AD,(AG - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML is Relation-like Function-like V18([:INT, the carrier of ML:], the carrier of ML) Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
[:INT, the carrier of ML:] is Relation-like non empty V35() set
[:[:INT, the carrier of ML:], the carrier of ML:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ML:], the carrier of ML:] is non empty V35() set
the of ML . ((AG - ZS),AD) is set
[(AG - ZS),AD] is set
{(AG - ZS),AD} is set
{(AG - ZS)} is non empty trivial V42(1) set
{{(AG - ZS),AD},{(AG - ZS)}} is set
the of ML . [(AG - ZS),AD] is set
(ML,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML . (AG,AD) is set
[AG,AD] is set
{AG,AD} is set
{AG} is non empty trivial V42(1) set
{{AG,AD},{AG}} is set
the of ML . [AG,AD] is set
(ML,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML . (ZS,AD) is set
[ZS,AD] is set
{ZS,AD} is set
{ZS} is non empty trivial V42(1) set
{{ZS,AD},{ZS}} is set
the of ML . [ZS,AD] is set
(ML,AD,AG) - (ML,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
- (ML,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
(ML,AD,AG) + (- (ML,AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML is Relation-like Function-like V18([: the carrier of ML, the carrier of ML:], the carrier of ML) Element of bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:]
[: the carrier of ML, the carrier of ML:] is Relation-like non empty set
[:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is Relation-like non empty set
bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is non empty set
the addF of ML . ((ML,AD,AG),(- (ML,AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[(ML,AD,AG),(- (ML,AD,ZS))] is set
{(ML,AD,AG),(- (ML,AD,ZS))} is set
{(ML,AD,AG)} is non empty trivial V42(1) set
{{(ML,AD,AG),(- (ML,AD,ZS))},{(ML,AD,AG)}} is set
the addF of ML . [(ML,AD,AG),(- (ML,AD,ZS))] is set
- ZS is V31() ext-real V79() integer set
AG + (- ZS) is V31() ext-real V79() integer set
(ML,AD,(AG + (- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML . ((AG + (- ZS)),AD) is set
[(AG + (- ZS)),AD] is set
{(AG + (- ZS)),AD} is set
{(AG + (- ZS))} is non empty trivial V42(1) set
{{(AG + (- ZS)),AD},{(AG + (- ZS))}} is set
the of ML . [(AG + (- ZS)),AD] is set
(ML,AD,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML . ((- ZS),AD) is set
[(- ZS),AD] is set
{(- ZS),AD} is set
{(- ZS)} is non empty trivial V42(1) set
{{(- ZS),AD},{(- ZS)}} is set
the of ML . [(- ZS),AD] is set
(ML,AD,AG) + (ML,AD,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . ((ML,AD,AG),(ML,AD,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[(ML,AD,AG),(ML,AD,(- ZS))] is set
{(ML,AD,AG),(ML,AD,(- ZS))} is set
{{(ML,AD,AG),(ML,AD,(- ZS))},{(ML,AD,AG)}} is set
the addF of ML . [(ML,AD,AG),(ML,AD,(- ZS))] is set
- AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
(ML,(- AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML . (ZS,(- AD)) is set
[ZS,(- AD)] is set
{ZS,(- AD)} is set
{{ZS,(- AD)},{ZS}} is set
the of ML . [ZS,(- AD)] is set
(ML,AD,AG) + (ML,(- AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . ((ML,AD,AG),(ML,(- AD),ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[(ML,AD,AG),(ML,(- AD),ZS)] is set
{(ML,AD,AG),(ML,(- AD),ZS)} is set
{{(ML,AD,AG),(ML,(- AD),ZS)},{(ML,AD,AG)}} is set
the addF of ML . [(ML,AD,AG),(ML,(- AD),ZS)] is set
AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . (AG,ML) is set
[AG,ML] is set
{AG,ML} is set
{AG} is non empty trivial V42(1) set
{{AG,ML},{AG}} is set
the of ZS . [AG,ML] is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,AD) is set
[AG,AD] is set
{AG,AD} is set
{{AG,AD},{AG}} is set
the of ZS . [AG,AD] is set
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,ML,AG) - (ZS,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- (ZS,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,ML,AG) + (- (ZS,AD,AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS . ((ZS,ML,AG),(- (ZS,AD,AG))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(ZS,ML,AG),(- (ZS,AD,AG))] is set
{(ZS,ML,AG),(- (ZS,AD,AG))} is set
{(ZS,ML,AG)} is non empty trivial V42(1) set
{{(ZS,ML,AG),(- (ZS,AD,AG))},{(ZS,ML,AG)}} is set
the addF of ZS . [(ZS,ML,AG),(- (ZS,AD,AG))] is set
ML - AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
ML + (- AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . (ML,(- AD)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[ML,(- AD)] is set
{ML,(- AD)} is set
{ML} is non empty trivial V42(1) set
{{ML,(- AD)},{ML}} is set
the addF of ZS . [ML,(- AD)] is set
(ZS,(ML - AD),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(ML - AD)) is set
[AG,(ML - AD)] is set
{AG,(ML - AD)} is set
{{AG,(ML - AD)},{AG}} is set
the of ZS . [AG,(ML - AD)] is set
AG is V31() ext-real V79() integer set
ZS is V31() ext-real V79() integer set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ML is non empty set
0. ML is V51(ML) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the ZeroF of ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
(ML,AD,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML is Relation-like Function-like V18([:INT, the carrier of ML:], the carrier of ML) Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
[:INT, the carrier of ML:] is Relation-like non empty V35() set
[:[:INT, the carrier of ML:], the carrier of ML:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ML:], the carrier of ML:] is non empty V35() set
the of ML . (AG,AD) is set
[AG,AD] is set
{AG,AD} is set
{AG} is non empty trivial V42(1) set
{{AG,AD},{AG}} is set
the of ML . [AG,AD] is set
(ML,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML . (ZS,AD) is set
[ZS,AD] is set
{ZS,AD} is set
{ZS} is non empty trivial V42(1) set
{{ZS,AD},{ZS}} is set
the of ML . [ZS,AD] is set
(ML,AD,AG) - (ML,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
- (ML,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
(ML,AD,AG) + (- (ML,AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML is Relation-like Function-like V18([: the carrier of ML, the carrier of ML:], the carrier of ML) Element of bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:]
[: the carrier of ML, the carrier of ML:] is Relation-like non empty set
[:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is Relation-like non empty set
bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is non empty set
the addF of ML . ((ML,AD,AG),(- (ML,AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[(ML,AD,AG),(- (ML,AD,ZS))] is set
{(ML,AD,AG),(- (ML,AD,ZS))} is set
{(ML,AD,AG)} is non empty trivial V42(1) set
{{(ML,AD,AG),(- (ML,AD,ZS))},{(ML,AD,AG)}} is set
the addF of ML . [(ML,AD,AG),(- (ML,AD,ZS))] is set
AG - ZS is V31() ext-real V79() integer set
(ML,AD,(AG - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML . ((AG - ZS),AD) is set
[(AG - ZS),AD] is set
{(AG - ZS),AD} is set
{(AG - ZS)} is non empty trivial V42(1) set
{{(AG - ZS),AD},{(AG - ZS)}} is set
the of ML . [(AG - ZS),AD] is set
- ZS is V31() ext-real V79() integer set
(- ZS) + AG is V31() ext-real V79() integer set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
<*> the carrier of AG is Relation-like non-empty empty-yielding NAT -defined the carrier of AG -valued Function-like functional empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() ext-real non positive non negative V35() V40() V42( {} ) V79() FinSequence-like FinSubsequence-like FinSequence-membered integer FinSequence of the carrier of AG
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
Sum (<*> the carrier of AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
bool [:NAT, the carrier of AG:] is non empty V35() set
len (<*> the carrier of AG) is Relation-like non-empty empty-yielding functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() ext-real non positive non negative V35() V40() V42( {} ) V79() FinSequence-like FinSequence-membered integer Element of NAT
ML is Relation-like Function-like V18( NAT , the carrier of AG) Element of bool [:NAT, the carrier of AG:]
ML . (len (<*> the carrier of AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML . 0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is Relation-like NAT -defined the carrier of AG -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of AG
len ZS is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Sum ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
<*> the carrier of AG is Relation-like non-empty empty-yielding NAT -defined the carrier of AG -valued Function-like functional empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() ext-real non positive non negative V35() V40() V42( {} ) V79() FinSequence-like FinSubsequence-like FinSequence-membered integer FinSequence of the carrier of AG
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
dom ML is Element of bool NAT
Sum ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
AD is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Sum AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(Sum AD),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . (AG,(Sum AD)) is set
[AG,(Sum AD)] is set
{AG,(Sum AD)} is set
{AG} is non empty trivial V42(1) set
{{AG,(Sum AD)},{AG}} is set
the of ZS . [AG,(Sum AD)] is set
Seg (len ML) is V35() V42( len ML) Element of bool NAT
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
MLI is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len MLI is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
Seg (len Z0) is V35() V42( len Z0) Element of bool NAT
Seg CA is V35() V42(CA) Element of bool NAT
Z0 | (Seg CA) is Relation-like NAT -defined Seg CA -defined NAT -defined the carrier of ZS -valued Function-like FinSubsequence-like Element of bool [:NAT, the carrier of ZS:]
[:NAT, the carrier of ZS:] is Relation-like non empty V35() set
bool [:NAT, the carrier of ZS:] is non empty V35() set
MLI | (Seg CA) is Relation-like NAT -defined Seg CA -defined NAT -defined the carrier of ZS -valued Function-like FinSubsequence-like Element of bool [:NAT, the carrier of ZS:]
i is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len i is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
v is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len v is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Seg (len v) is V35() V42( len v) Element of bool NAT
dom v is Element of bool NAT
v1 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
i . v1 is set
dom i is Element of bool NAT
MLI . v1 is set
Z0 . v1 is set
(ZS,a1,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,a1) is set
[AG,a1] is set
{AG,a1} is set
{{AG,a1},{AG}} is set
the of ZS . [AG,a1] is set
v . v1 is set
dom Z0 is Element of bool NAT
dom MLI is Element of bool NAT
Z0 . (CA + 1) is set
MLI . (CA + 1) is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,a1,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,a1) is set
[AG,a1] is set
{AG,a1} is set
{{AG,a1},{AG}} is set
the of ZS . [AG,a1] is set
Seg (len i) is V35() V42( len i) Element of bool NAT
Sum Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
Sum v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(Sum v) + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS . ((Sum v),v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(Sum v),v1] is set
{(Sum v),v1} is set
{(Sum v)} is non empty trivial V42(1) set
{{(Sum v),v1},{(Sum v)}} is set
the addF of ZS . [(Sum v),v1] is set
Sum i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(Sum i),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(Sum i)) is set
[AG,(Sum i)] is set
{AG,(Sum i)} is set
{{AG,(Sum i)},{AG}} is set
the of ZS . [AG,(Sum i)] is set
(ZS,(Sum i),AG) + (ZS,a1,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . ((ZS,(Sum i),AG),(ZS,a1,AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(ZS,(Sum i),AG),(ZS,a1,AG)] is set
{(ZS,(Sum i),AG),(ZS,a1,AG)} is set
{(ZS,(Sum i),AG)} is non empty trivial V42(1) set
{{(ZS,(Sum i),AG),(ZS,a1,AG)},{(ZS,(Sum i),AG)}} is set
the addF of ZS . [(ZS,(Sum i),AG),(ZS,a1,AG)] is set
(Sum i) + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS . ((Sum i),a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[(Sum i),a1] is set
{(Sum i),a1} is set
{(Sum i)} is non empty trivial V42(1) set
{{(Sum i),a1},{(Sum i)}} is set
the addF of ZS . [(Sum i),a1] is set
(ZS,((Sum i) + a1),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,((Sum i) + a1)) is set
[AG,((Sum i) + a1)] is set
{AG,((Sum i) + a1)} is set
{{AG,((Sum i) + a1)},{AG}} is set
the of ZS . [AG,((Sum i) + a1)] is set
Sum MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(Sum MLI),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(Sum MLI)) is set
[AG,(Sum MLI)] is set
{AG,(Sum MLI)} is set
{{AG,(Sum MLI)},{AG}} is set
the of ZS . [AG,(Sum MLI)] is set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
MLI is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len MLI is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
Seg (len Z0) is V35() V42( len Z0) Element of bool NAT
Sum Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
Sum MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(Sum MLI),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(Sum MLI)) is set
[AG,(Sum MLI)] is set
{AG,(Sum MLI)} is set
{{AG,(Sum MLI)},{AG}} is set
the of ZS . [AG,(Sum MLI)] is set
CA is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Seg (len CA) is V35() V42( len CA) Element of bool NAT
Sum CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
Sum Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(Sum Z0),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(Sum Z0)) is set
[AG,(Sum Z0)] is set
{AG,(Sum Z0)} is set
{{AG,(Sum Z0)},{AG}} is set
the of ZS . [AG,(Sum Z0)] is set
CA is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Seg (len CA) is V35() V42( len CA) Element of bool NAT
Sum CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
Sum Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(Sum Z0),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(Sum Z0)) is set
[AG,(Sum Z0)] is set
{AG,(Sum Z0)} is set
{{AG,(Sum Z0)},{AG}} is set
the of ZS . [AG,(Sum Z0)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
<*> the carrier of AG is Relation-like non-empty empty-yielding NAT -defined the carrier of AG -valued Function-like functional empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V31() ext-real non positive non negative V35() V40() V42( {} ) V79() FinSequence-like FinSubsequence-like FinSequence-membered integer FinSequence of the carrier of AG
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
Sum (<*> the carrier of AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is V31() ext-real V79() integer set
(AG,(Sum (<*> the carrier of AG)),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ZS,(Sum (<*> the carrier of AG))) is set
[ZS,(Sum (<*> the carrier of AG))] is set
{ZS,(Sum (<*> the carrier of AG))} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(Sum (<*> the carrier of AG))},{ZS}} is set
the of AG . [ZS,(Sum (<*> the carrier of AG))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is V31() ext-real V79() integer set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
<*ML,AD*> is Relation-like NAT -defined the carrier of AG -valued Function-like non empty V35() V42(2) FinSequence-like FinSubsequence-like FinSequence of the carrier of AG
Sum <*ML,AD*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,(Sum <*ML,AD*>),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ZS,(Sum <*ML,AD*>)) is set
[ZS,(Sum <*ML,AD*>)] is set
{ZS,(Sum <*ML,AD*>)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(Sum <*ML,AD*>)},{ZS}} is set
the of AG . [ZS,(Sum <*ML,AD*>)] is set
(AG,ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,ML) is set
[ZS,ML] is set
{ZS,ML} is set
{{ZS,ML},{ZS}} is set
the of AG . [ZS,ML] is set
(AG,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,AD) is set
[ZS,AD] is set
{ZS,AD} is set
{{ZS,AD},{ZS}} is set
the of AG . [ZS,AD] is set
(AG,ML,ZS) + (AG,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((AG,ML,ZS),(AG,AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ML,ZS),(AG,AD,ZS)] is set
{(AG,ML,ZS),(AG,AD,ZS)} is set
{(AG,ML,ZS)} is non empty trivial V42(1) set
{{(AG,ML,ZS),(AG,AD,ZS)},{(AG,ML,ZS)}} is set
the addF of AG . [(AG,ML,ZS),(AG,AD,ZS)] is set
ML + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the addF of AG . [ML,AD] is set
(AG,(ML + AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,(ML + AD)) is set
[ZS,(ML + AD)] is set
{ZS,(ML + AD)} is set
{{ZS,(ML + AD)},{ZS}} is set
the of AG . [ZS,(ML + AD)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is V31() ext-real V79() integer set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
<*ML,AD,CA*> is Relation-like NAT -defined the carrier of AG -valued Function-like non empty V35() V42(3) FinSequence-like FinSubsequence-like FinSequence of the carrier of AG
Sum <*ML,AD,CA*> is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,(Sum <*ML,AD,CA*>),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ZS,(Sum <*ML,AD,CA*>)) is set
[ZS,(Sum <*ML,AD,CA*>)] is set
{ZS,(Sum <*ML,AD,CA*>)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(Sum <*ML,AD,CA*>)},{ZS}} is set
the of AG . [ZS,(Sum <*ML,AD,CA*>)] is set
(AG,ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,ML) is set
[ZS,ML] is set
{ZS,ML} is set
{{ZS,ML},{ZS}} is set
the of AG . [ZS,ML] is set
(AG,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,AD) is set
[ZS,AD] is set
{ZS,AD} is set
{{ZS,AD},{ZS}} is set
the of AG . [ZS,AD] is set
(AG,ML,ZS) + (AG,AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((AG,ML,ZS),(AG,AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ML,ZS),(AG,AD,ZS)] is set
{(AG,ML,ZS),(AG,AD,ZS)} is set
{(AG,ML,ZS)} is non empty trivial V42(1) set
{{(AG,ML,ZS),(AG,AD,ZS)},{(AG,ML,ZS)}} is set
the addF of AG . [(AG,ML,ZS),(AG,AD,ZS)] is set
(AG,CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,CA) is set
[ZS,CA] is set
{ZS,CA} is set
{{ZS,CA},{ZS}} is set
the of AG . [ZS,CA] is set
((AG,ML,ZS) + (AG,AD,ZS)) + (AG,CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG,ML,ZS) + (AG,AD,ZS)),(AG,CA,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG,ML,ZS) + (AG,AD,ZS)),(AG,CA,ZS)] is set
{((AG,ML,ZS) + (AG,AD,ZS)),(AG,CA,ZS)} is set
{((AG,ML,ZS) + (AG,AD,ZS))} is non empty trivial V42(1) set
{{((AG,ML,ZS) + (AG,AD,ZS)),(AG,CA,ZS)},{((AG,ML,ZS) + (AG,AD,ZS))}} is set
the addF of AG . [((AG,ML,ZS) + (AG,AD,ZS)),(AG,CA,ZS)] is set
ML + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the addF of AG . [ML,AD] is set
(ML + AD) + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + AD),CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + AD),CA] is set
{(ML + AD),CA} is set
{(ML + AD)} is non empty trivial V42(1) set
{{(ML + AD),CA},{(ML + AD)}} is set
the addF of AG . [(ML + AD),CA] is set
(AG,((ML + AD) + CA),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,((ML + AD) + CA)) is set
[ZS,((ML + AD) + CA)] is set
{ZS,((ML + AD) + CA)} is set
{{ZS,((ML + AD) + CA)},{ZS}} is set
the of AG . [ZS,((ML + AD) + CA)] is set
(AG,(ML + AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ZS,(ML + AD)) is set
[ZS,(ML + AD)] is set
{ZS,(ML + AD)} is set
{{ZS,(ML + AD)},{ZS}} is set
the of AG . [ZS,(ML + AD)] is set
(AG,(ML + AD),ZS) + (AG,CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,(ML + AD),ZS),(AG,CA,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,(ML + AD),ZS),(AG,CA,ZS)] is set
{(AG,(ML + AD),ZS),(AG,CA,ZS)} is set
{(AG,(ML + AD),ZS)} is non empty trivial V42(1) set
{{(AG,(ML + AD),ZS),(AG,CA,ZS)},{(AG,(ML + AD),ZS)}} is set
the addF of AG . [(AG,(ML + AD),ZS),(AG,CA,ZS)] is set
AG is V31() ext-real V79() integer set
- AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,ML,(- AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . ((- AG),ML) is set
[(- AG),ML] is set
{(- AG),ML} is set
{(- AG)} is non empty trivial V42(1) set
{{(- AG),ML},{(- AG)}} is set
the of ZS . [(- AG),ML] is set
(ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,ML) is set
[AG,ML] is set
{AG,ML} is set
{AG} is non empty trivial V42(1) set
{{AG,ML},{AG}} is set
the of ZS . [AG,ML] is set
- (ZS,ML,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(- ML),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,(- ML)) is set
[AG,(- ML)] is set
{AG,(- ML)} is set
{{AG,(- ML)},{AG}} is set
the of ZS . [AG,(- ML)] is set
AG is V31() ext-real V79() integer set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
dom ML is Element of bool NAT
Sum ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
(ZS,(Sum ML),AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS . (AG,(Sum ML)) is set
[AG,(Sum ML)] is set
{AG,(Sum ML)} is set
{AG} is non empty trivial V42(1) set
{{AG,(Sum ML)},{AG}} is set
the of ZS . [AG,(Sum ML)] is set
AD is Relation-like NAT -defined the carrier of ZS -valued Function-like V35() FinSequence-like FinSubsequence-like FinSequence of the carrier of ZS
len AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Sum AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
Seg (len ML) is V35() V42( len ML) Element of bool NAT
dom AD is Element of bool NAT
Seg (len AD) is V35() V42( len AD) Element of bool NAT
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
ML . CA is set
ML /. CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
AD . CA is set
(ZS,Z0,AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS . (AG,Z0) is set
[AG,Z0] is set
{AG,Z0} is set
{{AG,Z0},{AG}} is set
the of ZS . [AG,Z0] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is Element of bool the carrier of AG
the Element of ZS is Element of ZS
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (0,AD) is set
[0,AD] is set
{0,AD} is set
{0} is non empty trivial V42(1) set
{{0,AD},{0}} is set
the of AG . [0,AD] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is Element of bool the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ML,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . ((- 1),ML) is set
[(- 1),ML] is set
{(- 1),ML} is set
{(- 1)} is non empty trivial V42(1) set
{{(- 1),ML},{(- 1)}} is set
the of AG . [(- 1),ML] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is Element of bool the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML - AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (- AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,(- AD)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- AD)] is set
{ML,(- AD)} is set
{ML} is non empty trivial V42(1) set
{{ML,(- AD)},{ML}} is set
the addF of AG . [ML,(- AD)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is Element of bool the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the addF of AG . [ML,AD] is set
ML is V31() ext-real V79() integer set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ML,AD) is set
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the of AG . [ML,AD] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is Element of bool the carrier of AG
ML is Element of bool the carrier of AG
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in ML ) } is set
AD is Element of bool the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AG . [CA,Z0] is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,v] is set
{MLI,v} is set
{MLI} is non empty trivial V42(1) set
{{MLI,v},{MLI}} is set
the addF of AG . [MLI,v] is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
i + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (i,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the addF of AG . [i,v1] is set
(MLI + v) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + v),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + v),i] is set
{(MLI + v),i} is set
{(MLI + v)} is non empty trivial V42(1) set
{{(MLI + v),i},{(MLI + v)}} is set
the addF of AG . [(MLI + v),i] is set
((MLI + v) + i) + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((MLI + v) + i),v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((MLI + v) + i),v1] is set
{((MLI + v) + i),v1} is set
{((MLI + v) + i)} is non empty trivial V42(1) set
{{((MLI + v) + i),v1},{((MLI + v) + i)}} is set
the addF of AG . [((MLI + v) + i),v1] is set
MLI + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,i] is set
{MLI,i} is set
{{MLI,i},{MLI}} is set
the addF of AG . [MLI,i] is set
(MLI + i) + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + i),v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + i),v] is set
{(MLI + i),v} is set
{(MLI + i)} is non empty trivial V42(1) set
{{(MLI + i),v},{(MLI + i)}} is set
the addF of AG . [(MLI + i),v] is set
((MLI + i) + v) + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((MLI + i) + v),v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((MLI + i) + v),v1] is set
{((MLI + i) + v),v1} is set
{((MLI + i) + v)} is non empty trivial V42(1) set
{{((MLI + i) + v),v1},{((MLI + i) + v)}} is set
the addF of AG . [((MLI + i) + v),v1] is set
v + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,v1] is set
{v,v1} is set
{v} is non empty trivial V42(1) set
{{v,v1},{v}} is set
the addF of AG . [v,v1] is set
(MLI + i) + (v + v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + i),(v + v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + i),(v + v1)] is set
{(MLI + i),(v + v1)} is set
{{(MLI + i),(v + v1)},{(MLI + i)}} is set
the addF of AG . [(MLI + i),(v + v1)] is set
CA is V31() ext-real V79() integer set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,Z0,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (CA,Z0) is set
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the of AG . [CA,Z0] is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (MLI,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,v] is set
{MLI,v} is set
{MLI} is non empty trivial V42(1) set
{{MLI,v},{MLI}} is set
the addF of AG . [MLI,v] is set
(AG,MLI,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (CA,MLI) is set
[CA,MLI] is set
{CA,MLI} is set
{{CA,MLI},{CA}} is set
the of AG . [CA,MLI] is set
(AG,v,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (CA,v) is set
[CA,v] is set
{CA,v} is set
{{CA,v},{CA}} is set
the of AG . [CA,v] is set
(AG,MLI,CA) + (AG,v,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,MLI,CA),(AG,v,CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,MLI,CA),(AG,v,CA)] is set
{(AG,MLI,CA),(AG,v,CA)} is set
{(AG,MLI,CA)} is non empty trivial V42(1) set
{{(AG,MLI,CA),(AG,v,CA)},{(AG,MLI,CA)}} is set
the addF of AG . [(AG,MLI,CA),(AG,v,CA)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{(0. AG)} is non empty trivial V42(1) Element of bool the carrier of AG
ZS is Element of bool the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the addF of AG . [ML,AD] is set
ML is V31() ext-real V79() integer set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ML,AD) is set
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the of AG . [ML,AD] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is (AG) Element of bool the carrier of AG
ML is (AG) Element of bool the carrier of AG
ZS /\ ML is Element of bool the carrier of AG
AD is Element of bool the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AG . [CA,Z0] is set
CA is V31() ext-real V79() integer set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,Z0,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (CA,Z0) is set
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the of AG . [CA,Z0] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
[:INT, the carrier of AG:] is Relation-like non empty V35() set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the addF of AG || the carrier of AG is Relation-like Function-like set
the addF of AG | [: the carrier of AG, the carrier of AG:] is Relation-like set
the of AG | [:INT, the carrier of AG:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
the carrier of AD is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
the carrier of AG is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the carrier of ZS is non empty set
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the carrier of ZS is non empty set
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
0. ML is V51(ML) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the carrier of ML is non empty set
the ZeroF of ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,ML] is set
{ZS,ML} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ML},{ZS}} is set
the addF of AG . [ZS,ML] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of AD is non empty set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
the addF of AD is Relation-like Function-like V18([: the carrier of AD, the carrier of AD:], the carrier of AD) Element of bool [:[: the carrier of AD, the carrier of AD:], the carrier of AD:]
[: the carrier of AD, the carrier of AD:] is Relation-like non empty set
[:[: the carrier of AD, the carrier of AD:], the carrier of AD:] is Relation-like non empty set
bool [:[: the carrier of AD, the carrier of AD:], the carrier of AD:] is non empty set
the addF of AD . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AD . [CA,Z0] is set
the addF of AG || the carrier of AD is Relation-like Function-like set
the addF of AG | [: the carrier of AD, the carrier of AD:] is Relation-like set
[CA,Z0] is Element of [: the carrier of AD, the carrier of AD:]
( the addF of AG || the carrier of AD) . [CA,Z0] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer set
(AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ML,ZS) is set
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
the of AG . [ML,ZS] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of AD is non empty set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
(AD,CA,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
the of AD is Relation-like Function-like V18([:INT, the carrier of AD:], the carrier of AD) Element of bool [:[:INT, the carrier of AD:], the carrier of AD:]
[:INT, the carrier of AD:] is Relation-like non empty V35() set
[:[:INT, the carrier of AD:], the carrier of AD:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AD:], the carrier of AD:] is non empty V35() set
the of AD . (ML,CA) is set
[ML,CA] is set
{ML,CA} is set
{{ML,CA},{ML}} is set
the of AD . [ML,CA] is set
Z0 is V31() ext-real V79() integer Element of INT
(AD,CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
the of AD . (Z0,CA) is set
[Z0,CA] is set
{Z0,CA} is set
{Z0} is non empty trivial V42(1) set
{{Z0,CA},{Z0}} is set
the of AD . [Z0,CA] is set
the of AG | [:INT, the carrier of AD:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[Z0,CA] is Element of [:INT, the carrier of AD:]
( the of AG | [:INT, the carrier of AD:]) . [Z0,CA] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
- AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
(AG,ZS,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . ((- 1),ZS) is set
[(- 1),ZS] is set
{(- 1),ZS} is set
{(- 1)} is non empty trivial V42(1) set
{{(- 1),ZS},{(- 1)}} is set
the of AG . [(- 1),ZS] is set
(ML,AD,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the of ML is Relation-like Function-like V18([:INT, the carrier of ML:], the carrier of ML) Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
[:INT, the carrier of ML:] is Relation-like non empty V35() set
[:[:INT, the carrier of ML:], the carrier of ML:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ML:], the carrier of ML:] is non empty V35() set
the of ML . ((- 1),AD) is set
[(- 1),AD] is set
{(- 1),AD} is set
{{(- 1),AD},{(- 1)}} is set
the of ML . [(- 1),AD] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ML)] is set
{ZS,(- ML)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- ML)},{ZS}} is set
the addF of AG . [ZS,(- ML)] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of AD is non empty set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
CA - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
CA + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
the addF of AD is Relation-like Function-like V18([: the carrier of AD, the carrier of AD:], the carrier of AD) Element of bool [:[: the carrier of AD, the carrier of AD:], the carrier of AD:]
[: the carrier of AD, the carrier of AD:] is Relation-like non empty set
[:[: the carrier of AD, the carrier of AD:], the carrier of AD:] is Relation-like non empty set
bool [:[: the carrier of AD, the carrier of AD:], the carrier of AD:] is non empty set
the addF of AD . (CA,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
[CA,(- Z0)] is set
{CA,(- Z0)} is set
{CA} is non empty trivial V42(1) set
{{CA,(- Z0)},{CA}} is set
the addF of AD . [CA,(- Z0)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is Element of bool the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of CA is non empty set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of CA
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of CA
v + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of CA
the addF of CA is Relation-like Function-like V18([: the carrier of CA, the carrier of CA:], the carrier of CA) Element of bool [:[: the carrier of CA, the carrier of CA:], the carrier of CA:]
[: the carrier of CA, the carrier of CA:] is Relation-like non empty set
[:[: the carrier of CA, the carrier of CA:], the carrier of CA:] is Relation-like non empty set
bool [:[: the carrier of CA, the carrier of CA:], the carrier of CA:] is non empty set
the addF of CA . (v,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of CA
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
the addF of CA . [v,i] is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
Z0 is V31() ext-real V79() integer set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,MLI,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (Z0,MLI) is set
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the of AG . [Z0,MLI] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of CA is non empty set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of CA
(CA,v,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of CA
the of CA is Relation-like Function-like V18([:INT, the carrier of CA:], the carrier of CA) Element of bool [:[:INT, the carrier of CA:], the carrier of CA:]
[:INT, the carrier of CA:] is Relation-like non empty V35() set
[:[:INT, the carrier of CA:], the carrier of CA:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of CA:], the carrier of CA:] is non empty V35() set
the of CA . (Z0,v) is set
[Z0,v] is set
{Z0,v} is set
{{Z0,v},{Z0}} is set
the of CA . [Z0,v] is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG || the carrier of AG is Relation-like Function-like set
the addF of AG | [: the carrier of AG, the carrier of AG:] is Relation-like set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG | [:INT, the carrier of AG:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the carrier of ZS is non empty set
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the carrier of ZS is non empty set
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the carrier of ZS is non empty set
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,ML] is set
{ZS,ML} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ML},{ZS}} is set
the addF of AG . [ZS,ML] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
bool the carrier of AG is non empty set
the carrier of AD is non empty set
CA is Element of bool the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer set
(AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ML,ZS) is set
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
the of AG . [ML,ZS] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
bool the carrier of AG is non empty set
the carrier of AD is non empty set
CA is Element of bool the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . ((- 1),ZS) is set
[(- 1),ZS] is set
{(- 1),ZS} is set
{(- 1)} is non empty trivial V42(1) set
{{(- 1),ZS},{(- 1)}} is set
the of AG . [(- 1),ZS] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ML)] is set
{ZS,(- ML)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- ML)},{ZS}} is set
the addF of AG . [ZS,(- ML)] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
[:INT, the carrier of AG:] is Relation-like non empty V35() set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is Element of bool the carrier of AG
the addF of AG || ZS is Relation-like Function-like set
[:ZS,ZS:] is Relation-like set
the addF of AG | [:ZS,ZS:] is Relation-like set
[:INT,ZS:] is Relation-like set
the of AG | [:INT,ZS:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
ML is non empty set
[:ML,ML:] is Relation-like non empty set
[:[:ML,ML:],ML:] is Relation-like non empty set
bool [:[:ML,ML:],ML:] is non empty set
[:INT,ML:] is Relation-like non empty V35() set
[:[:INT,ML:],ML:] is Relation-like non empty V35() set
bool [:[:INT,ML:],ML:] is non empty V35() set
AD is Element of ML
CA is Relation-like Function-like V18([:ML,ML:],ML) Element of bool [:[:ML,ML:],ML:]
Z0 is Relation-like Function-like V18([:INT,ML:],ML) Element of bool [:[:INT,ML:],ML:]
(ML,AD,CA,Z0) is non empty () ()
the carrier of (ML,AD,CA,Z0) is non empty set
v is V31() ext-real V79() integer set
i is Element of the carrier of (ML,AD,CA,Z0)
((ML,AD,CA,Z0),i,v) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) is Relation-like Function-like V18([:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[:INT, the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
[:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty V35() set
the of (ML,AD,CA,Z0) . (v,i) is set
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
the of (ML,AD,CA,Z0) . [v,i] is set
the of AG . (v,i) is set
the of AG . [v,i] is set
v1 is V31() ext-real V79() integer Element of INT
[v1,i] is Element of [:INT, the carrier of (ML,AD,CA,Z0):]
{v1,i} is set
{v1} is non empty trivial V42(1) set
{{v1,i},{v1}} is set
the of AG . [v1,i] is set
v is Element of the carrier of (ML,AD,CA,Z0)
i is Element of the carrier of (ML,AD,CA,Z0)
v + i is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) is Relation-like Function-like V18([: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
[:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty set
the addF of (ML,AD,CA,Z0) . (v,i) is Element of the carrier of (ML,AD,CA,Z0)
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
the addF of (ML,AD,CA,Z0) . [v,i] is set
the addF of AG . (v,i) is set
the addF of AG . [v,i] is set
[v,i] is Element of [: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):]
the addF of AG . [v,i] is set
v1 is Element of the carrier of (ML,AD,CA,Z0)
a1 is Element of the carrier of (ML,AD,CA,Z0)
v1 + a1 is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) is Relation-like Function-like V18([: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
[:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty set
the addF of (ML,AD,CA,Z0) . (v1,a1) is Element of the carrier of (ML,AD,CA,Z0)
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of (ML,AD,CA,Z0) . [v1,a1] is set
a1 + v1 is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . (a1,v1) is Element of the carrier of (ML,AD,CA,Z0)
[a1,v1] is set
{a1,v1} is set
{a1} is non empty trivial V42(1) set
{{a1,v1},{a1}} is set
the addF of (ML,AD,CA,Z0) . [a1,v1] is set
b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
b1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
the addF of AG . [b1,v1] is set
v1 + b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,b1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,b1] is set
{v1,b1} is set
{v1} is non empty trivial V42(1) set
{{v1,b1},{v1}} is set
the addF of AG . [v1,b1] is set
v1 is Element of the carrier of (ML,AD,CA,Z0)
a1 is Element of the carrier of (ML,AD,CA,Z0)
v1 + a1 is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) is Relation-like Function-like V18([: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
[:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty set
the addF of (ML,AD,CA,Z0) . (v1,a1) is Element of the carrier of (ML,AD,CA,Z0)
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of (ML,AD,CA,Z0) . [v1,a1] is set
b1 is Element of the carrier of (ML,AD,CA,Z0)
(v1 + a1) + b1 is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . ((v1 + a1),b1) is Element of the carrier of (ML,AD,CA,Z0)
[(v1 + a1),b1] is set
{(v1 + a1),b1} is set
{(v1 + a1)} is non empty trivial V42(1) set
{{(v1 + a1),b1},{(v1 + a1)}} is set
the addF of (ML,AD,CA,Z0) . [(v1 + a1),b1] is set
a1 + b1 is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . (a1,b1) is Element of the carrier of (ML,AD,CA,Z0)
[a1,b1] is set
{a1,b1} is set
{a1} is non empty trivial V42(1) set
{{a1,b1},{a1}} is set
the addF of (ML,AD,CA,Z0) . [a1,b1] is set
v1 + (a1 + b1) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . (v1,(a1 + b1)) is Element of the carrier of (ML,AD,CA,Z0)
[v1,(a1 + b1)] is set
{v1,(a1 + b1)} is set
{{v1,(a1 + b1)},{v1}} is set
the addF of (ML,AD,CA,Z0) . [v1,(a1 + b1)] is set
x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((v1 + a1),x) is set
[(v1 + a1),x] is set
{(v1 + a1),x} is set
{{(v1 + a1),x},{(v1 + a1)}} is set
the addF of AG . [(v1 + a1),x] is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,v] is set
{v1,v} is set
{v1} is non empty trivial V42(1) set
{{v1,v},{v1}} is set
the addF of AG . [v1,v] is set
(v1 + v) + x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((v1 + v),x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(v1 + v),x] is set
{(v1 + v),x} is set
{(v1 + v)} is non empty trivial V42(1) set
{{(v1 + v),x},{(v1 + v)}} is set
the addF of AG . [(v1 + v),x] is set
v + x is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,x] is set
{v,x} is set
{v} is non empty trivial V42(1) set
{{v,x},{v}} is set
the addF of AG . [v,x] is set
v1 + (v + x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,(v + x)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,(v + x)] is set
{v1,(v + x)} is set
{{v1,(v + x)},{v1}} is set
the addF of AG . [v1,(v + x)] is set
the addF of AG . (v1,(a1 + b1)) is set
[v1,(a1 + b1)] is set
{v1,(a1 + b1)} is set
{{v1,(a1 + b1)},{v1}} is set
the addF of AG . [v1,(a1 + b1)] is set
v1 is Element of the carrier of (ML,AD,CA,Z0)
0. (ML,AD,CA,Z0) is V51((ML,AD,CA,Z0)) Element of the carrier of (ML,AD,CA,Z0)
the ZeroF of (ML,AD,CA,Z0) is Element of the carrier of (ML,AD,CA,Z0)
v1 + (0. (ML,AD,CA,Z0)) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) is Relation-like Function-like V18([: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
[:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty set
the addF of (ML,AD,CA,Z0) . (v1,(0. (ML,AD,CA,Z0))) is Element of the carrier of (ML,AD,CA,Z0)
[v1,(0. (ML,AD,CA,Z0))] is set
{v1,(0. (ML,AD,CA,Z0))} is set
{v1} is non empty trivial V42(1) set
{{v1,(0. (ML,AD,CA,Z0))},{v1}} is set
the addF of (ML,AD,CA,Z0) . [v1,(0. (ML,AD,CA,Z0))] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (a1,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,(0. AG)] is set
{a1,(0. AG)} is set
{a1} is non empty trivial V42(1) set
{{a1,(0. AG)},{a1}} is set
the addF of AG . [a1,(0. AG)] is set
v1 is Element of the carrier of (ML,AD,CA,Z0)
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 + b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (a1,b1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,b1] is set
{a1,b1} is set
{a1} is non empty trivial V42(1) set
{{a1,b1},{a1}} is set
the addF of AG . [a1,b1] is set
- a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,a1,(- 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((- 1),a1) is set
[(- 1),a1] is set
{(- 1),a1} is set
{(- 1)} is non empty trivial V42(1) set
{{(- 1),a1},{(- 1)}} is set
the of AG . [(- 1),a1] is set
((ML,AD,CA,Z0),v1,(- 1)) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) is Relation-like Function-like V18([:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[:INT, the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
[:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty V35() set
the of (ML,AD,CA,Z0) . ((- 1),v1) is set
[(- 1),v1] is set
{(- 1),v1} is set
{{(- 1),v1},{(- 1)}} is set
the of (ML,AD,CA,Z0) . [(- 1),v1] is set
v1 is Element of the carrier of (ML,AD,CA,Z0)
v1 + v1 is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) is Relation-like Function-like V18([: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
[:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty set
the addF of (ML,AD,CA,Z0) . (v1,v1) is Element of the carrier of (ML,AD,CA,Z0)
[v1,v1] is set
{v1,v1} is set
{v1} is non empty trivial V42(1) set
{{v1,v1},{v1}} is set
the addF of (ML,AD,CA,Z0) . [v1,v1] is set
0. (ML,AD,CA,Z0) is V51((ML,AD,CA,Z0)) Element of the carrier of (ML,AD,CA,Z0)
the ZeroF of (ML,AD,CA,Z0) is Element of the carrier of (ML,AD,CA,Z0)
v1 is V31() ext-real V79() integer set
a1 is Element of the carrier of (ML,AD,CA,Z0)
b1 is Element of the carrier of (ML,AD,CA,Z0)
a1 + b1 is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) is Relation-like Function-like V18([: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
[:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty set
the addF of (ML,AD,CA,Z0) . (a1,b1) is Element of the carrier of (ML,AD,CA,Z0)
[a1,b1] is set
{a1,b1} is set
{a1} is non empty trivial V42(1) set
{{a1,b1},{a1}} is set
the addF of (ML,AD,CA,Z0) . [a1,b1] is set
((ML,AD,CA,Z0),(a1 + b1),v1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) is Relation-like Function-like V18([:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[:INT, the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
[:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty V35() set
the of (ML,AD,CA,Z0) . (v1,(a1 + b1)) is set
[v1,(a1 + b1)] is set
{v1,(a1 + b1)} is set
{v1} is non empty trivial V42(1) set
{{v1,(a1 + b1)},{v1}} is set
the of (ML,AD,CA,Z0) . [v1,(a1 + b1)] is set
((ML,AD,CA,Z0),a1,v1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (v1,a1) is set
[v1,a1] is set
{v1,a1} is set
{{v1,a1},{v1}} is set
the of (ML,AD,CA,Z0) . [v1,a1] is set
((ML,AD,CA,Z0),b1,v1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (v1,b1) is set
[v1,b1] is set
{v1,b1} is set
{{v1,b1},{v1}} is set
the of (ML,AD,CA,Z0) . [v1,b1] is set
((ML,AD,CA,Z0),a1,v1) + ((ML,AD,CA,Z0),b1,v1) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . (((ML,AD,CA,Z0),a1,v1),((ML,AD,CA,Z0),b1,v1)) is Element of the carrier of (ML,AD,CA,Z0)
[((ML,AD,CA,Z0),a1,v1),((ML,AD,CA,Z0),b1,v1)] is set
{((ML,AD,CA,Z0),a1,v1),((ML,AD,CA,Z0),b1,v1)} is set
{((ML,AD,CA,Z0),a1,v1)} is non empty trivial V42(1) set
{{((ML,AD,CA,Z0),a1,v1),((ML,AD,CA,Z0),b1,v1)},{((ML,AD,CA,Z0),a1,v1)}} is set
the addF of (ML,AD,CA,Z0) . [((ML,AD,CA,Z0),a1,v1),((ML,AD,CA,Z0),b1,v1)] is set
x is V31() ext-real V79() integer set
((ML,AD,CA,Z0),(a1 + b1),x) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (x,(a1 + b1)) is set
[x,(a1 + b1)] is set
{x,(a1 + b1)} is set
{x} is non empty trivial V42(1) set
{{x,(a1 + b1)},{x}} is set
the of (ML,AD,CA,Z0) . [x,(a1 + b1)] is set
the of AG . (x,(a1 + b1)) is set
the of AG . [x,(a1 + b1)] is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,v] is set
{v1,v} is set
{v1} is non empty trivial V42(1) set
{{v1,v},{v1}} is set
the addF of AG . [v1,v] is set
(AG,(v1 + v),x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (x,(v1 + v)) is set
[x,(v1 + v)] is set
{x,(v1 + v)} is set
{{x,(v1 + v)},{x}} is set
the of AG . [x,(v1 + v)] is set
(AG,v1,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (x,v1) is set
[x,v1] is set
{x,v1} is set
{{x,v1},{x}} is set
the of AG . [x,v1] is set
(AG,v,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (x,v) is set
[x,v] is set
{x,v} is set
{{x,v},{x}} is set
the of AG . [x,v] is set
(AG,v1,x) + (AG,v,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,v1,x),(AG,v,x)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,v1,x),(AG,v,x)] is set
{(AG,v1,x),(AG,v,x)} is set
{(AG,v1,x)} is non empty trivial V42(1) set
{{(AG,v1,x),(AG,v,x)},{(AG,v1,x)}} is set
the addF of AG . [(AG,v1,x),(AG,v,x)] is set
((ML,AD,CA,Z0),b1,x) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (x,b1) is set
[x,b1] is set
{x,b1} is set
{{x,b1},{x}} is set
the of (ML,AD,CA,Z0) . [x,b1] is set
the addF of AG . (( the of AG . (x,v1)),((ML,AD,CA,Z0),b1,x)) is set
[( the of AG . (x,v1)),((ML,AD,CA,Z0),b1,x)] is set
{( the of AG . (x,v1)),((ML,AD,CA,Z0),b1,x)} is set
{( the of AG . (x,v1))} is non empty trivial V42(1) set
{{( the of AG . (x,v1)),((ML,AD,CA,Z0),b1,x)},{( the of AG . (x,v1))}} is set
the addF of AG . [( the of AG . (x,v1)),((ML,AD,CA,Z0),b1,x)] is set
((ML,AD,CA,Z0),a1,x) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (x,a1) is set
[x,a1] is set
{x,a1} is set
{{x,a1},{x}} is set
the of (ML,AD,CA,Z0) . [x,a1] is set
the addF of AG . (((ML,AD,CA,Z0),a1,x),((ML,AD,CA,Z0),b1,x)) is set
[((ML,AD,CA,Z0),a1,x),((ML,AD,CA,Z0),b1,x)] is set
{((ML,AD,CA,Z0),a1,x),((ML,AD,CA,Z0),b1,x)} is set
{((ML,AD,CA,Z0),a1,x)} is non empty trivial V42(1) set
{{((ML,AD,CA,Z0),a1,x),((ML,AD,CA,Z0),b1,x)},{((ML,AD,CA,Z0),a1,x)}} is set
the addF of AG . [((ML,AD,CA,Z0),a1,x),((ML,AD,CA,Z0),b1,x)] is set
((ML,AD,CA,Z0),a1,x) + ((ML,AD,CA,Z0),b1,x) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . (((ML,AD,CA,Z0),a1,x),((ML,AD,CA,Z0),b1,x)) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . [((ML,AD,CA,Z0),a1,x),((ML,AD,CA,Z0),b1,x)] is set
v1 is V31() ext-real V79() integer set
a1 is V31() ext-real V79() integer set
v1 + a1 is V31() ext-real V79() integer set
b1 is Element of the carrier of (ML,AD,CA,Z0)
((ML,AD,CA,Z0),b1,(v1 + a1)) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) is Relation-like Function-like V18([:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[:INT, the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
[:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty V35() set
the of (ML,AD,CA,Z0) . ((v1 + a1),b1) is set
[(v1 + a1),b1] is set
{(v1 + a1),b1} is set
{(v1 + a1)} is non empty trivial V42(1) set
{{(v1 + a1),b1},{(v1 + a1)}} is set
the of (ML,AD,CA,Z0) . [(v1 + a1),b1] is set
((ML,AD,CA,Z0),b1,v1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (v1,b1) is set
[v1,b1] is set
{v1,b1} is set
{v1} is non empty trivial V42(1) set
{{v1,b1},{v1}} is set
the of (ML,AD,CA,Z0) . [v1,b1] is set
((ML,AD,CA,Z0),b1,a1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (a1,b1) is set
[a1,b1] is set
{a1,b1} is set
{a1} is non empty trivial V42(1) set
{{a1,b1},{a1}} is set
the of (ML,AD,CA,Z0) . [a1,b1] is set
((ML,AD,CA,Z0),b1,v1) + ((ML,AD,CA,Z0),b1,a1) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) is Relation-like Function-like V18([: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
[:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty set
bool [:[: the carrier of (ML,AD,CA,Z0), the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty set
the addF of (ML,AD,CA,Z0) . (((ML,AD,CA,Z0),b1,v1),((ML,AD,CA,Z0),b1,a1)) is Element of the carrier of (ML,AD,CA,Z0)
[((ML,AD,CA,Z0),b1,v1),((ML,AD,CA,Z0),b1,a1)] is set
{((ML,AD,CA,Z0),b1,v1),((ML,AD,CA,Z0),b1,a1)} is set
{((ML,AD,CA,Z0),b1,v1)} is non empty trivial V42(1) set
{{((ML,AD,CA,Z0),b1,v1),((ML,AD,CA,Z0),b1,a1)},{((ML,AD,CA,Z0),b1,v1)}} is set
the addF of (ML,AD,CA,Z0) . [((ML,AD,CA,Z0),b1,v1),((ML,AD,CA,Z0),b1,a1)] is set
v is V31() ext-real V79() integer set
x is V31() ext-real V79() integer set
v + x is V31() ext-real V79() integer set
((ML,AD,CA,Z0),b1,(v + x)) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . ((v + x),b1) is set
[(v + x),b1] is set
{(v + x),b1} is set
{(v + x)} is non empty trivial V42(1) set
{{(v + x),b1},{(v + x)}} is set
the of (ML,AD,CA,Z0) . [(v + x),b1] is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,v1,(v + x)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((v + x),v1) is set
[(v + x),v1] is set
{(v + x),v1} is set
{{(v + x),v1},{(v + x)}} is set
the of AG . [(v + x),v1] is set
(AG,v1,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (v,v1) is set
[v,v1] is set
{v,v1} is set
{v} is non empty trivial V42(1) set
{{v,v1},{v}} is set
the of AG . [v,v1] is set
(AG,v1,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (x,v1) is set
[x,v1] is set
{x,v1} is set
{x} is non empty trivial V42(1) set
{{x,v1},{x}} is set
the of AG . [x,v1] is set
(AG,v1,v) + (AG,v1,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,v1,v),(AG,v1,x)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,v1,v),(AG,v1,x)] is set
{(AG,v1,v),(AG,v1,x)} is set
{(AG,v1,v)} is non empty trivial V42(1) set
{{(AG,v1,v),(AG,v1,x)},{(AG,v1,v)}} is set
the addF of AG . [(AG,v1,v),(AG,v1,x)] is set
((ML,AD,CA,Z0),b1,x) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (x,b1) is set
[x,b1] is set
{x,b1} is set
{{x,b1},{x}} is set
the of (ML,AD,CA,Z0) . [x,b1] is set
the addF of AG . (( the of AG . (v,v1)),((ML,AD,CA,Z0),b1,x)) is set
[( the of AG . (v,v1)),((ML,AD,CA,Z0),b1,x)] is set
{( the of AG . (v,v1)),((ML,AD,CA,Z0),b1,x)} is set
{( the of AG . (v,v1))} is non empty trivial V42(1) set
{{( the of AG . (v,v1)),((ML,AD,CA,Z0),b1,x)},{( the of AG . (v,v1))}} is set
the addF of AG . [( the of AG . (v,v1)),((ML,AD,CA,Z0),b1,x)] is set
((ML,AD,CA,Z0),b1,v) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (v,b1) is set
[v,b1] is set
{v,b1} is set
{{v,b1},{v}} is set
the of (ML,AD,CA,Z0) . [v,b1] is set
the addF of AG . (((ML,AD,CA,Z0),b1,v),((ML,AD,CA,Z0),b1,x)) is set
[((ML,AD,CA,Z0),b1,v),((ML,AD,CA,Z0),b1,x)] is set
{((ML,AD,CA,Z0),b1,v),((ML,AD,CA,Z0),b1,x)} is set
{((ML,AD,CA,Z0),b1,v)} is non empty trivial V42(1) set
{{((ML,AD,CA,Z0),b1,v),((ML,AD,CA,Z0),b1,x)},{((ML,AD,CA,Z0),b1,v)}} is set
the addF of AG . [((ML,AD,CA,Z0),b1,v),((ML,AD,CA,Z0),b1,x)] is set
((ML,AD,CA,Z0),b1,v) + ((ML,AD,CA,Z0),b1,x) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . (((ML,AD,CA,Z0),b1,v),((ML,AD,CA,Z0),b1,x)) is Element of the carrier of (ML,AD,CA,Z0)
the addF of (ML,AD,CA,Z0) . [((ML,AD,CA,Z0),b1,v),((ML,AD,CA,Z0),b1,x)] is set
v1 is V31() ext-real V79() integer set
a1 is V31() ext-real V79() integer set
v1 * a1 is V31() ext-real V79() integer set
b1 is Element of the carrier of (ML,AD,CA,Z0)
((ML,AD,CA,Z0),b1,(v1 * a1)) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) is Relation-like Function-like V18([:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[:INT, the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
[:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty V35() set
the of (ML,AD,CA,Z0) . ((v1 * a1),b1) is set
[(v1 * a1),b1] is set
{(v1 * a1),b1} is set
{(v1 * a1)} is non empty trivial V42(1) set
{{(v1 * a1),b1},{(v1 * a1)}} is set
the of (ML,AD,CA,Z0) . [(v1 * a1),b1] is set
((ML,AD,CA,Z0),b1,a1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (a1,b1) is set
[a1,b1] is set
{a1,b1} is set
{a1} is non empty trivial V42(1) set
{{a1,b1},{a1}} is set
the of (ML,AD,CA,Z0) . [a1,b1] is set
((ML,AD,CA,Z0),((ML,AD,CA,Z0),b1,a1),v1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (v1,((ML,AD,CA,Z0),b1,a1)) is set
[v1,((ML,AD,CA,Z0),b1,a1)] is set
{v1,((ML,AD,CA,Z0),b1,a1)} is set
{v1} is non empty trivial V42(1) set
{{v1,((ML,AD,CA,Z0),b1,a1)},{v1}} is set
the of (ML,AD,CA,Z0) . [v1,((ML,AD,CA,Z0),b1,a1)] is set
v is V31() ext-real V79() integer set
x is V31() ext-real V79() integer set
v * x is V31() ext-real V79() integer set
((ML,AD,CA,Z0),b1,(v * x)) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . ((v * x),b1) is set
[(v * x),b1] is set
{(v * x),b1} is set
{(v * x)} is non empty trivial V42(1) set
{{(v * x),b1},{(v * x)}} is set
the of (ML,AD,CA,Z0) . [(v * x),b1] is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,v1,(v * x)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((v * x),v1) is set
[(v * x),v1] is set
{(v * x),v1} is set
{{(v * x),v1},{(v * x)}} is set
the of AG . [(v * x),v1] is set
(AG,v1,x) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (x,v1) is set
[x,v1] is set
{x,v1} is set
{x} is non empty trivial V42(1) set
{{x,v1},{x}} is set
the of AG . [x,v1] is set
(AG,(AG,v1,x),v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (v,(AG,v1,x)) is set
[v,(AG,v1,x)] is set
{v,(AG,v1,x)} is set
{v} is non empty trivial V42(1) set
{{v,(AG,v1,x)},{v}} is set
the of AG . [v,(AG,v1,x)] is set
((ML,AD,CA,Z0),b1,x) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (x,b1) is set
[x,b1] is set
{x,b1} is set
{{x,b1},{x}} is set
the of (ML,AD,CA,Z0) . [x,b1] is set
the of AG . (v,((ML,AD,CA,Z0),b1,x)) is set
[v,((ML,AD,CA,Z0),b1,x)] is set
{v,((ML,AD,CA,Z0),b1,x)} is set
{{v,((ML,AD,CA,Z0),b1,x)},{v}} is set
the of AG . [v,((ML,AD,CA,Z0),b1,x)] is set
((ML,AD,CA,Z0),((ML,AD,CA,Z0),b1,x),v) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) . (v,((ML,AD,CA,Z0),b1,x)) is set
the of (ML,AD,CA,Z0) . [v,((ML,AD,CA,Z0),b1,x)] is set
v1 is Element of the carrier of (ML,AD,CA,Z0)
((ML,AD,CA,Z0),v1,1) is Element of the carrier of (ML,AD,CA,Z0)
the of (ML,AD,CA,Z0) is Relation-like Function-like V18([:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0)) Element of bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):]
[:INT, the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
[:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of (ML,AD,CA,Z0):], the carrier of (ML,AD,CA,Z0):] is non empty V35() set
the of (ML,AD,CA,Z0) . (1,v1) is set
[1,v1] is set
{1,v1} is set
{1} is non empty trivial V42(1) set
{{1,v1},{1}} is set
the of (ML,AD,CA,Z0) . [1,v1] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,a1,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (1,a1) is set
[1,a1] is set
{1,a1} is set
{{1,a1},{1}} is set
the of AG . [1,a1] is set
0. (ML,AD,CA,Z0) is V51((ML,AD,CA,Z0)) Element of the carrier of (ML,AD,CA,Z0)
the ZeroF of (ML,AD,CA,Z0) is Element of the carrier of (ML,AD,CA,Z0)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
the carrier of ZS is non empty set
the carrier of AG is non empty set
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of ZS || the carrier of AG is Relation-like Function-like set
the addF of ZS | [: the carrier of AG, the carrier of AG:] is Relation-like set
the addF of AG || the carrier of ZS is Relation-like Function-like set
the addF of AG | [: the carrier of ZS, the carrier of ZS:] is Relation-like set
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG | [:INT, the carrier of ZS:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the of ZS | [:INT, the carrier of AG:] is Relation-like Function-like Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
the carrier of ZS is non empty set
the carrier of ML is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. ML is V51(ML) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the ZeroF of ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of ML is Relation-like Function-like V18([: the carrier of ML, the carrier of ML:], the carrier of ML) Element of bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:]
[: the carrier of ML, the carrier of ML:] is Relation-like non empty set
[:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is Relation-like non empty set
bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is non empty set
the addF of ML || the carrier of AG is Relation-like Function-like set
the addF of ML | [: the carrier of AG, the carrier of AG:] is Relation-like set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
[:INT, the carrier of ML:] is Relation-like non empty V35() set
the of ML is Relation-like Function-like V18([:INT, the carrier of ML:], the carrier of ML) Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
[:[:INT, the carrier of ML:], the carrier of ML:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ML:], the carrier of ML:] is non empty V35() set
the of ML | [:INT, the carrier of AG:] is Relation-like Function-like Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS || the carrier of AG is Relation-like Function-like set
the addF of ZS | [: the carrier of AG, the carrier of AG:] is Relation-like set
the addF of ML || the carrier of ZS is Relation-like Function-like set
the addF of ML | [: the carrier of ZS, the carrier of ZS:] is Relation-like set
( the addF of ML || the carrier of ZS) || the carrier of AG is Relation-like Function-like set
( the addF of ML || the carrier of ZS) | [: the carrier of AG, the carrier of AG:] is Relation-like set
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the of ZS | [:INT, the carrier of AG:] is Relation-like Function-like Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
the of ML | [:INT, the carrier of ZS:] is Relation-like Function-like Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
( the of ML | [:INT, the carrier of ZS:]) | [:INT, the carrier of AG:] is Relation-like Function-like Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
the carrier of AG is non empty set
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[: the carrier of ML, the carrier of ML:] is Relation-like non empty set
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. ML is V51(ML) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the ZeroF of ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ML is Relation-like Function-like V18([: the carrier of ML, the carrier of ML:], the carrier of ML) Element of bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:]
[:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is Relation-like non empty set
bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is non empty set
the addF of ML || the carrier of ZS is Relation-like Function-like set
the addF of ML | [: the carrier of ZS, the carrier of ZS:] is Relation-like set
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
[:INT, the carrier of ML:] is Relation-like non empty V35() set
the of ML is Relation-like Function-like V18([:INT, the carrier of ML:], the carrier of ML) Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
[:[:INT, the carrier of ML:], the carrier of ML:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ML:], the carrier of ML:] is non empty V35() set
the of ML | [:INT, the carrier of ZS:] is Relation-like Function-like Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
the addF of AG || the carrier of ZS is Relation-like Function-like set
the addF of AG | [: the carrier of ZS, the carrier of ZS:] is Relation-like set
the addF of AG || the carrier of ML is Relation-like Function-like set
the addF of AG | [: the carrier of ML, the carrier of ML:] is Relation-like set
the of AG | [:INT, the carrier of ZS:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
the of AG | [:INT, the carrier of ML:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
the carrier of ML is non empty set
AD is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
ZS is Element of bool the carrier of AG
the addF of AG || ZS is Relation-like Function-like set
[:ZS,ZS:] is Relation-like set
the addF of AG | [:ZS,ZS:] is Relation-like set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
[:INT,ZS:] is Relation-like set
the of AG | [:INT,ZS:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
( the carrier of AG,(0. AG), the addF of AG, the of AG) is non empty () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ML is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
the carrier of ML is non empty set
AD is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
ZS is Element of bool the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is Element of bool the carrier of AG
[:INT, the carrier of AG:] is Relation-like non empty V35() set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
[:INT,ZS:] is Relation-like set
the of AG | [:INT,ZS:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
dom the of AG is set
dom ( the of AG | [:INT,ZS:]) is set
[:INT, the carrier of AG:] /\ [:INT,ZS:] is Relation-like set
ML is non empty set
[:INT,ML:] is Relation-like non empty V35() set
Z0 is set
v is V31() ext-real V79() integer Element of INT
[v,Z0] is set
{v,Z0} is set
{v} is non empty trivial V42(1) set
{{v,Z0},{v}} is set
[1,Z0] is set
{1,Z0} is set
{1} is non empty trivial V42(1) set
{{1,Z0},{1}} is set
( the of AG | [:INT,ZS:]) . [1,Z0] is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,MLI,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (1,MLI) is set
[1,MLI] is set
{1,MLI} is set
{{1,MLI},{1}} is set
the of AG . [1,MLI] is set
MLI is set
( the of AG | [:INT,ZS:]) . MLI is set
v is set
i is set
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is V31() ext-real V79() integer set
(AG,a1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (v1,a1) is set
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the of AG . [v1,a1] is set
rng ( the of AG | [:INT,ZS:]) is set
[:[:INT,ML:],ML:] is Relation-like non empty V35() set
bool [:[:INT,ML:],ML:] is non empty V35() set
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG || ZS is Relation-like Function-like set
[:ZS,ZS:] is Relation-like set
the addF of AG | [:ZS,ZS:] is Relation-like set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
dom the addF of AG is set
dom ( the addF of AG || ZS) is set
[:ZS,ZS:] is Relation-like Element of bool [: the carrier of AG, the carrier of AG:]
bool [: the carrier of AG, the carrier of AG:] is non empty set
[: the carrier of AG, the carrier of AG:] /\ [:ZS,ZS:] is Relation-like Element of bool [: the carrier of AG, the carrier of AG:]
[:ML,ML:] is Relation-like non empty set
i is set
v is Element of ML
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
( the addF of AG || ZS) . [v,i] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (a1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,v1] is set
{a1,v1} is set
{a1} is non empty trivial V42(1) set
{{a1,v1},{a1}} is set
the addF of AG . [a1,v1] is set
v1 is set
( the addF of AG || ZS) . v1 is set
a1 is set
b1 is set
[a1,b1] is set
{a1,b1} is set
{a1} is non empty trivial V42(1) set
{{a1,b1},{a1}} is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,v] is set
{v1,v} is set
{v1} is non empty trivial V42(1) set
{{v1,v},{v1}} is set
the addF of AG . [v1,v] is set
rng ( the addF of AG || ZS) is set
[:[:ML,ML:],ML:] is Relation-like non empty set
bool [:[:ML,ML:],ML:] is non empty set
v is Element of ML
i is Relation-like Function-like V18([:ML,ML:],ML) Element of bool [:[:ML,ML:],ML:]
Z0 is Relation-like Function-like V18([:INT,ML:],ML) Element of bool [:[:INT,ML:],ML:]
(ML,v,i,Z0) is non empty () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
bool the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ML is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty set
ML is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
AD is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
ML + AD is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
[:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,AD) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,AD] is set
CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
(ML + AD) + CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . ((ML + AD),CA) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[(ML + AD),CA] is set
{(ML + AD),CA} is set
{(ML + AD)} is non empty trivial V42(1) set
{{(ML + AD),CA},{(ML + AD)}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [(ML + AD),CA] is set
AD + CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (AD,CA) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [AD,CA] is set
ML + (AD + CA) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,(AD + CA)) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[ML,(AD + CA)] is set
{ML,(AD + CA)} is set
{{ML,(AD + CA)},{ML}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,(AD + CA)] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Z0 + MLI) + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((Z0 + MLI),v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(Z0 + MLI),v] is set
{(Z0 + MLI),v} is set
{(Z0 + MLI)} is non empty trivial V42(1) set
{{(Z0 + MLI),v},{(Z0 + MLI)}} is set
the addF of AG . [(Z0 + MLI),v] is set
MLI + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,v] is set
{MLI,v} is set
{MLI} is non empty trivial V42(1) set
{{MLI,v},{MLI}} is set
the addF of AG . [MLI,v] is set
Z0 + (MLI + v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(MLI + v)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(MLI + v)] is set
{Z0,(MLI + v)} is set
{{Z0,(MLI + v)},{Z0}} is set
the addF of AG . [Z0,(MLI + v)] is set
0. ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is V51(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the ZeroF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
ML is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
ML + (0. ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
[:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,(0. ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG))) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[ML,(0. ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG))] is set
{ML,(0. ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG))} is set
{ML} is non empty trivial V42(1) set
{{ML,(0. ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG))},{ML}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,(0. ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG))] is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(0. AG)] is set
{AD,(0. AG)} is set
{AD} is non empty trivial V42(1) set
{{AD,(0. AG)},{AD}} is set
the addF of AG . [AD,(0. AG)] is set
ML is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the addF of AG . [AD,CA] is set
Z0 is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
ML + Z0 is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
[:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,Z0) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[ML,Z0] is set
{ML,Z0} is set
{ML} is non empty trivial V42(1) set
{{ML,Z0},{ML}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,Z0] is set
ML is V31() ext-real V79() integer set
AD is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
AD + CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
[:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (AD,CA) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [AD,CA] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),(AD + CA),ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
[:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty V35() set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,(AD + CA)) is set
[ML,(AD + CA)] is set
{ML,(AD + CA)} is set
{ML} is non empty trivial V42(1) set
{{ML,(AD + CA)},{ML}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,(AD + CA)] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,AD) is set
[ML,AD] is set
{ML,AD} is set
{{ML,AD},{ML}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,AD] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,CA) is set
[ML,CA] is set
{ML,CA} is set
{{ML,CA},{ML}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,CA] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML) + (( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . ((( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML)) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML)] is set
{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML)} is set
{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML)} is non empty trivial V42(1) set
{{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML)},{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML)}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML)] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
(AG,(Z0 + MLI),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,(Z0 + MLI)) is set
[ML,(Z0 + MLI)] is set
{ML,(Z0 + MLI)} is set
{{ML,(Z0 + MLI)},{ML}} is set
the of AG . [ML,(Z0 + MLI)] is set
(AG,Z0,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,Z0) is set
[ML,Z0] is set
{ML,Z0} is set
{{ML,Z0},{ML}} is set
the of AG . [ML,Z0] is set
(AG,MLI,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,MLI) is set
[ML,MLI] is set
{ML,MLI} is set
{{ML,MLI},{ML}} is set
the of AG . [ML,MLI] is set
(AG,Z0,ML) + (AG,MLI,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,Z0,ML),(AG,MLI,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,Z0,ML),(AG,MLI,ML)] is set
{(AG,Z0,ML),(AG,MLI,ML)} is set
{(AG,Z0,ML)} is non empty trivial V42(1) set
{{(AG,Z0,ML),(AG,MLI,ML)},{(AG,Z0,ML)}} is set
the addF of AG . [(AG,Z0,ML),(AG,MLI,ML)] is set
ML is V31() ext-real V79() integer set
AD is V31() ext-real V79() integer set
ML * AD is V31() ext-real V79() integer set
CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,(ML * AD)) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
[:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty V35() set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . ((ML * AD),CA) is set
[(ML * AD),CA] is set
{(ML * AD),CA} is set
{(ML * AD)} is non empty trivial V42(1) set
{{(ML * AD),CA},{(ML * AD)}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [(ML * AD),CA] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (AD,CA) is set
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [AD,CA] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD),ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)) is set
[ML,(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)] is set
{ML,(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)} is set
{ML} is non empty trivial V42(1) set
{{ML,(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)},{ML}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,Z0,(ML * AD)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((ML * AD),Z0) is set
[(ML * AD),Z0] is set
{(ML * AD),Z0} is set
{{(ML * AD),Z0},{(ML * AD)}} is set
the of AG . [(ML * AD),Z0] is set
(AG,Z0,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (AD,Z0) is set
[AD,Z0] is set
{AD,Z0} is set
{{AD,Z0},{AD}} is set
the of AG . [AD,Z0] is set
(AG,(AG,Z0,AD),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,(AG,Z0,AD)) is set
[ML,(AG,Z0,AD)] is set
{ML,(AG,Z0,AD)} is set
{{ML,(AG,Z0,AD)},{ML}} is set
the of AG . [ML,(AG,Z0,AD)] is set
ML is V31() ext-real V79() integer set
AD is V31() ext-real V79() integer set
ML + AD is V31() ext-real V79() integer set
CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,(ML + AD)) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
[:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty V35() set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . ((ML + AD),CA) is set
[(ML + AD),CA] is set
{(ML + AD),CA} is set
{(ML + AD)} is non empty trivial V42(1) set
{{(ML + AD),CA},{(ML + AD)}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [(ML + AD),CA] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,CA) is set
[ML,CA] is set
{ML,CA} is set
{ML} is non empty trivial V42(1) set
{{ML,CA},{ML}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,CA] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (AD,CA) is set
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [AD,CA] is set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML) + (( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
[:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . ((( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)] is set
{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)} is set
{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML)} is non empty trivial V42(1) set
{{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)},{(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML)}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,ML),(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),CA,AD)] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,Z0,(ML + AD)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((ML + AD),Z0) is set
[(ML + AD),Z0] is set
{(ML + AD),Z0} is set
{{(ML + AD),Z0},{(ML + AD)}} is set
the of AG . [(ML + AD),Z0] is set
(AG,Z0,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,Z0) is set
[ML,Z0] is set
{ML,Z0} is set
{{ML,Z0},{ML}} is set
the of AG . [ML,Z0] is set
(AG,Z0,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (AD,Z0) is set
[AD,Z0] is set
{AD,Z0} is set
{{AD,Z0},{AD}} is set
the of AG . [AD,Z0] is set
(AG,Z0,ML) + (AG,Z0,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,Z0,ML),(AG,Z0,AD)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,Z0,ML),(AG,Z0,AD)] is set
{(AG,Z0,ML),(AG,Z0,AD)} is set
{(AG,Z0,ML)} is non empty trivial V42(1) set
{{(AG,Z0,ML),(AG,Z0,AD)},{(AG,Z0,ML)}} is set
the addF of AG . [(AG,Z0,ML),(AG,Z0,AD)] is set
AD is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + CA is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
[:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (AD,CA) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [AD,CA] is set
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
ML is V31() ext-real V79() integer set
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),AD,ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
[:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty V35() set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,AD) is set
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,AD] is set
(AG,Z0,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (ML,Z0) is set
[ML,Z0] is set
{ML,Z0} is set
{{ML,Z0},{ML}} is set
the of AG . [ML,Z0] is set
ML is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
AD is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
ML + AD is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
[:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty set
bool [:[: the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG), the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (ML,AD) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [ML,AD] is set
AD + ML is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (AD,ML) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
[AD,ML] is set
{AD,ML} is set
{AD} is non empty trivial V42(1) set
{{AD,ML},{AD}} is set
the addF of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [AD,ML] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,CA] is set
{Z0,CA} is set
{Z0} is non empty trivial V42(1) set
{{Z0,CA},{Z0}} is set
the addF of AG . [Z0,CA] is set
ML is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
(( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG),ML,1) is Element of the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is Relation-like Function-like V18([:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG)) Element of bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):]
[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
[:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):], the carrier of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG):] is non empty V35() set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . (1,ML) is set
[1,ML] is set
{1,ML} is set
{1} is non empty trivial V42(1) set
{{1,ML},{1}} is set
the of ( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) . [1,ML] is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (1,AD) is set
[1,AD] is set
{1,AD} is set
{{1,AD},{1}} is set
the of AG . [1,AD] is set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the of ML is Relation-like Function-like V18([:INT, the carrier of ML:], the carrier of ML) Element of bool [:[:INT, the carrier of ML:], the carrier of ML:]
the carrier of ML is non empty set
[:INT, the carrier of ML:] is Relation-like non empty V35() set
[:[:INT, the carrier of ML:], the carrier of ML:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ML:], the carrier of ML:] is non empty V35() set
the of AG | [:INT, the carrier of ML:] is Relation-like Function-like Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
0. ML is V51(ML) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the ZeroF of ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of ML is Relation-like Function-like V18([: the carrier of ML, the carrier of ML:], the carrier of ML) Element of bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:]
[: the carrier of ML, the carrier of ML:] is Relation-like non empty set
[:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is Relation-like non empty set
bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is non empty set
the addF of AG || the carrier of ML is Relation-like Function-like set
the addF of AG | [: the carrier of ML, the carrier of ML:] is Relation-like set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ZS)
the carrier of (ZS) is non empty set
the carrier of ZS is non empty set
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
{(0. ZS)} is non empty trivial V42(1) (ZS) Element of bool the carrier of ZS
bool the carrier of ZS is non empty set
the carrier of (AG) is non empty set
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
bool the carrier of AG is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ZS)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ML)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ZS)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of (AG) is non empty set
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
bool the carrier of AG is non empty set
the carrier of ZS is non empty set
0. ZS is V51(ZS) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the ZeroF of ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
{(0. ZS)} is non empty trivial V42(1) (ZS) Element of bool the carrier of ZS
bool the carrier of ZS is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ZS)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ML)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
bool the carrier of AG is non empty set
CA is set
Z0 is set
Z0 is Element of bool the carrier of AG
MLI is set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,v] is set
{ZS,v} is set
{ZS} is non empty trivial V42(1) set
{{ZS,v},{ZS}} is set
the addF of AG . [ZS,v] is set
MLI is set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,v] is set
{ZS,v} is set
{ZS} is non empty trivial V42(1) set
{{ZS,v},{ZS}} is set
the addF of AG . [ZS,v] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,(0. AG),ZS) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ ((0. AG) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
the carrier of ZS is non empty set
AD is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(0. AG) + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((0. AG),CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),CA] is set
{(0. AG),CA} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),CA},{(0. AG)}} is set
the addF of AG . [(0. AG),CA] is set
AD is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(0. AG) + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((0. AG),CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),CA] is set
{(0. AG),CA} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),CA},{(0. AG)}} is set
the addF of AG . [(0. AG),CA] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is Element of bool the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,(0. AG),ZS) is Element of bool the carrier of AG
{ ((0. AG) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,AD] is set
{ZS,AD} is set
{ZS} is non empty trivial V42(1) set
{{ZS,AD},{ZS}} is set
the addF of AG . [ZS,AD] is set
- AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(0. AG)] is set
{ZS,(0. AG)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(0. AG)},{ZS}} is set
the addF of AG . [ZS,(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,(0. AG),ZS) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ ((0. AG) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
the carrier of ZS is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,(AG)) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in (AG) } is set
{ZS} is non empty trivial V42(1) Element of bool the carrier of AG
ML is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,AD] is set
{ZS,AD} is set
{ZS} is non empty trivial V42(1) set
{{ZS,AD},{ZS}} is set
the addF of AG . [ZS,AD] is set
the carrier of (AG) is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
ML is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(0. AG)] is set
{ZS,(0. AG)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(0. AG)},{ZS}} is set
the addF of AG . [ZS,(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
the carrier of ML is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(0. AG)] is set
{ZS,(0. AG)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(0. AG)},{ZS}} is set
the addF of AG . [ZS,(0. AG)] is set
AD is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,CA] is set
{ZS,CA} is set
{{ZS,CA},{ZS}} is set
the addF of AG . [ZS,CA] is set
AD is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
CA - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
CA + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML is Relation-like Function-like V18([: the carrier of ML, the carrier of ML:], the carrier of ML) Element of bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:]
[: the carrier of ML, the carrier of ML:] is Relation-like non empty set
[:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is Relation-like non empty set
bool [:[: the carrier of ML, the carrier of ML:], the carrier of ML:] is non empty set
the addF of ML . (CA,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[CA,(- Z0)] is set
{CA,(- Z0)} is set
{CA} is non empty trivial V42(1) set
{{CA,(- Z0)},{CA}} is set
the addF of ML . [CA,(- Z0)] is set
Z0 + (CA - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . (Z0,(CA - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[Z0,(CA - Z0)] is set
{Z0,(CA - Z0)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(CA - Z0)},{Z0}} is set
the addF of ML . [Z0,(CA - Z0)] is set
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[CA,Z0] is set
{CA,Z0} is set
{{CA,Z0},{CA}} is set
the addF of ML . [CA,Z0] is set
(CA + Z0) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
(CA + Z0) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . ((CA + Z0),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[(CA + Z0),(- Z0)] is set
{(CA + Z0),(- Z0)} is set
{(CA + Z0)} is non empty trivial V42(1) set
{{(CA + Z0),(- Z0)},{(CA + Z0)}} is set
the addF of ML . [(CA + Z0),(- Z0)] is set
Z0 - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
Z0 + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . (Z0,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[Z0,(- Z0)] is set
{Z0,(- Z0)} is set
{{Z0,(- Z0)},{Z0}} is set
the addF of ML . [Z0,(- Z0)] is set
CA + (Z0 - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . (CA,(Z0 - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[CA,(Z0 - Z0)] is set
{CA,(Z0 - Z0)} is set
{{CA,(Z0 - Z0)},{CA}} is set
the addF of ML . [CA,(Z0 - Z0)] is set
0. ML is V51(ML) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the ZeroF of ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
CA + (0. ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
the addF of ML . (CA,(0. ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
[CA,(0. ML)] is set
{CA,(0. ML)} is set
{{CA,(0. ML)},{CA}} is set
the addF of ML . [CA,(0. ML)] is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI - v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (- v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(- v)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(- v)] is set
{MLI,(- v)} is set
{MLI} is non empty trivial V42(1) set
{{MLI,(- v)},{MLI}} is set
the addF of AG . [MLI,(- v)] is set
v + (MLI - v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,(MLI - v)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,(MLI - v)] is set
{v,(MLI - v)} is set
{v} is non empty trivial V42(1) set
{{v,(MLI - v)},{v}} is set
the addF of AG . [v,(MLI - v)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,(AG)) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in (AG) } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
the carrier of ML is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AD is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
the carrier of ML is non empty set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AD)
(AD,CA,Z0) is Element of bool the carrier of AD
bool the carrier of AD is non empty set
{ (CA + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AD : b1 in Z0 } is set
the carrier of Z0 is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer set
(AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ML,ZS) is set
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
the of AG . [ML,ZS] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,(AG,ZS,ML),AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ ((AG,ZS,ML) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
the carrier of AD is non empty set
CA is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,ML) + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((AG,ZS,ML),Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ZS,ML),Z0] is set
{(AG,ZS,ML),Z0} is set
{(AG,ZS,ML)} is non empty trivial V42(1) set
{{(AG,ZS,ML),Z0},{(AG,ZS,ML)}} is set
the addF of AG . [(AG,ZS,ML),Z0] is set
CA is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 - (AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- (AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (- (AG,ZS,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (Z0,(- (AG,ZS,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- (AG,ZS,ML))] is set
{Z0,(- (AG,ZS,ML))} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- (AG,ZS,ML))},{Z0}} is set
the addF of AG . [Z0,(- (AG,ZS,ML))] is set
(AG,ZS,ML) + (Z0 - (AG,ZS,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,ZS,ML),(Z0 - (AG,ZS,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ZS,ML),(Z0 - (AG,ZS,ML))] is set
{(AG,ZS,ML),(Z0 - (AG,ZS,ML))} is set
{(AG,ZS,ML)} is non empty trivial V42(1) set
{{(AG,ZS,ML),(Z0 - (AG,ZS,ML))},{(AG,ZS,ML)}} is set
the addF of AG . [(AG,ZS,ML),(Z0 - (AG,ZS,ML))] is set
Z0 + (AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(AG,ZS,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(AG,ZS,ML)] is set
{Z0,(AG,ZS,ML)} is set
{{Z0,(AG,ZS,ML)},{Z0}} is set
the addF of AG . [Z0,(AG,ZS,ML)] is set
(Z0 + (AG,ZS,ML)) - (AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Z0 + (AG,ZS,ML)) + (- (AG,ZS,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((Z0 + (AG,ZS,ML)),(- (AG,ZS,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(Z0 + (AG,ZS,ML)),(- (AG,ZS,ML))] is set
{(Z0 + (AG,ZS,ML)),(- (AG,ZS,ML))} is set
{(Z0 + (AG,ZS,ML))} is non empty trivial V42(1) set
{{(Z0 + (AG,ZS,ML)),(- (AG,ZS,ML))},{(Z0 + (AG,ZS,ML))}} is set
the addF of AG . [(Z0 + (AG,ZS,ML)),(- (AG,ZS,ML))] is set
(AG,ZS,ML) - (AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,ML) + (- (AG,ZS,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AG,ZS,ML),(- (AG,ZS,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ZS,ML),(- (AG,ZS,ML))] is set
{(AG,ZS,ML),(- (AG,ZS,ML))} is set
{{(AG,ZS,ML),(- (AG,ZS,ML))},{(AG,ZS,ML)}} is set
the addF of AG . [(AG,ZS,ML),(- (AG,ZS,ML))] is set
Z0 + ((AG,ZS,ML) - (AG,ZS,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,((AG,ZS,ML) - (AG,ZS,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,((AG,ZS,ML) - (AG,ZS,ML))] is set
{Z0,((AG,ZS,ML) - (AG,ZS,ML))} is set
{{Z0,((AG,ZS,ML) - (AG,ZS,ML))},{Z0}} is set
the addF of AG . [Z0,((AG,ZS,ML) - (AG,ZS,ML))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(0. AG)] is set
{Z0,(0. AG)} is set
{{Z0,(0. AG)},{Z0}} is set
the addF of AG . [Z0,(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
the addF of AG . [ML,ZS] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,(ML + ZS),AD) is Element of bool the carrier of AG
{ ((ML + ZS) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,Z0] is set
{ML,Z0} is set
{{ML,Z0},{ML}} is set
the addF of AG . [ML,Z0] is set
Z0 - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- ZS)] is set
{Z0,(- ZS)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- ZS)},{Z0}} is set
the addF of AG . [Z0,(- ZS)] is set
(ML + ZS) + (Z0 - ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + ZS),(Z0 - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + ZS),(Z0 - ZS)] is set
{(ML + ZS),(Z0 - ZS)} is set
{(ML + ZS)} is non empty trivial V42(1) set
{{(ML + ZS),(Z0 - ZS)},{(ML + ZS)}} is set
the addF of AG . [(ML + ZS),(Z0 - ZS)] is set
ZS + (Z0 - ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(Z0 - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(Z0 - ZS)] is set
{ZS,(Z0 - ZS)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(Z0 - ZS)},{ZS}} is set
the addF of AG . [ZS,(Z0 - ZS)] is set
ML + (ZS + (Z0 - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(ZS + (Z0 - ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(ZS + (Z0 - ZS))] is set
{ML,(ZS + (Z0 - ZS))} is set
{{ML,(ZS + (Z0 - ZS))},{ML}} is set
the addF of AG . [ML,(ZS + (Z0 - ZS))] is set
Z0 + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,ZS] is set
{Z0,ZS} is set
{{Z0,ZS},{Z0}} is set
the addF of AG . [Z0,ZS] is set
(Z0 + ZS) - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Z0 + ZS) + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((Z0 + ZS),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(Z0 + ZS),(- ZS)] is set
{(Z0 + ZS),(- ZS)} is set
{(Z0 + ZS)} is non empty trivial V42(1) set
{{(Z0 + ZS),(- ZS)},{(Z0 + ZS)}} is set
the addF of AG . [(Z0 + ZS),(- ZS)] is set
ML + ((Z0 + ZS) - ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,((Z0 + ZS) - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((Z0 + ZS) - ZS)] is set
{ML,((Z0 + ZS) - ZS)} is set
{{ML,((Z0 + ZS) - ZS)},{ML}} is set
the addF of AG . [ML,((Z0 + ZS) - ZS)] is set
ZS - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
Z0 + (ZS - ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(ZS - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(ZS - ZS)] is set
{Z0,(ZS - ZS)} is set
{{Z0,(ZS - ZS)},{Z0}} is set
the addF of AG . [Z0,(ZS - ZS)] is set
ML + (Z0 + (ZS - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(Z0 + (ZS - ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(Z0 + (ZS - ZS))] is set
{ML,(Z0 + (ZS - ZS))} is set
{{ML,(Z0 + (ZS - ZS))},{ML}} is set
the addF of AG . [ML,(Z0 + (ZS - ZS))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(0. AG)] is set
{Z0,(0. AG)} is set
{{Z0,(0. AG)},{Z0}} is set
the addF of AG . [Z0,(0. AG)] is set
ML + (Z0 + (0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(Z0 + (0. AG))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(Z0 + (0. AG))] is set
{ML,(Z0 + (0. AG))} is set
{{ML,(Z0 + (0. AG))},{ML}} is set
the addF of AG . [ML,(Z0 + (0. AG))] is set
CA is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ML + ZS) + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + ZS),Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + ZS),Z0] is set
{(ML + ZS),Z0} is set
{(ML + ZS)} is non empty trivial V42(1) set
{{(ML + ZS),Z0},{(ML + ZS)}} is set
the addF of AG . [(ML + ZS),Z0] is set
ZS + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,Z0] is set
{ZS,Z0} is set
{ZS} is non empty trivial V42(1) set
{{ZS,Z0},{ZS}} is set
the addF of AG . [ZS,Z0] is set
ML + (ZS + Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(ZS + Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(ZS + Z0)] is set
{ML,(ZS + Z0)} is set
{{ML,(ZS + Z0)},{ML}} is set
the addF of AG . [ML,(ZS + Z0)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{{ML,(0. AG)},{ML}} is set
the addF of AG . [ML,(0. AG)] is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ML + ZS) + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + ZS),CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + ZS),CA] is set
{(ML + ZS),CA} is set
{(ML + ZS)} is non empty trivial V42(1) set
{{(ML + ZS),CA},{(ML + ZS)}} is set
the addF of AG . [(ML + ZS),CA] is set
ZS + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,CA] is set
{ZS,CA} is set
{ZS} is non empty trivial V42(1) set
{{ZS,CA},{ZS}} is set
the addF of AG . [ZS,CA] is set
ML + (ZS + CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(ZS + CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(ZS + CA)] is set
{ML,(ZS + CA)} is set
{{ML,(ZS + CA)},{ML}} is set
the addF of AG . [ML,(ZS + CA)] is set
- CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- ZS)] is set
{ML,(- ZS)} is set
{ML} is non empty trivial V42(1) set
{{ML,(- ZS)},{ML}} is set
the addF of AG . [ML,(- ZS)] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,(ML - ZS),AD) is Element of bool the carrier of AG
{ ((ML - ZS) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
- (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,(ML + (- ZS)),AD) is Element of bool the carrier of AG
{ ((ML + (- ZS)) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,ZS,AD) is Element of bool the carrier of AG
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,CA] is set
{ML,CA} is set
{ML} is non empty trivial V42(1) set
{{ML,CA},{ML}} is set
the addF of AG . [ML,CA] is set
Z0 is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,MLI] is set
{ML,MLI} is set
{{ML,MLI},{ML}} is set
the addF of AG . [ML,MLI] is set
ZS - CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- CA)] is set
{ZS,(- CA)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- CA)},{ZS}} is set
the addF of AG . [ZS,(- CA)] is set
CA - CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + (- CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,(- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- CA)] is set
{CA,(- CA)} is set
{CA} is non empty trivial V42(1) set
{{CA,(- CA)},{CA}} is set
the addF of AG . [CA,(- CA)] is set
ML + (CA - CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(CA - CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(CA - CA)] is set
{ML,(CA - CA)} is set
{{ML,(CA - CA)},{ML}} is set
the addF of AG . [ML,(CA - CA)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{{ML,(0. AG)},{ML}} is set
the addF of AG . [ML,(0. AG)] is set
MLI + (- CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(- CA)] is set
{MLI,(- CA)} is set
{MLI} is non empty trivial V42(1) set
{{MLI,(- CA)},{MLI}} is set
the addF of AG . [MLI,(- CA)] is set
ZS + (MLI + (- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(MLI + (- CA))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(MLI + (- CA))] is set
{ZS,(MLI + (- CA))} is set
{{ZS,(MLI + (- CA))},{ZS}} is set
the addF of AG . [ZS,(MLI + (- CA))] is set
MLI - CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (- CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (MLI - CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(MLI - CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(MLI - CA)] is set
{ZS,(MLI - CA)} is set
{{ZS,(MLI - CA)},{ZS}} is set
the addF of AG . [ZS,(MLI - CA)] is set
Z0 is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,MLI] is set
{ZS,MLI} is set
{ZS} is non empty trivial V42(1) set
{{ZS,MLI},{ZS}} is set
the addF of AG . [ZS,MLI] is set
CA + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,MLI] is set
{CA,MLI} is set
{CA} is non empty trivial V42(1) set
{{CA,MLI},{CA}} is set
the addF of AG . [CA,MLI] is set
ML + (CA + MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(CA + MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(CA + MLI)] is set
{ML,(CA + MLI)} is set
{{ML,(CA + MLI)},{ML}} is set
the addF of AG . [ML,(CA + MLI)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,CA) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in CA } is set
(AG,AD,CA) is Element of bool the carrier of AG
{ (AD + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in CA } is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,Z0] is set
{ML,Z0} is set
{ML} is non empty trivial V42(1) set
{{ML,Z0},{ML}} is set
the addF of AG . [ML,Z0] is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,MLI] is set
{AD,MLI} is set
{AD} is non empty trivial V42(1) set
{{AD,MLI},{AD}} is set
the addF of AG . [AD,MLI] is set
v is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,i] is set
{ML,i} is set
{{ML,i},{ML}} is set
the addF of AG . [ML,i] is set
MLI - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(- Z0)] is set
{MLI,(- Z0)} is set
{MLI} is non empty trivial V42(1) set
{{MLI,(- Z0)},{MLI}} is set
the addF of AG . [MLI,(- Z0)] is set
(MLI - Z0) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI - Z0),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI - Z0),i] is set
{(MLI - Z0),i} is set
{(MLI - Z0)} is non empty trivial V42(1) set
{{(MLI - Z0),i},{(MLI - Z0)}} is set
the addF of AG . [(MLI - Z0),i] is set
ZS - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- Z0)] is set
{ZS,(- Z0)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- Z0)},{ZS}} is set
the addF of AG . [ZS,(- Z0)] is set
Z0 - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- Z0)] is set
{Z0,(- Z0)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- Z0)},{Z0}} is set
the addF of AG . [Z0,(- Z0)] is set
ML + (Z0 - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(Z0 - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(Z0 - Z0)] is set
{ML,(Z0 - Z0)} is set
{{ML,(Z0 - Z0)},{ML}} is set
the addF of AG . [ML,(Z0 - Z0)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{{ML,(0. AG)},{ML}} is set
the addF of AG . [ML,(0. AG)] is set
AD + (MLI - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,(MLI - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(MLI - Z0)] is set
{AD,(MLI - Z0)} is set
{{AD,(MLI - Z0)},{AD}} is set
the addF of AG . [AD,(MLI - Z0)] is set
(AD + (MLI - Z0)) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AD + (MLI - Z0)),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AD + (MLI - Z0)),i] is set
{(AD + (MLI - Z0)),i} is set
{(AD + (MLI - Z0))} is non empty trivial V42(1) set
{{(AD + (MLI - Z0)),i},{(AD + (MLI - Z0))}} is set
the addF of AG . [(AD + (MLI - Z0)),i] is set
AD + ((MLI - Z0) + i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,((MLI - Z0) + i)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,((MLI - Z0) + i)] is set
{AD,((MLI - Z0) + i)} is set
{{AD,((MLI - Z0) + i)},{AD}} is set
the addF of AG . [AD,((MLI - Z0) + i)] is set
v is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,i] is set
{AD,i} is set
{{AD,i},{AD}} is set
the addF of AG . [AD,i] is set
Z0 - MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (- MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(- MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- MLI)] is set
{Z0,(- MLI)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- MLI)},{Z0}} is set
the addF of AG . [Z0,(- MLI)] is set
(Z0 - MLI) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((Z0 - MLI),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(Z0 - MLI),i] is set
{(Z0 - MLI),i} is set
{(Z0 - MLI)} is non empty trivial V42(1) set
{{(Z0 - MLI),i},{(Z0 - MLI)}} is set
the addF of AG . [(Z0 - MLI),i] is set
ZS - MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- MLI)] is set
{ZS,(- MLI)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- MLI)},{ZS}} is set
the addF of AG . [ZS,(- MLI)] is set
MLI - MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (- MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(- MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(- MLI)] is set
{MLI,(- MLI)} is set
{MLI} is non empty trivial V42(1) set
{{MLI,(- MLI)},{MLI}} is set
the addF of AG . [MLI,(- MLI)] is set
AD + (MLI - MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,(MLI - MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(MLI - MLI)] is set
{AD,(MLI - MLI)} is set
{{AD,(MLI - MLI)},{AD}} is set
the addF of AG . [AD,(MLI - MLI)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(0. AG)] is set
{AD,(0. AG)} is set
{{AD,(0. AG)},{AD}} is set
the addF of AG . [AD,(0. AG)] is set
ML + (Z0 - MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(Z0 - MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(Z0 - MLI)] is set
{ML,(Z0 - MLI)} is set
{{ML,(Z0 - MLI)},{ML}} is set
the addF of AG . [ML,(Z0 - MLI)] is set
(ML + (Z0 - MLI)) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + (Z0 - MLI)),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + (Z0 - MLI)),i] is set
{(ML + (Z0 - MLI)),i} is set
{(ML + (Z0 - MLI))} is non empty trivial V42(1) set
{{(ML + (Z0 - MLI)),i},{(ML + (Z0 - MLI))}} is set
the addF of AG . [(ML + (Z0 - MLI)),i] is set
ML + ((Z0 - MLI) + i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,((Z0 - MLI) + i)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((Z0 - MLI) + i)] is set
{ML,((Z0 - MLI) + i)} is set
{{ML,((Z0 - MLI) + i)},{ML}} is set
the addF of AG . [ML,((Z0 - MLI) + i)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer set
(AG,ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
the of AG . (ML,ZS) is set
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
the of AG . [ML,ZS] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
ML - 1 is V31() ext-real V79() integer set
(AG,ZS,(ML - 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . ((ML - 1),ZS) is set
[(ML - 1),ZS] is set
{(ML - 1),ZS} is set
{(ML - 1)} is non empty trivial V42(1) set
{{(ML - 1),ZS},{(ML - 1)}} is set
the of AG . [(ML - 1),ZS] is set
(ML - 1) + 1 is V31() ext-real V79() integer set
(AG,ZS,((ML - 1) + 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (((ML - 1) + 1),ZS) is set
[((ML - 1) + 1),ZS] is set
{((ML - 1) + 1),ZS} is set
{((ML - 1) + 1)} is non empty trivial V42(1) set
{{((ML - 1) + 1),ZS},{((ML - 1) + 1)}} is set
the of AG . [((ML - 1) + 1),ZS] is set
(AG,ZS,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the of AG . (1,ZS) is set
[1,ZS] is set
{1,ZS} is set
{1} is non empty trivial V42(1) set
{{1,ZS},{1}} is set
the of AG . [1,ZS] is set
(AG,ZS,(ML - 1)) + (AG,ZS,1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((AG,ZS,(ML - 1)),(AG,ZS,1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AG,ZS,(ML - 1)),(AG,ZS,1)] is set
{(AG,ZS,(ML - 1)),(AG,ZS,1)} is set
{(AG,ZS,(ML - 1))} is non empty trivial V42(1) set
{{(AG,ZS,(ML - 1)),(AG,ZS,1)},{(AG,ZS,(ML - 1))}} is set
the addF of AG . [(AG,ZS,(ML - 1)),(AG,ZS,1)] is set
ZS + (AG,ZS,(ML - 1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(AG,ZS,(ML - 1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(AG,ZS,(ML - 1))] is set
{ZS,(AG,ZS,(ML - 1))} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(AG,ZS,(ML - 1))},{ZS}} is set
the addF of AG . [ZS,(AG,ZS,(ML - 1))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,ML] is set
{ZS,ML} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ML},{ZS}} is set
the addF of AG . [ZS,ML] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,CA] is set
{ML,CA} is set
{ML} is non empty trivial V42(1) set
{{ML,CA},{ML}} is set
the addF of AG . [ML,CA] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ML)] is set
{ZS,(- ML)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- ML)},{ZS}} is set
the addF of AG . [ZS,(- ML)] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(- ML) + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ML),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ML),ZS] is set
{(- ML),ZS} is set
{(- ML)} is non empty trivial V42(1) set
{{(- ML),ZS},{(- ML)}} is set
the addF of AG . [(- ML),ZS] is set
- (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,CA] is set
{ML,CA} is set
{ML} is non empty trivial V42(1) set
{{ML,CA},{ML}} is set
the addF of AG . [ML,CA] is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,CA] is set
{ML,CA} is set
{ML} is non empty trivial V42(1) set
{{ML,CA},{ML}} is set
the addF of AG . [ML,CA] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,CA] is set
{ML,CA} is set
{ML} is non empty trivial V42(1) set
{{ML,CA},{ML}} is set
the addF of AG . [ML,CA] is set
- CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- Z0)] is set
{ML,(- Z0)} is set
{{ML,(- Z0)},{ML}} is set
the addF of AG . [ML,(- Z0)] is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML - CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (- CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,(- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- CA)] is set
{ML,(- CA)} is set
{ML} is non empty trivial V42(1) set
{{ML,(- CA)},{ML}} is set
the addF of AG . [ML,(- CA)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ML)] is set
{ZS,(- ML)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- ML)},{ZS}} is set
the addF of AG . [ZS,(- ML)] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,CA,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (CA + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AG . [CA,Z0] is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,MLI] is set
{CA,MLI} is set
{{CA,MLI},{CA}} is set
the addF of AG . [CA,MLI] is set
MLI + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,CA] is set
{MLI,CA} is set
{MLI} is non empty trivial V42(1) set
{{MLI,CA},{MLI}} is set
the addF of AG . [MLI,CA] is set
- CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(- CA) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(- CA) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- CA),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- CA),(- Z0)] is set
{(- CA),(- Z0)} is set
{(- CA)} is non empty trivial V42(1) set
{{(- CA),(- Z0)},{(- CA)}} is set
the addF of AG . [(- CA),(- Z0)] is set
(MLI + CA) + ((- CA) - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + CA),((- CA) - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + CA),((- CA) - Z0)] is set
{(MLI + CA),((- CA) - Z0)} is set
{(MLI + CA)} is non empty trivial V42(1) set
{{(MLI + CA),((- CA) - Z0)},{(MLI + CA)}} is set
the addF of AG . [(MLI + CA),((- CA) - Z0)] is set
(MLI + CA) + (- CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + CA),(- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + CA),(- CA)] is set
{(MLI + CA),(- CA)} is set
{{(MLI + CA),(- CA)},{(MLI + CA)}} is set
the addF of AG . [(MLI + CA),(- CA)] is set
((MLI + CA) + (- CA)) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((MLI + CA) + (- CA)) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((MLI + CA) + (- CA)),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((MLI + CA) + (- CA)),(- Z0)] is set
{((MLI + CA) + (- CA)),(- Z0)} is set
{((MLI + CA) + (- CA))} is non empty trivial V42(1) set
{{((MLI + CA) + (- CA)),(- Z0)},{((MLI + CA) + (- CA))}} is set
the addF of AG . [((MLI + CA) + (- CA)),(- Z0)] is set
CA + (- CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,(- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- CA)] is set
{CA,(- CA)} is set
{{CA,(- CA)},{CA}} is set
the addF of AG . [CA,(- CA)] is set
MLI + (CA + (- CA)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(CA + (- CA))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(CA + (- CA))] is set
{MLI,(CA + (- CA))} is set
{{MLI,(CA + (- CA))},{MLI}} is set
the addF of AG . [MLI,(CA + (- CA))] is set
(MLI + (CA + (- CA))) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(MLI + (CA + (- CA))) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + (CA + (- CA))),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + (CA + (- CA))),(- Z0)] is set
{(MLI + (CA + (- CA))),(- Z0)} is set
{(MLI + (CA + (- CA)))} is non empty trivial V42(1) set
{{(MLI + (CA + (- CA))),(- Z0)},{(MLI + (CA + (- CA)))}} is set
the addF of AG . [(MLI + (CA + (- CA))),(- Z0)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(0. AG)] is set
{MLI,(0. AG)} is set
{{MLI,(0. AG)},{MLI}} is set
the addF of AG . [MLI,(0. AG)] is set
(MLI + (0. AG)) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(MLI + (0. AG)) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + (0. AG)),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + (0. AG)),(- Z0)] is set
{(MLI + (0. AG)),(- Z0)} is set
{(MLI + (0. AG))} is non empty trivial V42(1) set
{{(MLI + (0. AG)),(- Z0)},{(MLI + (0. AG))}} is set
the addF of AG . [(MLI + (0. AG)),(- Z0)] is set
MLI - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(- Z0)] is set
{MLI,(- Z0)} is set
{{MLI,(- Z0)},{MLI}} is set
the addF of AG . [MLI,(- Z0)] is set
- (ZS - ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
ZS + (- (ZS - ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- (ZS - ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- (ZS - ML))] is set
{ZS,(- (ZS - ML))} is set
{{ZS,(- (ZS - ML))},{ZS}} is set
the addF of AG . [ZS,(- (ZS - ML))] is set
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(- ZS) + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ZS),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ZS),ML] is set
{(- ZS),ML} is set
{(- ZS)} is non empty trivial V42(1) set
{{(- ZS),ML},{(- ZS)}} is set
the addF of AG . [(- ZS),ML] is set
ZS + ((- ZS) + ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,((- ZS) + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,((- ZS) + ML)] is set
{ZS,((- ZS) + ML)} is set
{{ZS,((- ZS) + ML)},{ZS}} is set
the addF of AG . [ZS,((- ZS) + ML)] is set
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
(ZS + (- ZS)) + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + (- ZS)),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + (- ZS)),ML] is set
{(ZS + (- ZS)),ML} is set
{(ZS + (- ZS))} is non empty trivial V42(1) set
{{(ZS + (- ZS)),ML},{(ZS + (- ZS))}} is set
the addF of AG . [(ZS + (- ZS)),ML] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(0. AG) + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),ML] is set
{(0. AG),ML} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),ML},{(0. AG)}} is set
the addF of AG . [(0. AG),ML] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,ML,AD) is Element of bool the carrier of AG
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ML,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,CA] is set
{ML,CA} is set
{ML} is non empty trivial V42(1) set
{{ML,CA},{ML}} is set
the addF of AG . [ML,CA] is set
ML - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- ZS)] is set
{ML,(- ZS)} is set
{{ML,(- ZS)},{ML}} is set
the addF of AG . [ML,(- ZS)] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,Z0] is set
{ZS,Z0} is set
{ZS} is non empty trivial V42(1) set
{{ZS,Z0},{ZS}} is set
the addF of AG . [ZS,Z0] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ML + CA) - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ML + CA) + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + CA),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + CA),(- ZS)] is set
{(ML + CA),(- ZS)} is set
{(ML + CA)} is non empty trivial V42(1) set
{{(ML + CA),(- ZS)},{(ML + CA)}} is set
the addF of AG . [(ML + CA),(- ZS)] is set
CA + (ML - ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,(ML - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(ML - ZS)] is set
{CA,(ML - ZS)} is set
{CA} is non empty trivial V42(1) set
{{CA,(ML - ZS)},{CA}} is set
the addF of AG . [CA,(ML - ZS)] is set
- CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{{ML,ZS},{ML}} is set
the addF of AG . [ML,ZS] is set
(ML + ZS) - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ML + ZS) + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + ZS),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + ZS),(- ZS)] is set
{(ML + ZS),(- ZS)} is set
{(ML + ZS)} is non empty trivial V42(1) set
{{(ML + ZS),(- ZS)},{(ML + ZS)}} is set
the addF of AG . [(ML + ZS),(- ZS)] is set
ZS - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
ML + (ZS - ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(ZS - ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(ZS - ZS)] is set
{ML,(ZS - ZS)} is set
{{ML,(ZS - ZS)},{ML}} is set
the addF of AG . [ML,(ZS - ZS)] is set
ML + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{{ML,(0. AG)},{ML}} is set
the addF of AG . [ML,(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,ML,AD) is Element of bool the carrier of AG
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,CA] is set
{ZS,CA} is set
{ZS} is non empty trivial V42(1) set
{{ZS,CA},{ZS}} is set
the addF of AG . [ZS,CA] is set
ZS - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ML)] is set
{ZS,(- ML)} is set
{{ZS,(- ML)},{ZS}} is set
the addF of AG . [ZS,(- ML)] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- Z0)] is set
{ZS,(- Z0)} is set
{{ZS,(- Z0)},{ZS}} is set
the addF of AG . [ZS,(- Z0)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ZS + CA) - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ZS + CA) + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + CA),(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + CA),(- ML)] is set
{(ZS + CA),(- ML)} is set
{(ZS + CA)} is non empty trivial V42(1) set
{{(ZS + CA),(- ML)},{(ZS + CA)}} is set
the addF of AG . [(ZS + CA),(- ML)] is set
CA + (ZS - ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,(ZS - ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(ZS - ML)] is set
{CA,(ZS - ML)} is set
{CA} is non empty trivial V42(1) set
{{CA,(ZS - ML)},{CA}} is set
the addF of AG . [CA,(ZS - ML)] is set
- CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
(ZS - ZS) + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS - ZS),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS - ZS),ML] is set
{(ZS - ZS),ML} is set
{(ZS - ZS)} is non empty trivial V42(1) set
{{(ZS - ZS),ML},{(ZS - ZS)}} is set
the addF of AG . [(ZS - ZS),ML] is set
(0. AG) + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),ML] is set
{(0. AG),ML} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),ML},{(0. AG)}} is set
the addF of AG . [(0. AG),ML] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,AD) is Element of bool the carrier of AG
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
the carrier of ML is non empty set
the carrier of AD is non empty set
CA is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,Z0] is set
{ZS,Z0} is set
{ZS} is non empty trivial V42(1) set
{{ZS,Z0},{ZS}} is set
the addF of AG . [ZS,Z0] is set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,v] is set
{ZS,v} is set
{{ZS,v},{ZS}} is set
the addF of AG . [ZS,v] is set
CA is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,Z0] is set
{ZS,Z0} is set
{ZS} is non empty trivial V42(1) set
{{ZS,Z0},{ZS}} is set
the addF of AG . [ZS,Z0] is set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,v] is set
{ZS,v} is set
{{ZS,v},{ZS}} is set
the addF of AG . [ZS,v] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,CA) is Element of bool the carrier of AG
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in CA } is set
the carrier of CA is non empty set
the carrier of AD is non empty set
the carrier of AD \ the carrier of CA is Element of bool the carrier of AD
bool the carrier of AD is non empty set
the Element of the carrier of AD \ the carrier of CA is Element of the carrier of AD \ the carrier of CA
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,i] is set
{ZS,i} is set
{ZS} is non empty trivial V42(1) set
{{ZS,i},{ZS}} is set
the addF of AG . [ZS,i] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,a1] is set
{ML,a1} is set
{ML} is non empty trivial V42(1) set
{{ML,a1},{ML}} is set
the addF of AG . [ML,a1] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(0. AG) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),i] is set
{(0. AG),i} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),i},{(0. AG)}} is set
the addF of AG . [(0. AG),i] is set
ZS - ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
(ZS - ZS) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS - ZS),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS - ZS),i] is set
{(ZS - ZS),i} is set
{(ZS - ZS)} is non empty trivial V42(1) set
{{(ZS - ZS),i},{(ZS - ZS)}} is set
the addF of AG . [(ZS - ZS),i] is set
(- ZS) + (ML + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ZS),(ML + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ZS),(ML + a1)] is set
{(- ZS),(ML + a1)} is set
{(- ZS)} is non empty trivial V42(1) set
{{(- ZS),(ML + a1)},{(- ZS)}} is set
the addF of AG . [(- ZS),(ML + a1)] is set
ZS + ((- ZS) + (ML + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,((- ZS) + (ML + a1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,((- ZS) + (ML + a1))] is set
{ZS,((- ZS) + (ML + a1))} is set
{{ZS,((- ZS) + (ML + a1))},{ZS}} is set
the addF of AG . [ZS,((- ZS) + (ML + a1))] is set
(AG,(ZS + ((- ZS) + (ML + a1))),AD) is Element of bool the carrier of AG
{ ((ZS + ((- ZS) + (ML + a1))) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(ZS - ZS) + (ML + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS - ZS),(ML + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS - ZS),(ML + a1)] is set
{(ZS - ZS),(ML + a1)} is set
{{(ZS - ZS),(ML + a1)},{(ZS - ZS)}} is set
the addF of AG . [(ZS - ZS),(ML + a1)] is set
(0. AG) + (ML + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),(ML + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),(ML + a1)] is set
{(0. AG),(ML + a1)} is set
{{(0. AG),(ML + a1)},{(0. AG)}} is set
the addF of AG . [(0. AG),(ML + a1)] is set
(AG,(ML + a1),CA) is Element of bool the carrier of AG
{ ((ML + a1) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in CA } is set
(AG,(ML + a1),AD) is Element of bool the carrier of AG
{ ((ML + a1) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
the carrier of CA \ the carrier of AD is Element of bool the carrier of CA
bool the carrier of CA is non empty set
the Element of the carrier of CA \ the carrier of AD is Element of the carrier of CA \ the carrier of AD
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,i] is set
{ML,i} is set
{{ML,i},{ML}} is set
the addF of AG . [ML,i] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,a1] is set
{ZS,a1} is set
{{ZS,a1},{ZS}} is set
the addF of AG . [ZS,a1] is set
(0. AG) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),i] is set
{(0. AG),i} is set
{{(0. AG),i},{(0. AG)}} is set
the addF of AG . [(0. AG),i] is set
ML - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- ML)] is set
{ML,(- ML)} is set
{{ML,(- ML)},{ML}} is set
the addF of AG . [ML,(- ML)] is set
(ML - ML) + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML - ML),i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML - ML),i] is set
{(ML - ML),i} is set
{(ML - ML)} is non empty trivial V42(1) set
{{(ML - ML),i},{(ML - ML)}} is set
the addF of AG . [(ML - ML),i] is set
(- ML) + (ZS + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ML),(ZS + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ML),(ZS + a1)] is set
{(- ML),(ZS + a1)} is set
{(- ML)} is non empty trivial V42(1) set
{{(- ML),(ZS + a1)},{(- ML)}} is set
the addF of AG . [(- ML),(ZS + a1)] is set
ML + ((- ML) + (ZS + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,((- ML) + (ZS + a1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((- ML) + (ZS + a1))] is set
{ML,((- ML) + (ZS + a1))} is set
{{ML,((- ML) + (ZS + a1))},{ML}} is set
the addF of AG . [ML,((- ML) + (ZS + a1))] is set
(AG,(ML + ((- ML) + (ZS + a1))),CA) is Element of bool the carrier of AG
{ ((ML + ((- ML) + (ZS + a1))) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in CA } is set
(ML - ML) + (ZS + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML - ML),(ZS + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML - ML),(ZS + a1)] is set
{(ML - ML),(ZS + a1)} is set
{{(ML - ML),(ZS + a1)},{(ML - ML)}} is set
the addF of AG . [(ML - ML),(ZS + a1)] is set
(0. AG) + (ZS + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),(ZS + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),(ZS + a1)] is set
{(0. AG),(ZS + a1)} is set
{{(0. AG),(ZS + a1)},{(0. AG)}} is set
the addF of AG . [(0. AG),(ZS + a1)] is set
(AG,(ZS + a1),AD) is Element of bool the carrier of AG
{ ((ZS + a1) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,(ZS + a1),CA) is Element of bool the carrier of AG
{ ((ZS + a1) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in CA } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is (AG,ZS)
the carrier of AG is non empty set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (AD + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is (AG,ZS)
CA is (AG,ML)
the carrier of AG is non empty set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,Z0,ZS) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (Z0 + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,MLI,ML) is Element of bool the carrier of AG
{ (MLI + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{ZS} is non empty trivial V42(1) Element of bool the carrier of AG
bool the carrier of AG is non empty set
(AG,ZS,(AG)) is Element of bool the carrier of AG
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in (AG) } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is Element of bool the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ML,(AG)) is Element of bool the carrier of AG
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in (AG) } is set
{ML} is non empty trivial V42(1) Element of bool the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,(0. AG),ZS) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ ((0. AG) + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
the left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
bool the carrier of AG is non empty set
ML is Element of bool the carrier of AG
(AG, the left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG,(AG)) is Element of bool the carrier of AG
{ ( the left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in (AG) } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ZS is Element of bool the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ML,(AG)) is Element of bool the carrier of AG
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in (AG) } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is (AG,ZS)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (AD + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
AD is (AG,ML)
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,CA,ML) is Element of bool the carrier of AG
{ (CA + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
CA is (AG,AD)
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,ML,AD) is Element of bool the carrier of AG
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
CA is (AG,AD)
(AG,ZS,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ZS + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
(AG,ML,AD) is Element of bool the carrier of AG
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS - ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ML)] is set
{ZS,(- ML)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(- ML)},{ZS}} is set
the addF of AG . [ZS,(- ML)] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
CA is (AG,AD)
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,Z0,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (Z0 + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,CA,AD) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (CA + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in AD } is set
Z0 is (AG,AD)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is (AG,ML)
CA is (AG,ML)
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,Z0,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (Z0 + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,MLI,ML) is Element of bool the carrier of AG
{ (MLI + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in ML ) } is set
bool the carrier of AG is non empty set
the carrier of ZS is non empty set
the carrier of ML is non empty set
MLI is set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v,i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
the addF of AG . [v,i] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(0. AG) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((0. AG),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),(0. AG)] is set
{(0. AG),(0. AG)} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),(0. AG)},{(0. AG)}} is set
the addF of AG . [(0. AG),(0. AG)] is set
MLI is Element of bool the carrier of AG
AD is Element of bool the carrier of AG
CA is Element of bool the carrier of AG
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in AD & b2 in CA ) } is set
v is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
i + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (i,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the addF of AG . [i,v1] is set
v is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
i + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (i,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the addF of AG . [i,v1] is set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AD is non empty set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of CA is non empty set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AD is non empty set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in CA & b2 in Z0 ) } is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in Z0 & b2 in CA ) } is set
i is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of AG . [v1,a1] is set
i is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of AG . [v1,a1] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
the carrier of ZS /\ the carrier of ML is set
the carrier of AG is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG /\ the carrier of AG is set
bool the carrier of AG is non empty set
MLI is Element of bool the carrier of AG
v is Element of bool the carrier of AG
i is Element of bool the carrier of AG
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AD is non empty set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of CA is non empty set
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AD is non empty set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of CA is non empty set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of Z0 is non empty set
the carrier of CA /\ the carrier of Z0 is set
the carrier of Z0 /\ the carrier of CA is set
AG is set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (ZS)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (ZS)
(ZS,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ZS)
the carrier of (ZS,ML,AD) is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS : ( b1 in ML & b2 in AD ) } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of ZS . [CA,Z0] is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the addF of ZS . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of ZS . [CA,Z0] is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS : ( b1 in ML & b2 in AD ) } is set
the carrier of (ZS,ML,AD) is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (AD,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(0. AG)] is set
{AD,(0. AG)} is set
{AD} is non empty trivial V42(1) set
{{AD,(0. AG)},{AD}} is set
the addF of AG . [AD,(0. AG)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(0. AG) + AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((0. AG),AD) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),AD] is set
{(0. AG),AD} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),AD},{(0. AG)}} is set
the addF of AG . [(0. AG),AD] is set
AG is set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (ZS)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (ZS)
(ZS,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (ZS)
the carrier of (ZS,ML,AD) is non empty set
the carrier of ML is non empty set
the carrier of AD is non empty set
the carrier of ML /\ the carrier of AD is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,ML) is non empty set
AD is set
the carrier of AG is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in ML ) } is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (MLI,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(0. AG)] is set
{MLI,(0. AG)} is set
{MLI} is non empty trivial V42(1) set
{{MLI,(0. AG)},{MLI}} is set
the addF of AG . [MLI,(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ML is non empty set
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,ML) is non empty set
AD is set
the carrier of AG is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in ML ) } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AG . [CA,Z0] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in ML ) } is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ML & b2 in AD ) } is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in (AG,ZS,ML) & b2 in AD ) } is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in (AG,ML,AD) ) } is set
the carrier of (AG,ZS,(AG,ML,AD)) is non empty set
i is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of AG . [v1,a1] is set
the carrier of (AG,ZS,ML) is non empty set
b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
b1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
the addF of AG . [b1,v1] is set
v1 + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of AG . [v1,a1] is set
the carrier of (AG,ML,AD) is non empty set
b1 + (v1 + a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (b1,(v1 + a1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,(v1 + a1)] is set
{b1,(v1 + a1)} is set
{{b1,(v1 + a1)},{b1}} is set
the addF of AG . [b1,(v1 + a1)] is set
i is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of AG . [v1,a1] is set
the carrier of (AG,ML,AD) is non empty set
b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
b1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
the addF of AG . [b1,v1] is set
v1 + b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,b1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,b1] is set
{v1,b1} is set
{{v1,b1},{v1}} is set
the addF of AG . [v1,b1] is set
the carrier of (AG,ZS,ML) is non empty set
(v1 + b1) + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((v1 + b1),v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(v1 + b1),v1] is set
{(v1 + b1),v1} is set
{(v1 + b1)} is non empty trivial V42(1) set
{{(v1 + b1),v1},{(v1 + b1)}} is set
the addF of AG . [(v1 + b1),v1] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
the carrier of (AG,ZS,ML) is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
the carrier of ML is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG),ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG) is non empty set
the carrier of ZS is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,(AG),ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
the carrier of ZS /\ the carrier of ZS is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS is non empty set
the carrier of ML is non empty set
the carrier of AD is non empty set
the carrier of (AG,ZS,(AG,ML,AD)) is non empty set
the carrier of (AG,ML,AD) is non empty set
the carrier of ZS /\ the carrier of (AG,ML,AD) is set
the carrier of ML /\ the carrier of AD is set
the carrier of ZS /\ ( the carrier of ML /\ the carrier of AD) is set
the carrier of ZS /\ the carrier of ML is set
( the carrier of ZS /\ the carrier of ML) /\ the carrier of AD is set
the carrier of (AG,ZS,ML) is non empty set
the carrier of (AG,ZS,ML) /\ the carrier of AD is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,ML) is non empty set
the carrier of ML is non empty set
the carrier of ZS /\ the carrier of ML is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,ML) is non empty set
the carrier of ZS is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ML is non empty set
the carrier of ZS is non empty set
the carrier of (AG,ML,ZS) is non empty set
the carrier of ML /\ the carrier of ZS is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,(AG),ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of ZS is non empty set
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
bool the carrier of AG is non empty set
{(0. AG)} /\ the carrier of ZS is Element of bool the carrier of AG
the carrier of (AG,(AG),ZS) is non empty set
the carrier of (AG) is non empty set
the carrier of (AG) /\ the carrier of ZS is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG),ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,(AG),ZS) is non empty set
the carrier of ZS is non empty set
the carrier of AG /\ the carrier of ZS is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,ML) is non empty set
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,ML) is non empty set
the carrier of ZS is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,(AG,ZS,ML),ML) is non empty set
the carrier of ML is non empty set
AD is set
the carrier of AG is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in (AG,ZS,ML) & b2 in ML ) } is set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AG . [CA,Z0] is set
AD is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,(AG,ZS,ML)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,(AG,ZS,ML)) is non empty set
AD is set
the carrier of (AG,ZS,ML) is non empty set
the carrier of ZS /\ the carrier of (AG,ZS,ML) is set
AD is set
the carrier of AG is non empty set
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (CA,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(0. AG)] is set
{CA,(0. AG)} is set
{CA} is non empty trivial V42(1) set
{{CA,(0. AG)},{CA}} is set
the addF of AG . [CA,(0. AG)] is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in ML ) } is set
the carrier of (AG,ZS,ML) is non empty set
the carrier of ZS /\ the carrier of (AG,ZS,ML) is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,(AG,ML,ZS)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,(AG,ZS,ML),(AG,ML,AD)) is non empty set
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ML,(AG,ZS,AD)) is non empty set
CA is set
the carrier of AG is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in (AG,ZS,ML) & b2 in (AG,ML,AD) ) } is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ML,(AG,ZS,AD)) is non empty set
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,(AG,ZS,ML),(AG,ML,AD)) is non empty set
CA is set
the carrier of ML is non empty set
the carrier of (AG,ZS,AD) is non empty set
the carrier of ML /\ the carrier of (AG,ZS,AD) is set
the carrier of AG is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in AD ) } is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
MLI + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,Z0] is set
{MLI,Z0} is set
{MLI} is non empty trivial V42(1) set
{{MLI,Z0},{MLI}} is set
the addF of AG . [MLI,Z0] is set
(MLI + Z0) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(MLI + Z0) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + Z0),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + Z0),(- Z0)] is set
{(MLI + Z0),(- Z0)} is set
{(MLI + Z0)} is non empty trivial V42(1) set
{{(MLI + Z0),(- Z0)},{(MLI + Z0)}} is set
the addF of AG . [(MLI + Z0),(- Z0)] is set
Z0 - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- Z0)] is set
{Z0,(- Z0)} is set
{{Z0,(- Z0)},{Z0}} is set
the addF of AG . [Z0,(- Z0)] is set
MLI + (Z0 - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(Z0 - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(Z0 - Z0)] is set
{MLI,(Z0 - Z0)} is set
{{MLI,(Z0 - Z0)},{MLI}} is set
the addF of AG . [MLI,(Z0 - Z0)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(0. AG)] is set
{MLI,(0. AG)} is set
{{MLI,(0. AG)},{MLI}} is set
the addF of AG . [MLI,(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,(AG,ML,AD)) is non empty set
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ML,ZS),(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,(AG,ML,ZS),(AG,ZS,AD)) is non empty set
CA is set
the carrier of AG is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in (AG,ML,AD) ) } is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in AD ) } is set
the carrier of (AG,ZS,AD) is non empty set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ML & b2 in ZS ) } is set
the carrier of (AG,ML,ZS) is non empty set
the carrier of (AG,ML,ZS) /\ the carrier of (AG,ZS,AD) is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ML,ZS),(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ML,(AG,ZS,AD)) is non empty set
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,(AG,ZS,ML),(AG,ML,AD)) is non empty set
the carrier of AG is non empty set
bool the carrier of AG is non empty set
the carrier of ML is non empty set
CA is Element of bool the carrier of AG
the carrier of ZS is non empty set
Z0 is set
the carrier of (AG,ZS,ML) is non empty set
the carrier of (AG,ML,AD) is non empty set
the carrier of (AG,ZS,ML) /\ the carrier of (AG,ML,AD) is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ZS & b2 in ML ) } is set
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (MLI,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,v] is set
{MLI,v} is set
{MLI} is non empty trivial V42(1) set
{{MLI,v},{MLI}} is set
the addF of AG . [MLI,v] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(MLI + v) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + v),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + v),(0. AG)] is set
{(MLI + v),(0. AG)} is set
{(MLI + v)} is non empty trivial V42(1) set
{{(MLI + v),(0. AG)},{(MLI + v)}} is set
the addF of AG . [(MLI + v),(0. AG)] is set
{ (b1 + b2) where b1, b2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : ( b1 in ML & b2 in (AG,ZS,AD) ) } is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,(AG,ZS,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,AD,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,(AG,AD,ML)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,AD),ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,AD),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,AD),AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,(AG,ZS,AD),AD),ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,AD,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,(AG,AD,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,(AG,AD,AD)),ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,AD),ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,ZS,ML),AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ML is non empty set
the carrier of ZS \/ the carrier of ML is set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of Z0 is non empty set
v is set
the carrier of AG is non empty set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ML
bool the carrier of AG is non empty set
a1 is Element of bool the carrier of AG
b1 is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of ZS
x is Element of bool the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,v1] is set
{v,v1} is set
{v} is non empty trivial V42(1) set
{{v,v1},{v}} is set
the addF of AG . [v,v1] is set
(v + v1) - v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(v + v1) + (- v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((v + v1),(- v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(v + v1),(- v1)] is set
{(v + v1),(- v1)} is set
{(v + v1)} is non empty trivial V42(1) set
{{(v + v1),(- v1)},{(v + v1)}} is set
the addF of AG . [(v + v1),(- v1)] is set
v1 - v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + (- v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,(- v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,(- v1)] is set
{v1,(- v1)} is set
{v1} is non empty trivial V42(1) set
{{v1,(- v1)},{v1}} is set
the addF of AG . [v1,(- v1)] is set
v + (v1 - v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,(v1 - v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,(v1 - v1)] is set
{v,(v1 - v1)} is set
{{v,(v1 - v1)},{v}} is set
the addF of AG . [v,(v1 - v1)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,(0. AG)] is set
{v,(0. AG)} is set
{{v,(0. AG)},{v}} is set
the addF of AG . [v,(0. AG)] is set
x is Element of bool the carrier of AG
v1 + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,v] is set
{v1,v} is set
{{v1,v},{v1}} is set
the addF of AG . [v1,v] is set
(v1 + v) - v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(v1 + v) + (- v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((v1 + v),(- v)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(v1 + v),(- v)] is set
{(v1 + v),(- v)} is set
{(v1 + v)} is non empty trivial V42(1) set
{{(v1 + v),(- v)},{(v1 + v)}} is set
the addF of AG . [(v1 + v),(- v)] is set
v - v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + (- v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,(- v)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,(- v)] is set
{v,(- v)} is set
{{v,(- v)},{v}} is set
the addF of AG . [v,(- v)] is set
v1 + (v - v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,(v - v)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,(v - v)] is set
{v1,(v - v)} is set
{{v1,(v - v)},{v1}} is set
the addF of AG . [v1,(v - v)] is set
v1 + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,(0. AG)] is set
{v1,(0. AG)} is set
{{v1,(0. AG)},{v1}} is set
the addF of AG . [v1,(0. AG)] is set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of Z0 is non empty set
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of MLI is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
bool the carrier of AG is non empty set
ZS is set
AD is set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is set
the carrier of Z0 is non empty set
CA is set
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of MLI is non empty set
ML is Relation-like Function-like set
AD is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of CA is non empty set
Z0 is set
[AD,Z0] is set
{AD,Z0} is set
{AD} is non empty trivial V42(1) set
{{AD,Z0},{AD}} is set
CA is set
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
dom ML is set
rng ML is set
AD is set
CA is set
ML . CA is set
[CA,AD] is set
{CA,AD} is set
{CA} is non empty trivial V42(1) set
{{CA,AD},{CA}} is set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of Z0 is non empty set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of CA is non empty set
Z0 is set
[Z0,AD] is set
{Z0,AD} is set
{Z0} is non empty trivial V42(1) set
{{Z0,AD},{Z0}} is set
ML . Z0 is set
ZS is set
ML is set
AD is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is set
the non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () ()
(AG) is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AG . [CA,Z0] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ML,ZS) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG),(AG)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is (AG,ZS)
CA is (AG,ML)
AD /\ CA is Element of bool the carrier of AG
bool the carrier of AG is non empty set
the Element of AD /\ CA is Element of AD /\ CA
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,v,ML) is Element of bool the carrier of AG
{ (v + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
(AG,v,ZS) is Element of bool the carrier of AG
{ (v + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
(AG,v,(AG,ZS,ML)) is Element of bool the carrier of AG
{ (v + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in (AG,ZS,ML) } is set
i is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,v1] is set
{v,v1} is set
{v} is non empty trivial V42(1) set
{{v,v1},{v}} is set
the addF of AG . [v,v1] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,a1] is set
{v,a1} is set
{{v,a1},{v}} is set
the addF of AG . [v,a1] is set
i is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (v,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,v1] is set
{v,v1} is set
{v} is non empty trivial V42(1) set
{{v,v1},{v}} is set
the addF of AG . [v,v1] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ML,ZS) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (ML + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
AD is (AG,ZS)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
the carrier of ZS is non empty set
the carrier of ML is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
Z0 is (AG,ZS)
MLI is (AG,ML)
Z0 /\ MLI is Element of bool the carrier of AG
bool the carrier of AG is non empty set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,v,ZS) is Element of bool the carrier of AG
{ (v + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
i + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (i,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the addF of AG . [i,v1] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,a1,ML) is Element of bool the carrier of AG
{ (a1 + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
b1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
the addF of AG . [b1,v1] is set
v1 + b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,b1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,b1] is set
{v1,b1} is set
{v1} is non empty trivial V42(1) set
{{v1,b1},{v1}} is set
the addF of AG . [v1,b1] is set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{v} is non empty trivial V42(1) Element of bool the carrier of AG
x is set
a1 - v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 + (- v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (a1,(- v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,(- v1)] is set
{a1,(- v1)} is set
{a1} is non empty trivial V42(1) set
{{a1,(- v1)},{a1}} is set
the addF of AG . [a1,(- v1)] is set
(AG,b1,ML) is Element of bool the carrier of AG
{ (b1 + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
v - i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + (- i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,(- i)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,(- i)] is set
{v,(- i)} is set
{v} is non empty trivial V42(1) set
{{v,(- i)},{v}} is set
the addF of AG . [v,(- i)] is set
(AG,v1,ZS) is Element of bool the carrier of AG
{ (v1 + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ZS } is set
x is set
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
C is (AG,(AG,ZS,ML))
c17 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{c17} is non empty trivial V42(1) Element of bool the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is (AG,ZS)
MLI /\ the carrier of ML is Element of bool the carrier of AG
bool the carrier of AG is non empty set
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{v} is non empty trivial V42(1) Element of bool the carrier of AG
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 - i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (- i) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (Z0,(- i)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- i)] is set
{Z0,(- i)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- i)},{Z0}} is set
the addF of AG . [Z0,(- i)] is set
i + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (i,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,v] is set
{i,v} is set
{i} is non empty trivial V42(1) set
{{i,v},{i}} is set
the addF of AG . [i,v] is set
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of ZS /\ the carrier of ML is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{Z0} is non empty trivial V42(1) Element of bool the carrier of AG
the carrier of (AG) is non empty set
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
the carrier of (AG,ZS,ML) is non empty set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the carrier of CA is non empty set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (CA)
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (CA)
(CA,Z0,MLI) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (CA)
the ZeroF of CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of CA
the addF of CA is Relation-like Function-like V18([: the carrier of CA, the carrier of CA:], the carrier of CA) Element of bool [:[: the carrier of CA, the carrier of CA:], the carrier of CA:]
[: the carrier of CA, the carrier of CA:] is Relation-like non empty set
[:[: the carrier of CA, the carrier of CA:], the carrier of CA:] is Relation-like non empty set
bool [:[: the carrier of CA, the carrier of CA:], the carrier of CA:] is non empty set
the of CA is Relation-like Function-like V18([:INT, the carrier of CA:], the carrier of CA) Element of bool [:[:INT, the carrier of CA:], the carrier of CA:]
[:INT, the carrier of CA:] is Relation-like non empty V35() set
[:[:INT, the carrier of CA:], the carrier of CA:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of CA:], the carrier of CA:] is non empty V35() set
( the carrier of CA, the ZeroF of CA, the addF of CA, the of CA) is non empty () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AD + CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (AD,CA) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the addF of AG . [AD,CA] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the addF of AG . [Z0,MLI] is set
(AG,AD,ML) is Element of bool the carrier of AG
bool the carrier of AG is non empty set
{ (AD + b1) where b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG : b1 in ML } is set
the carrier of ZS is non empty set
v is (AG,ML)
i is (AG,ZS)
i /\ v is Element of bool the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{v1} is non empty trivial V42(1) Element of bool the carrier of AG
CA - MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + (- MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,(- MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- MLI)] is set
{CA,(- MLI)} is set
{CA} is non empty trivial V42(1) set
{{CA,(- MLI)},{CA}} is set
the addF of AG . [CA,(- MLI)] is set
(AD + CA) - MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AD + CA) + (- MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((AD + CA),(- MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AD + CA),(- MLI)] is set
{(AD + CA),(- MLI)} is set
{(AD + CA)} is non empty trivial V42(1) set
{{(AD + CA),(- MLI)},{(AD + CA)}} is set
the addF of AG . [(AD + CA),(- MLI)] is set
AD + (CA - MLI) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (AD,(CA - MLI)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(CA - MLI)] is set
{AD,(CA - MLI)} is set
{{AD,(CA - MLI)},{AD}} is set
the addF of AG . [AD,(CA - MLI)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG) is non empty set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
{(0. AG)} is non empty trivial V42(1) (AG) Element of bool the carrier of AG
bool the carrier of AG is non empty set
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of (AG,ZS,ML) is non empty set
CA is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
MLI + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (MLI,v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,v] is set
{MLI,v} is set
{MLI} is non empty trivial V42(1) set
{{MLI,v},{MLI}} is set
the addF of AG . [MLI,v] is set
(MLI + v) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + v),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + v),(0. AG)] is set
{(MLI + v),(0. AG)} is set
{(MLI + v)} is non empty trivial V42(1) set
{{(MLI + v),(0. AG)},{(MLI + v)}} is set
the addF of AG . [(MLI + v),(0. AG)] is set
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (Z0,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- Z0)] is set
{Z0,(- Z0)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- Z0)},{Z0}} is set
the addF of AG . [Z0,(- Z0)] is set
(MLI + v) + (Z0 - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + v),(Z0 - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + v),(Z0 - Z0)] is set
{(MLI + v),(Z0 - Z0)} is set
{{(MLI + v),(Z0 - Z0)},{(MLI + v)}} is set
the addF of AG . [(MLI + v),(Z0 - Z0)] is set
(MLI + v) + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + v),Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + v),Z0] is set
{(MLI + v),Z0} is set
{{(MLI + v),Z0},{(MLI + v)}} is set
the addF of AG . [(MLI + v),Z0] is set
((MLI + v) + Z0) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((MLI + v) + Z0) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((MLI + v) + Z0),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((MLI + v) + Z0),(- Z0)] is set
{((MLI + v) + Z0),(- Z0)} is set
{((MLI + v) + Z0)} is non empty trivial V42(1) set
{{((MLI + v) + Z0),(- Z0)},{((MLI + v) + Z0)}} is set
the addF of AG . [((MLI + v) + Z0),(- Z0)] is set
MLI + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (MLI,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,Z0] is set
{MLI,Z0} is set
{{MLI,Z0},{MLI}} is set
the addF of AG . [MLI,Z0] is set
(MLI + Z0) + v is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + Z0),v) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + Z0),v] is set
{(MLI + Z0),v} is set
{(MLI + Z0)} is non empty trivial V42(1) set
{{(MLI + Z0),v},{(MLI + Z0)}} is set
the addF of AG . [(MLI + Z0),v] is set
((MLI + Z0) + v) - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((MLI + Z0) + v) + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((MLI + Z0) + v),(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((MLI + Z0) + v),(- Z0)] is set
{((MLI + Z0) + v),(- Z0)} is set
{((MLI + Z0) + v)} is non empty trivial V42(1) set
{{((MLI + Z0) + v),(- Z0)},{((MLI + Z0) + v)}} is set
the addF of AG . [((MLI + Z0) + v),(- Z0)] is set
v - Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + (- Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,(- Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,(- Z0)] is set
{v,(- Z0)} is set
{v} is non empty trivial V42(1) set
{{v,(- Z0)},{v}} is set
the addF of AG . [v,(- Z0)] is set
(MLI + Z0) + (v - Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((MLI + Z0),(v - Z0)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(MLI + Z0),(v - Z0)] is set
{(MLI + Z0),(v - Z0)} is set
{{(MLI + Z0),(v - Z0)},{(MLI + Z0)}} is set
the addF of AG . [(MLI + Z0),(v - Z0)] is set
v - (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v + (- (0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v,(- (0. AG))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v,(- (0. AG))] is set
{v,(- (0. AG))} is set
{{v,(- (0. AG))},{v}} is set
the addF of AG . [v,(- (0. AG))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + Z0 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (CA,Z0) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
the addF of AG . [CA,Z0] is set
[CA,Z0] is Element of [: the carrier of AG, the carrier of AG:]
[CA,Z0] `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,Z0] `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
([CA,Z0] `1) + ([CA,Z0] `2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (([CA,Z0] `1),([CA,Z0] `2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[([CA,Z0] `1),([CA,Z0] `2)] is set
{([CA,Z0] `1),([CA,Z0] `2)} is set
{([CA,Z0] `1)} is non empty trivial V42(1) set
{{([CA,Z0] `1),([CA,Z0] `2)},{([CA,Z0] `1)}} is set
the addF of AG . [([CA,Z0] `1),([CA,Z0] `2)] is set
CA is Element of [: the carrier of AG, the carrier of AG:]
CA `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(CA `1) + (CA `2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((CA `1),(CA `2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA `1),(CA `2)] is set
{(CA `1),(CA `2)} is set
{(CA `1)} is non empty trivial V42(1) set
{{(CA `1),(CA `2)},{(CA `1)}} is set
the addF of AG . [(CA `1),(CA `2)] is set
Z0 is Element of [: the carrier of AG, the carrier of AG:]
Z0 `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Z0 `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Z0 `1) + (Z0 `2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((Z0 `1),(Z0 `2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(Z0 `1),(Z0 `2)] is set
{(Z0 `1),(Z0 `2)} is set
{(Z0 `1)} is non empty trivial V42(1) set
{{(Z0 `1),(Z0 `2)},{(Z0 `1)}} is set
the addF of AG . [(Z0 `1),(Z0 `2)] is set
[(CA `1),(CA `2)] is Element of [: the carrier of AG, the carrier of AG:]
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
(AG,AD,ZS,ML) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML,ZS) is Element of [: the carrier of AG, the carrier of AG:]
(AG,AD,ML,ZS) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML,ZS) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((AG,AD,ML,ZS) `2) + ((AG,AD,ML,ZS) `1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)] is set
{((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)} is set
{((AG,AD,ML,ZS) `2)} is non empty trivial V42(1) set
{{((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)},{((AG,AD,ML,ZS) `2)}} is set
the addF of AG . [((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)] is set
((AG,AD,ZS,ML) `1) + ((AG,AD,ZS,ML) `2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)] is set
{((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)} is set
{((AG,AD,ZS,ML) `1)} is non empty trivial V42(1) set
{{((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)},{((AG,AD,ZS,ML) `1)}} is set
the addF of AG . [((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
(AG,AD,ZS,ML) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML,ZS) is Element of [: the carrier of AG, the carrier of AG:]
(AG,AD,ML,ZS) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML,ZS) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((AG,AD,ML,ZS) `2) + ((AG,AD,ML,ZS) `1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)] is set
{((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)} is set
{((AG,AD,ML,ZS) `2)} is non empty trivial V42(1) set
{{((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)},{((AG,AD,ML,ZS) `2)}} is set
the addF of AG . [((AG,AD,ML,ZS) `2),((AG,AD,ML,ZS) `1)] is set
(AG,AD,ZS,ML) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((AG,AD,ZS,ML) `1) + ((AG,AD,ZS,ML) `2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)] is set
{((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)} is set
{((AG,AD,ZS,ML) `1)} is non empty trivial V42(1) set
{{((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)},{((AG,AD,ZS,ML) `1)}} is set
the addF of AG . [((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
CA is Element of [: the carrier of AG, the carrier of AG:]
CA `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(CA `1) + (CA `2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((CA `1),(CA `2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA `1),(CA `2)] is set
{(CA `1),(CA `2)} is set
{(CA `1)} is non empty trivial V42(1) set
{{(CA `1),(CA `2)},{(CA `1)}} is set
the addF of AG . [(CA `1),(CA `2)] is set
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
(AG,AD,ZS,ML) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((AG,AD,ZS,ML) `1) + ((AG,AD,ZS,ML) `2) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)] is set
{((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)} is set
{((AG,AD,ZS,ML) `1)} is non empty trivial V42(1) set
{{((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)},{((AG,AD,ZS,ML) `1)}} is set
the addF of AG . [((AG,AD,ZS,ML) `1),((AG,AD,ZS,ML) `2)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
(AG,AD,ZS,ML) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,CA,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
(AG,CA,ZS,ML) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
(AG,AD,ZS,ML) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML,ZS) is Element of [: the carrier of AG, the carrier of AG:]
(AG,AD,ML,ZS) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG) (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG,ZS)
AD is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ZS,ML) is Element of [: the carrier of AG, the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
(AG,AD,ZS,ML) `2 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG,AD,ML,ZS) is Element of [: the carrier of AG, the carrier of AG:]
(AG,AD,ML,ZS) `1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
ZS is Element of (AG)
ML is Element of (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,AD,CA) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
Z0 is Element of (AG)
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
v is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,MLI,v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
ZS is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
ML is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
AD is set
CA is set
Z0 is Element of (AG)
MLI is Element of (AG)
ZS . (Z0,MLI) is Element of (AG)
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
ZS . [Z0,MLI] is set
v is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
i is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,v,i) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS . (AD,CA) is set
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
ZS . [AD,CA] is set
ML . (AD,CA) is set
ML . [AD,CA] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
ZS is Element of (AG)
ML is Element of (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,AD,CA) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
Z0 is Element of (AG)
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
v is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,MLI,v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
ZS is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
ML is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
AD is set
CA is set
Z0 is Element of (AG)
MLI is Element of (AG)
ZS . (Z0,MLI) is Element of (AG)
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
ZS . [Z0,MLI] is set
v is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
i is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,v,i) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ZS . (AD,CA) is set
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
ZS . [AD,CA] is set
ML . (AD,CA) is set
ML . [AD,CA] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
LattStr(# (AG),(AG),(AG) #) is non empty strict LattStr
the carrier of LattStr(# (AG),(AG),(AG) #) is non empty set
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
ML "/\" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_meet of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
AD "/\" ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) . (AD,ML) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[AD,ML] is set
{AD,ML} is set
{AD} is non empty trivial V42(1) set
{{AD,ML},{AD}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [AD,ML] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,CA,Z0) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
ML "/\" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_meet of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
(ML "/\" AD) "\/" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
the L_join of LattStr(# (AG),(AG),(AG) #) . ((ML "/\" AD),AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[(ML "/\" AD),AD] is set
{(ML "/\" AD),AD} is set
{(ML "/\" AD)} is non empty trivial V42(1) set
{{(ML "/\" AD),AD},{(ML "/\" AD)}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [(ML "/\" AD),AD] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,CA,Z0) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
MLI is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (MLI,AD) is set
[MLI,AD] is set
{MLI,AD} is set
{MLI} is non empty trivial V42(1) set
{{MLI,AD},{MLI}} is set
(AG) . [MLI,AD] is set
(AG,(AG,CA,Z0),Z0) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD "\/" CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_join of LattStr(# (AG),(AG),(AG) #) . (AD,CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [AD,CA] is set
ML "\/" (AD "\/" CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,(AD "\/" CA)) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,(AD "\/" CA)] is set
{ML,(AD "\/" CA)} is set
{ML} is non empty trivial V42(1) set
{{ML,(AD "\/" CA)},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,(AD "\/" CA)] is set
ML "\/" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{{ML,AD},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
(ML "\/" AD) "\/" CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . ((ML "\/" AD),CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[(ML "\/" AD),CA] is set
{(ML "\/" AD),CA} is set
{(ML "\/" AD)} is non empty trivial V42(1) set
{{(ML "\/" AD),CA},{(ML "\/" AD)}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [(ML "\/" AD),CA] is set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,Z0,MLI) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
v is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,MLI,v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
v1 is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (ML,v1) is set
[ML,v1] is set
{ML,v1} is set
{{ML,v1},{ML}} is set
(AG) . [ML,v1] is set
(AG,Z0,(AG,MLI,v)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,Z0,MLI),v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
i is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (i,CA) is set
[i,CA] is set
{i,CA} is set
{i} is non empty trivial V42(1) set
{{i,CA},{i}} is set
(AG) . [i,CA] is set
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
ML "\/" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
ML "/\" (ML "\/" AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
the L_meet of LattStr(# (AG),(AG),(AG) #) . (ML,(ML "\/" AD)) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,(ML "\/" AD)] is set
{ML,(ML "\/" AD)} is set
{{ML,(ML "\/" AD)},{ML}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [ML,(ML "\/" AD)] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,CA,Z0) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
MLI is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (ML,MLI) is set
[ML,MLI] is set
{ML,MLI} is set
{{ML,MLI},{ML}} is set
(AG) . [ML,MLI] is set
(AG,CA,(AG,CA,Z0)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD "/\" CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_meet of LattStr(# (AG),(AG),(AG) #) . (AD,CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [AD,CA] is set
ML "/\" (AD "/\" CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) . (ML,(AD "/\" CA)) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,(AD "/\" CA)] is set
{ML,(AD "/\" CA)} is set
{ML} is non empty trivial V42(1) set
{{ML,(AD "/\" CA)},{ML}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [ML,(AD "/\" CA)] is set
ML "/\" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{{ML,AD},{ML}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
(ML "/\" AD) "/\" CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) . ((ML "/\" AD),CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[(ML "/\" AD),CA] is set
{(ML "/\" AD),CA} is set
{(ML "/\" AD)} is non empty trivial V42(1) set
{{(ML "/\" AD),CA},{(ML "/\" AD)}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [(ML "/\" AD),CA] is set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,Z0,MLI) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
v is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,MLI,v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
v1 is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (ML,v1) is set
[ML,v1] is set
{ML,v1} is set
{{ML,v1},{ML}} is set
(AG) . [ML,v1] is set
(AG,Z0,(AG,MLI,v)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,Z0,MLI),v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
i is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (i,CA) is set
[i,CA] is set
{i,CA} is set
{i} is non empty trivial V42(1) set
{{i,CA},{i}} is set
(AG) . [i,CA] is set
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
ML "\/" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
AD "\/" ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . (AD,ML) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[AD,ML] is set
{AD,ML} is set
{AD} is non empty trivial V42(1) set
{{AD,ML},{AD}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [AD,ML] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,CA,Z0) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
LattStr(# (AG),(AG),(AG) #) is non empty strict LattStr
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
LattStr(# (AG),(AG),(AG) #) is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
the carrier of LattStr(# (AG),(AG),(AG) #) is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
ML "/\" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_meet of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
AD "/\" ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) . (AD,ML) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[AD,ML] is set
{AD,ML} is set
{AD} is non empty trivial V42(1) set
{{AD,ML},{AD}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [AD,ML] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,(AG),CA) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
LattStr(# (AG),(AG),(AG) #) is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
the carrier of LattStr(# (AG),(AG),(AG) #) is non empty set
(AG) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
ML "\/" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
AD "\/" ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . (AD,ML) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[AD,ML] is set
{AD,ML} is set
{AD} is non empty trivial V42(1) set
{{AD,ML},{AD}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [AD,ML] is set
CA is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
(AG,(AG),CA) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
LattStr(# (AG),(AG),(AG) #) is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
(AG) is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
LattStr(# (AG),(AG),(AG) #) is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
the carrier of LattStr(# (AG),(AG),(AG) #) is non empty set
ML is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
AD "/\" CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_meet of LattStr(# (AG),(AG),(AG) #) . (AD,CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [AD,CA] is set
ML "\/" (AD "/\" CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,(AD "/\" CA)) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,(AD "/\" CA)] is set
{ML,(AD "/\" CA)} is set
{ML} is non empty trivial V42(1) set
{{ML,(AD "/\" CA)},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,(AD "/\" CA)] is set
ML "\/" AD is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,AD) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,AD] is set
{ML,AD} is set
{{ML,AD},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,AD] is set
(ML "\/" AD) "/\" CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) . ((ML "\/" AD),CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[(ML "\/" AD),CA] is set
{(ML "\/" AD),CA} is set
{(ML "\/" AD)} is non empty trivial V42(1) set
{{(ML "\/" AD),CA},{(ML "\/" AD)}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [(ML "\/" AD),CA] is set
Z0 is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
MLI is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,Z0,MLI) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
v is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,MLI,v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,Z0,v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML "\/" CA is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . (ML,CA) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[ML,CA] is set
{ML,CA} is set
{{ML,CA},{ML}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [ML,CA] is set
v1 is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (ML,v1) is set
[ML,v1] is set
{ML,v1} is set
{{ML,v1},{ML}} is set
(AG) . [ML,v1] is set
(AG,Z0,(AG,MLI,v)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,(AG,Z0,MLI),v) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
i is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (i,CA) is set
[i,CA] is set
{i,CA} is set
{i} is non empty trivial V42(1) set
{{i,CA},{i}} is set
(AG) . [i,CA] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
ML is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AD is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ZS,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG,ML,AD) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
(AG) is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
[:(AG),(AG):] is Relation-like non empty set
[:[:(AG),(AG):],(AG):] is Relation-like non empty set
bool [:[:(AG),(AG):],(AG):] is non empty set
(AG) is Relation-like Function-like V18([:(AG),(AG):],(AG)) Element of bool [:[:(AG),(AG):],(AG):]
LattStr(# (AG),(AG),(AG) #) is non empty strict join-commutative join-associative meet-commutative meet-associative meet-absorbing join-absorbing Lattice-like LattStr
the carrier of LattStr(# (AG),(AG),(AG) #) is non empty set
Z0 is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
MLI is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
Z0 "\/" MLI is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
[:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is Relation-like non empty set
bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):] is non empty set
the L_join of LattStr(# (AG),(AG),(AG) #) . (Z0,MLI) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [Z0,MLI] is set
(AG,ZS,ML) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
v is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
Z0 "/\" v is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) is Relation-like Function-like V18([: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #)) Element of bool [:[: the carrier of LattStr(# (AG),(AG),(AG) #), the carrier of LattStr(# (AG),(AG),(AG) #):], the carrier of LattStr(# (AG),(AG),(AG) #):]
the L_meet of LattStr(# (AG),(AG),(AG) #) . (Z0,v) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[Z0,v] is set
{Z0,v} is set
{{Z0,v},{Z0}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [Z0,v] is set
MLI "/\" v is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_meet of LattStr(# (AG),(AG),(AG) #) . (MLI,v) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[MLI,v] is set
{MLI,v} is set
{MLI} is non empty trivial V42(1) set
{{MLI,v},{MLI}} is set
the L_meet of LattStr(# (AG),(AG),(AG) #) . [MLI,v] is set
(Z0 "/\" v) "\/" (MLI "/\" v) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
the L_join of LattStr(# (AG),(AG),(AG) #) . ((Z0 "/\" v),(MLI "/\" v)) is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
[(Z0 "/\" v),(MLI "/\" v)] is set
{(Z0 "/\" v),(MLI "/\" v)} is set
{(Z0 "/\" v)} is non empty trivial V42(1) set
{{(Z0 "/\" v),(MLI "/\" v)},{(Z0 "/\" v)}} is set
the L_join of LattStr(# (AG),(AG),(AG) #) . [(Z0 "/\" v),(MLI "/\" v)] is set
(AG) . (Z0,v) is set
(AG) . [Z0,v] is set
v1 is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (((AG) . (Z0,v)),v1) is set
[((AG) . (Z0,v)),v1] is set
{((AG) . (Z0,v)),v1} is set
{((AG) . (Z0,v))} is non empty trivial V42(1) set
{{((AG) . (Z0,v)),v1},{((AG) . (Z0,v))}} is set
(AG) . [((AG) . (Z0,v)),v1] is set
i is Element of the carrier of LattStr(# (AG),(AG),(AG) #)
(AG) . (i,v1) is set
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
(AG) . [i,v1] is set
(AG,(AG,ZS,AD),(AG,ML,AD)) is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () () (AG)
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the of AG is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG, the of AG) is non empty () ()
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () ()
the carrier of AG is non empty set
ZS is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() () () () () (AG)
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
AG is non empty addLoopStr
the carrier of AG is non empty set
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is V31() ext-real V79() integer Element of INT
- ZS is V31() ext-real V79() integer set
ML is Element of the carrier of AG
(Nat-mult-left AG) . (ZS,ML) is set
[ZS,ML] is set
{ZS,ML} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ML},{ZS}} is set
(Nat-mult-left AG) . [ZS,ML] is set
- ML is Element of the carrier of AG
(Nat-mult-left AG) . ((- ZS),(- ML)) is set
[(- ZS),(- ML)] is set
{(- ZS),(- ML)} is set
{(- ZS)} is non empty trivial V42(1) set
{{(- ZS),(- ML)},{(- ZS)}} is set
(Nat-mult-left AG) . [(- ZS),(- ML)] is set
AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (AD,ML) is Element of the carrier of AG
[AD,ML] is set
{AD,ML} is set
{AD} is non empty trivial V42(1) set
{{AD,ML},{AD}} is set
(Nat-mult-left AG) . [AD,ML] is set
CA is Element of the carrier of AG
AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (AD,(- ML)) is Element of the carrier of AG
[AD,(- ML)] is set
{AD,(- ML)} is set
{AD} is non empty trivial V42(1) set
{{AD,(- ML)},{AD}} is set
(Nat-mult-left AG) . [AD,(- ML)] is set
CA is Element of the carrier of AG
ZS is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
ML is V31() ext-real V79() integer Element of INT
AD is Element of the carrier of AG
ZS . (ML,AD) is Element of the carrier of AG
[ML,AD] is set
{ML,AD} is set
{ML} is non empty trivial V42(1) set
{{ML,AD},{ML}} is set
ZS . [ML,AD] is set
(Nat-mult-left AG) . (ML,AD) is set
(Nat-mult-left AG) . [ML,AD] is set
CA is V31() ext-real V79() integer Element of INT
Z0 is Element of the carrier of AG
ZS . (CA,Z0) is Element of the carrier of AG
[CA,Z0] is set
{CA,Z0} is set
{CA} is non empty trivial V42(1) set
{{CA,Z0},{CA}} is set
ZS . [CA,Z0] is set
- CA is V31() ext-real V79() integer set
- Z0 is Element of the carrier of AG
(Nat-mult-left AG) . ((- CA),(- Z0)) is set
[(- CA),(- Z0)] is set
{(- CA),(- Z0)} is set
{(- CA)} is non empty trivial V42(1) set
{{(- CA),(- Z0)},{(- CA)}} is set
(Nat-mult-left AG) . [(- CA),(- Z0)] is set
ZS is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
ML is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
AD is set
CA is set
ZS . (AD,CA) is set
[AD,CA] is set
{AD,CA} is set
{AD} is non empty trivial V42(1) set
{{AD,CA},{AD}} is set
ZS . [AD,CA] is set
ML . (AD,CA) is set
ML . [AD,CA] is set
Z0 is V31() ext-real V79() integer Element of INT
MLI is Element of the carrier of AG
(Nat-mult-left AG) . (Z0,MLI) is set
[Z0,MLI] is set
{Z0,MLI} is set
{Z0} is non empty trivial V42(1) set
{{Z0,MLI},{Z0}} is set
(Nat-mult-left AG) . [Z0,MLI] is set
Z0 is V31() ext-real V79() integer Element of INT
- Z0 is V31() ext-real V79() integer set
MLI is Element of the carrier of AG
- MLI is Element of the carrier of AG
(Nat-mult-left AG) . ((- Z0),(- MLI)) is set
[(- Z0),(- MLI)] is set
{(- Z0),(- MLI)} is set
{(- Z0)} is non empty trivial V42(1) set
{{(- Z0),(- MLI)},{(- Z0)}} is set
(Nat-mult-left AG) . [(- Z0),(- MLI)] is set
Z0 is V31() ext-real V79() integer Element of INT
AG is non empty addLoopStr
the carrier of AG is non empty set
ML is V31() ext-real V79() integer Element of INT
AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is Element of the carrier of AG
(AG) . (ML,ZS) is Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
(AG) . [ML,ZS] is set
AD * ZS is Element of the carrier of AG
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
(Nat-mult-left AG) . (AD,ZS) is Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(Nat-mult-left AG) . [AD,ZS] is set
AG is non empty addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
0. AG is V51(AG) Element of the carrier of AG
the ZeroF of AG is Element of the carrier of AG
ZS is Element of the carrier of AG
ML is V31() ext-real V79() integer Element of INT
(AG) . (ML,ZS) is Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
(AG) . [ML,ZS] is set
0 * ZS is Element of the carrier of AG
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
(Nat-mult-left AG) . (0,ZS) is Element of the carrier of AG
[0,ZS] is set
{0,ZS} is set
{0} is non empty trivial V42(1) set
{{0,ZS},{0}} is set
(Nat-mult-left AG) . [0,ZS] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (ZS,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(0. AG)] is set
{ZS,(0. AG)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(0. AG)},{ZS}} is set
(Nat-mult-left AG) . [ZS,(0. AG)] is set
(Nat-mult-left AG) . (0,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[0,(0. AG)] is set
{0,(0. AG)} is set
{0} is non empty trivial V42(1) set
{{0,(0. AG)},{0}} is set
(Nat-mult-left AG) . [0,(0. AG)] is set
ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{ML} is non empty trivial V42(1) set
{{ML,(0. AG)},{ML}} is set
(Nat-mult-left AG) . [ML,(0. AG)] is set
ML + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((ML + 1),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + 1),(0. AG)] is set
{(ML + 1),(0. AG)} is set
{(ML + 1)} is non empty trivial V42(1) set
{{(ML + 1),(0. AG)},{(ML + 1)}} is set
(Nat-mult-left AG) . [(ML + 1),(0. AG)] is set
(0. AG) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((0. AG),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),(0. AG)] is set
{(0. AG),(0. AG)} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),(0. AG)},{(0. AG)}} is set
the addF of AG . [(0. AG),(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS is V31() ext-real V79() integer Element of INT
(AG) . (ZS,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(0. AG)] is set
{ZS,(0. AG)} is set
{ZS} is non empty trivial V42(1) set
{{ZS,(0. AG)},{ZS}} is set
(AG) . [ZS,(0. AG)] is set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{ML} is non empty trivial V42(1) set
{{ML,(0. AG)},{ML}} is set
(Nat-mult-left AG) . [ML,(0. AG)] is set
- ZS is V31() ext-real V79() integer set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
- (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (ML,(- (0. AG))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- (0. AG))] is set
{ML,(- (0. AG))} is set
{ML} is non empty trivial V42(1) set
{{ML,(- (0. AG))},{ML}} is set
(Nat-mult-left AG) . [ML,(- (0. AG))] is set
(Nat-mult-left AG) . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{{ML,(0. AG)},{ML}} is set
(Nat-mult-left AG) . [ML,(0. AG)] is set
AG is non empty right_zeroed addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is Element of the carrier of AG
ML is V31() ext-real V79() integer Element of INT
(AG) . (ML,ZS) is Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
(AG) . [ML,ZS] is set
1 * ZS is Element of the carrier of AG
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
(Nat-mult-left AG) . (1,ZS) is Element of the carrier of AG
[1,ZS] is set
{1,ZS} is set
{1} is non empty trivial V42(1) set
{{1,ZS},{1}} is set
(Nat-mult-left AG) . [1,ZS] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
AD - ML is V31() ext-real V79() integer set
(Nat-mult-left AG) . (CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ZS] is set
{CA,ZS} is set
{CA} is non empty trivial V42(1) set
{{CA,ZS},{CA}} is set
(Nat-mult-left AG) . [CA,ZS] is set
(Nat-mult-left AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(Nat-mult-left AG) . [AD,ZS] is set
(Nat-mult-left AG) . (ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
(Nat-mult-left AG) . [ML,ZS] is set
((Nat-mult-left AG) . (AD,ZS)) - ((Nat-mult-left AG) . (ML,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ((Nat-mult-left AG) . (ML,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((Nat-mult-left AG) . (AD,ZS)) + (- ((Nat-mult-left AG) . (ML,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((Nat-mult-left AG) . (AD,ZS)),(- ((Nat-mult-left AG) . (ML,ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (AD,ZS)),(- ((Nat-mult-left AG) . (ML,ZS)))] is set
{((Nat-mult-left AG) . (AD,ZS)),(- ((Nat-mult-left AG) . (ML,ZS)))} is set
{((Nat-mult-left AG) . (AD,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (AD,ZS)),(- ((Nat-mult-left AG) . (ML,ZS)))},{((Nat-mult-left AG) . (AD,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (AD,ZS)),(- ((Nat-mult-left AG) . (ML,ZS)))] is set
AD * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA + ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(CA + ML) * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . ((CA + ML),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + ML),ZS] is set
{(CA + ML),ZS} is set
{(CA + ML)} is non empty trivial V42(1) set
{{(CA + ML),ZS},{(CA + ML)}} is set
(Nat-mult-left AG) . [(CA + ML),ZS] is set
CA * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(CA * ZS) + (ML * ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((CA * ZS),(ML * ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * ZS),(ML * ZS)] is set
{(CA * ZS),(ML * ZS)} is set
{(CA * ZS)} is non empty trivial V42(1) set
{{(CA * ZS),(ML * ZS)},{(CA * ZS)}} is set
the addF of AG . [(CA * ZS),(ML * ZS)] is set
(ML * ZS) - (ML * ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- (ML * ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(ML * ZS) + (- (ML * ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML * ZS),(- (ML * ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML * ZS),(- (ML * ZS))] is set
{(ML * ZS),(- (ML * ZS))} is set
{(ML * ZS)} is non empty trivial V42(1) set
{{(ML * ZS),(- (ML * ZS))},{(ML * ZS)}} is set
the addF of AG . [(ML * ZS),(- (ML * ZS))] is set
(CA * ZS) + ((ML * ZS) - (ML * ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((CA * ZS),((ML * ZS) - (ML * ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * ZS),((ML * ZS) - (ML * ZS))] is set
{(CA * ZS),((ML * ZS) - (ML * ZS))} is set
{{(CA * ZS),((ML * ZS) - (ML * ZS))},{(CA * ZS)}} is set
the addF of AG . [(CA * ZS),((ML * ZS) - (ML * ZS))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(CA * ZS) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((CA * ZS),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * ZS),(0. AG)] is set
{(CA * ZS),(0. AG)} is set
{{(CA * ZS),(0. AG)},{(CA * ZS)}} is set
the addF of AG . [(CA * ZS),(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
(Nat-mult-left AG) . [ML,ZS] is set
- ((Nat-mult-left AG) . (ML,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (ML,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- ZS)] is set
{ML,(- ZS)} is set
{{ML,(- ZS)},{ML}} is set
(Nat-mult-left AG) . [ML,(- ZS)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[0,ZS] is set
{0,ZS} is set
{0} is non empty trivial V42(1) set
{{0,ZS},{0}} is set
(Nat-mult-left AG) . [0,ZS] is set
(Nat-mult-left AG) . (0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[0,(- ZS)] is set
{0,(- ZS)} is set
{{0,(- ZS)},{0}} is set
(Nat-mult-left AG) . [0,(- ZS)] is set
((Nat-mult-left AG) . (0,ZS)) + ((Nat-mult-left AG) . (0,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,(- ZS)))] is set
{((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,(- ZS)))} is set
{((Nat-mult-left AG) . (0,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,(- ZS)))},{((Nat-mult-left AG) . (0,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,(- ZS)))] is set
(0. AG) + ((Nat-mult-left AG) . (0,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),((Nat-mult-left AG) . (0,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),((Nat-mult-left AG) . (0,(- ZS)))] is set
{(0. AG),((Nat-mult-left AG) . (0,(- ZS)))} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),((Nat-mult-left AG) . (0,(- ZS)))},{(0. AG)}} is set
the addF of AG . [(0. AG),((Nat-mult-left AG) . (0,(- ZS)))] is set
(0. AG) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),(0. AG)] is set
{(0. AG),(0. AG)} is set
{{(0. AG),(0. AG)},{(0. AG)}} is set
the addF of AG . [(0. AG),(0. AG)] is set
AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(Nat-mult-left AG) . [AD,ZS] is set
(Nat-mult-left AG) . (AD,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(- ZS)] is set
{AD,(- ZS)} is set
{{AD,(- ZS)},{AD}} is set
(Nat-mult-left AG) . [AD,(- ZS)] is set
((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,(- ZS)))] is set
{((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,(- ZS)))} is set
{((Nat-mult-left AG) . (AD,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,(- ZS)))},{((Nat-mult-left AG) . (AD,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,(- ZS)))] is set
AD + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((AD + 1),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AD + 1),ZS] is set
{(AD + 1),ZS} is set
{(AD + 1)} is non empty trivial V42(1) set
{{(AD + 1),ZS},{(AD + 1)}} is set
(Nat-mult-left AG) . [(AD + 1),ZS] is set
(Nat-mult-left AG) . ((AD + 1),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AD + 1),(- ZS)] is set
{(AD + 1),(- ZS)} is set
{{(AD + 1),(- ZS)},{(AD + 1)}} is set
(Nat-mult-left AG) . [(AD + 1),(- ZS)] is set
((Nat-mult-left AG) . ((AD + 1),ZS)) + ((Nat-mult-left AG) . ((AD + 1),(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . ((AD + 1),ZS)),((Nat-mult-left AG) . ((AD + 1),(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . ((AD + 1),ZS)),((Nat-mult-left AG) . ((AD + 1),(- ZS)))] is set
{((Nat-mult-left AG) . ((AD + 1),ZS)),((Nat-mult-left AG) . ((AD + 1),(- ZS)))} is set
{((Nat-mult-left AG) . ((AD + 1),ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . ((AD + 1),ZS)),((Nat-mult-left AG) . ((AD + 1),(- ZS)))},{((Nat-mult-left AG) . ((AD + 1),ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . ((AD + 1),ZS)),((Nat-mult-left AG) . ((AD + 1),(- ZS)))] is set
ZS + ((Nat-mult-left AG) . (AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,((Nat-mult-left AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,((Nat-mult-left AG) . (AD,ZS))] is set
{ZS,((Nat-mult-left AG) . (AD,ZS))} is set
{ZS} is non empty trivial V42(1) set
{{ZS,((Nat-mult-left AG) . (AD,ZS))},{ZS}} is set
the addF of AG . [ZS,((Nat-mult-left AG) . (AD,ZS))] is set
(ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . ((AD + 1),(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . ((AD + 1),(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . ((AD + 1),(- ZS)))] is set
{(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . ((AD + 1),(- ZS)))} is set
{(ZS + ((Nat-mult-left AG) . (AD,ZS)))} is non empty trivial V42(1) set
{{(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . ((AD + 1),(- ZS)))},{(ZS + ((Nat-mult-left AG) . (AD,ZS)))}} is set
the addF of AG . [(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . ((AD + 1),(- ZS)))] is set
(- ZS) + ((Nat-mult-left AG) . (AD,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ZS),((Nat-mult-left AG) . (AD,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ZS),((Nat-mult-left AG) . (AD,(- ZS)))] is set
{(- ZS),((Nat-mult-left AG) . (AD,(- ZS)))} is set
{(- ZS)} is non empty trivial V42(1) set
{{(- ZS),((Nat-mult-left AG) . (AD,(- ZS)))},{(- ZS)}} is set
the addF of AG . [(- ZS),((Nat-mult-left AG) . (AD,(- ZS)))] is set
(ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((- ZS) + ((Nat-mult-left AG) . (AD,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + ((Nat-mult-left AG) . (AD,ZS))),((- ZS) + ((Nat-mult-left AG) . (AD,(- ZS))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + ((Nat-mult-left AG) . (AD,ZS))),((- ZS) + ((Nat-mult-left AG) . (AD,(- ZS))))] is set
{(ZS + ((Nat-mult-left AG) . (AD,ZS))),((- ZS) + ((Nat-mult-left AG) . (AD,(- ZS))))} is set
{{(ZS + ((Nat-mult-left AG) . (AD,ZS))),((- ZS) + ((Nat-mult-left AG) . (AD,(- ZS))))},{(ZS + ((Nat-mult-left AG) . (AD,ZS)))}} is set
the addF of AG . [(ZS + ((Nat-mult-left AG) . (AD,ZS))),((- ZS) + ((Nat-mult-left AG) . (AD,(- ZS))))] is set
(ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . (AD,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . (AD,(- ZS)))] is set
{(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . (AD,(- ZS)))} is set
{{(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . (AD,(- ZS)))},{(ZS + ((Nat-mult-left AG) . (AD,ZS)))}} is set
the addF of AG . [(ZS + ((Nat-mult-left AG) . (AD,ZS))),((Nat-mult-left AG) . (AD,(- ZS)))] is set
((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS)))) + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS)))),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS)))),(- ZS)] is set
{((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS)))),(- ZS)} is set
{((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS))))} is non empty trivial V42(1) set
{{((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS)))),(- ZS)},{((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS))))}} is set
the addF of AG . [((ZS + ((Nat-mult-left AG) . (AD,ZS))) + ((Nat-mult-left AG) . (AD,(- ZS)))),(- ZS)] is set
ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))] is set
{ZS,(((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))} is set
{{ZS,(((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))},{ZS}} is set
the addF of AG . [ZS,(((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))] is set
(ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))) + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))),(- ZS)] is set
{(ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))),(- ZS)} is set
{(ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS)))))} is non empty trivial V42(1) set
{{(ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))),(- ZS)},{(ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS)))))}} is set
the addF of AG . [(ZS + (((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,(- ZS))))),(- ZS)] is set
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
((Nat-mult-left AG) . (ML,ZS)) + ((Nat-mult-left AG) . (ML,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (ML,ZS)),((Nat-mult-left AG) . (ML,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (ML,ZS)),((Nat-mult-left AG) . (ML,(- ZS)))] is set
{((Nat-mult-left AG) . (ML,ZS)),((Nat-mult-left AG) . (ML,(- ZS)))} is set
{((Nat-mult-left AG) . (ML,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (ML,ZS)),((Nat-mult-left AG) . (ML,(- ZS)))},{((Nat-mult-left AG) . (ML,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (ML,ZS)),((Nat-mult-left AG) . (ML,(- ZS)))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer Element of INT
AD is V31() ext-real V79() integer Element of INT
ML + AD is V31() ext-real V79() integer set
(AG) . ((ML + AD),ZS) is set
[(ML + AD),ZS] is set
{(ML + AD),ZS} is set
{(ML + AD)} is non empty trivial V42(1) set
{{(ML + AD),ZS},{(ML + AD)}} is set
(AG) . [(ML + AD),ZS] is set
(AG) . (ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
(AG) . [ML,ZS] is set
(AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(AG) . [AD,ZS] is set
((AG) . (ML,ZS)) + ((AG) . (AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((AG) . (ML,ZS)),((AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (ML,ZS)),((AG) . (AD,ZS))] is set
{((AG) . (ML,ZS)),((AG) . (AD,ZS))} is set
{((AG) . (ML,ZS))} is non empty trivial V42(1) set
{{((AG) . (ML,ZS)),((AG) . (AD,ZS))},{((AG) . (ML,ZS))}} is set
the addF of AG . [((AG) . (ML,ZS)),((AG) . (AD,ZS))] is set
- AD is V31() ext-real V79() integer set
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA - Z0 is V31() ext-real V79() integer set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
MLI is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (MLI,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,ZS] is set
{MLI,ZS} is set
{MLI} is non empty trivial V42(1) set
{{MLI,ZS},{MLI}} is set
(Nat-mult-left AG) . [MLI,ZS] is set
(Nat-mult-left AG) . (CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ZS] is set
{CA,ZS} is set
{CA} is non empty trivial V42(1) set
{{CA,ZS},{CA}} is set
(Nat-mult-left AG) . [CA,ZS] is set
(Nat-mult-left AG) . (Z0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,ZS] is set
{Z0,ZS} is set
{Z0} is non empty trivial V42(1) set
{{Z0,ZS},{Z0}} is set
(Nat-mult-left AG) . [Z0,ZS] is set
((Nat-mult-left AG) . (CA,ZS)) - ((Nat-mult-left AG) . (Z0,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ((Nat-mult-left AG) . (Z0,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((Nat-mult-left AG) . (CA,ZS)) + (- ((Nat-mult-left AG) . (Z0,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (CA,ZS)),(- ((Nat-mult-left AG) . (Z0,ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (CA,ZS)),(- ((Nat-mult-left AG) . (Z0,ZS)))] is set
{((Nat-mult-left AG) . (CA,ZS)),(- ((Nat-mult-left AG) . (Z0,ZS)))} is set
{((Nat-mult-left AG) . (CA,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (CA,ZS)),(- ((Nat-mult-left AG) . (Z0,ZS)))},{((Nat-mult-left AG) . (CA,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (CA,ZS)),(- ((Nat-mult-left AG) . (Z0,ZS)))] is set
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (Z0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- ZS)] is set
{Z0,(- ZS)} is set
{{Z0,(- ZS)},{Z0}} is set
(Nat-mult-left AG) . [Z0,(- ZS)] is set
((Nat-mult-left AG) . (CA,ZS)) + ((Nat-mult-left AG) . (Z0,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))] is set
{((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))} is set
{{((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))},{((Nat-mult-left AG) . (CA,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))] is set
((AG) . (ML,ZS)) + ((Nat-mult-left AG) . (Z0,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))] is set
{((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))} is set
{{((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))},{((AG) . (ML,ZS))}} is set
the addF of AG . [((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))] is set
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 - CA is V31() ext-real V79() integer set
CA - Z0 is V31() ext-real V79() integer set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
- (CA - Z0) is V31() ext-real V79() integer set
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . ((- (CA - Z0)),(- ZS)) is set
[(- (CA - Z0)),(- ZS)] is set
{(- (CA - Z0)),(- ZS)} is set
{(- (CA - Z0))} is non empty trivial V42(1) set
{{(- (CA - Z0)),(- ZS)},{(- (CA - Z0))}} is set
(Nat-mult-left AG) . [(- (CA - Z0)),(- ZS)] is set
MLI is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (MLI,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[MLI,(- ZS)] is set
{MLI,(- ZS)} is set
{MLI} is non empty trivial V42(1) set
{{MLI,(- ZS)},{MLI}} is set
(Nat-mult-left AG) . [MLI,(- ZS)] is set
(Nat-mult-left AG) . (Z0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- ZS)] is set
{Z0,(- ZS)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- ZS)},{Z0}} is set
(Nat-mult-left AG) . [Z0,(- ZS)] is set
(Nat-mult-left AG) . (CA,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- ZS)] is set
{CA,(- ZS)} is set
{CA} is non empty trivial V42(1) set
{{CA,(- ZS)},{CA}} is set
(Nat-mult-left AG) . [CA,(- ZS)] is set
((Nat-mult-left AG) . (Z0,(- ZS))) - ((Nat-mult-left AG) . (CA,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ((Nat-mult-left AG) . (CA,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
((Nat-mult-left AG) . (Z0,(- ZS))) + (- ((Nat-mult-left AG) . (CA,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (Z0,(- ZS))),(- ((Nat-mult-left AG) . (CA,(- ZS))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (Z0,(- ZS))),(- ((Nat-mult-left AG) . (CA,(- ZS))))] is set
{((Nat-mult-left AG) . (Z0,(- ZS))),(- ((Nat-mult-left AG) . (CA,(- ZS))))} is set
{((Nat-mult-left AG) . (Z0,(- ZS)))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (Z0,(- ZS))),(- ((Nat-mult-left AG) . (CA,(- ZS))))},{((Nat-mult-left AG) . (Z0,(- ZS)))}} is set
the addF of AG . [((Nat-mult-left AG) . (Z0,(- ZS))),(- ((Nat-mult-left AG) . (CA,(- ZS))))] is set
- (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,(- (- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- (- ZS))] is set
{CA,(- (- ZS))} is set
{{CA,(- (- ZS))},{CA}} is set
(Nat-mult-left AG) . [CA,(- (- ZS))] is set
((Nat-mult-left AG) . (Z0,(- ZS))) + ((Nat-mult-left AG) . (CA,(- (- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,(- (- ZS))))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,(- (- ZS))))] is set
{((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,(- (- ZS))))} is set
{{((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,(- (- ZS))))},{((Nat-mult-left AG) . (Z0,(- ZS)))}} is set
the addF of AG . [((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,(- (- ZS))))] is set
(Nat-mult-left AG) . (CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ZS] is set
{CA,ZS} is set
{{CA,ZS},{CA}} is set
(Nat-mult-left AG) . [CA,ZS] is set
((Nat-mult-left AG) . (Z0,(- ZS))) + ((Nat-mult-left AG) . (CA,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,ZS))] is set
{((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,ZS))} is set
{{((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,ZS))},{((Nat-mult-left AG) . (Z0,(- ZS)))}} is set
the addF of AG . [((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (CA,ZS))] is set
((AG) . (AD,ZS)) + ((Nat-mult-left AG) . (CA,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ZS))] is set
{((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ZS))} is set
{((AG) . (AD,ZS))} is non empty trivial V42(1) set
{{((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ZS))},{((AG) . (AD,ZS))}} is set
the addF of AG . [((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ZS))] is set
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer Element of INT
AD is V31() ext-real V79() integer Element of INT
ML + AD is V31() ext-real V79() integer set
(AG) . ((ML + AD),ZS) is set
[(ML + AD),ZS] is set
{(ML + AD),ZS} is set
{(ML + AD)} is non empty trivial V42(1) set
{{(ML + AD),ZS},{(ML + AD)}} is set
(AG) . [(ML + AD),ZS] is set
(AG) . (ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
(AG) . [ML,ZS] is set
(AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(AG) . [AD,ZS] is set
((AG) . (ML,ZS)) + ((AG) . (AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((AG) . (ML,ZS)),((AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (ML,ZS)),((AG) . (AD,ZS))] is set
{((AG) . (ML,ZS)),((AG) . (AD,ZS))} is set
{((AG) . (ML,ZS))} is non empty trivial V42(1) set
{{((AG) . (ML,ZS)),((AG) . (AD,ZS))},{((AG) . (ML,ZS))}} is set
the addF of AG . [((AG) . (ML,ZS)),((AG) . (AD,ZS))] is set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA + Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(CA + Z0) * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
(Nat-mult-left AG) . ((CA + Z0),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + Z0),ZS] is set
{(CA + Z0),ZS} is set
{(CA + Z0)} is non empty trivial V42(1) set
{{(CA + Z0),ZS},{(CA + Z0)}} is set
(Nat-mult-left AG) . [(CA + Z0),ZS] is set
CA * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ZS] is set
{CA,ZS} is set
{CA} is non empty trivial V42(1) set
{{CA,ZS},{CA}} is set
(Nat-mult-left AG) . [CA,ZS] is set
Z0 * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (Z0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,ZS] is set
{Z0,ZS} is set
{Z0} is non empty trivial V42(1) set
{{Z0,ZS},{Z0}} is set
(Nat-mult-left AG) . [Z0,ZS] is set
(CA * ZS) + (Z0 * ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((CA * ZS),(Z0 * ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * ZS),(Z0 * ZS)] is set
{(CA * ZS),(Z0 * ZS)} is set
{(CA * ZS)} is non empty trivial V42(1) set
{{(CA * ZS),(Z0 * ZS)},{(CA * ZS)}} is set
the addF of AG . [(CA * ZS),(Z0 * ZS)] is set
((AG) . (ML,ZS)) + ((Nat-mult-left AG) . (Z0,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,ZS))] is set
{((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,ZS))} is set
{{((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,ZS))},{((AG) . (ML,ZS))}} is set
the addF of AG . [((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,ZS))] is set
- ML is V31() ext-real V79() integer set
- AD is V31() ext-real V79() integer set
- (ML + AD) is V31() ext-real V79() integer set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA + Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(CA + Z0) * (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
(Nat-mult-left AG) . ((CA + Z0),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + Z0),(- ZS)] is set
{(CA + Z0),(- ZS)} is set
{(CA + Z0)} is non empty trivial V42(1) set
{{(CA + Z0),(- ZS)},{(CA + Z0)}} is set
(Nat-mult-left AG) . [(CA + Z0),(- ZS)] is set
CA * (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- ZS)] is set
{CA,(- ZS)} is set
{CA} is non empty trivial V42(1) set
{{CA,(- ZS)},{CA}} is set
(Nat-mult-left AG) . [CA,(- ZS)] is set
Z0 * (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (Z0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- ZS)] is set
{Z0,(- ZS)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- ZS)},{Z0}} is set
(Nat-mult-left AG) . [Z0,(- ZS)] is set
(CA * (- ZS)) + (Z0 * (- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((CA * (- ZS)),(Z0 * (- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * (- ZS)),(Z0 * (- ZS))] is set
{(CA * (- ZS)),(Z0 * (- ZS))} is set
{(CA * (- ZS))} is non empty trivial V42(1) set
{{(CA * (- ZS)),(Z0 * (- ZS))},{(CA * (- ZS))}} is set
the addF of AG . [(CA * (- ZS)),(Z0 * (- ZS))] is set
((AG) . (ML,ZS)) + ((Nat-mult-left AG) . (Z0,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))] is set
{((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))} is set
{{((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))},{((AG) . (ML,ZS))}} is set
the addF of AG . [((AG) . (ML,ZS)),((Nat-mult-left AG) . (Z0,(- ZS)))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,ML] is set
{ZS,ML} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ML},{ZS}} is set
the addF of AG . [ZS,ML] is set
AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (AD,(ZS + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(ZS + ML)] is set
{AD,(ZS + ML)} is set
{AD} is non empty trivial V42(1) set
{{AD,(ZS + ML)},{AD}} is set
(Nat-mult-left AG) . [AD,(ZS + ML)] is set
(Nat-mult-left AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{{AD,ZS},{AD}} is set
(Nat-mult-left AG) . [AD,ZS] is set
(Nat-mult-left AG) . (AD,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ML] is set
{AD,ML} is set
{{AD,ML},{AD}} is set
(Nat-mult-left AG) . [AD,ML] is set
((Nat-mult-left AG) . (AD,ZS)) + ((Nat-mult-left AG) . (AD,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,ML))] is set
{((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,ML))} is set
{((Nat-mult-left AG) . (AD,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,ML))},{((Nat-mult-left AG) . (AD,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (AD,ZS)),((Nat-mult-left AG) . (AD,ML))] is set
(Nat-mult-left AG) . (0,(ZS + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[0,(ZS + ML)] is set
{0,(ZS + ML)} is set
{0} is non empty trivial V42(1) set
{{0,(ZS + ML)},{0}} is set
(Nat-mult-left AG) . [0,(ZS + ML)] is set
(Nat-mult-left AG) . (0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[0,ZS] is set
{0,ZS} is set
{{0,ZS},{0}} is set
(Nat-mult-left AG) . [0,ZS] is set
(Nat-mult-left AG) . (0,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[0,ML] is set
{0,ML} is set
{{0,ML},{0}} is set
(Nat-mult-left AG) . [0,ML] is set
((Nat-mult-left AG) . (0,ZS)) + ((Nat-mult-left AG) . (0,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,ML))] is set
{((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,ML))} is set
{((Nat-mult-left AG) . (0,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,ML))},{((Nat-mult-left AG) . (0,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (0,ZS)),((Nat-mult-left AG) . (0,ML))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(0. AG) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((0. AG),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0. AG),(0. AG)] is set
{(0. AG),(0. AG)} is set
{(0. AG)} is non empty trivial V42(1) set
{{(0. AG),(0. AG)},{(0. AG)}} is set
the addF of AG . [(0. AG),(0. AG)] is set
((Nat-mult-left AG) . (0,ZS)) + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (0,ZS)),(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (0,ZS)),(0. AG)] is set
{((Nat-mult-left AG) . (0,ZS)),(0. AG)} is set
{{((Nat-mult-left AG) . (0,ZS)),(0. AG)},{((Nat-mult-left AG) . (0,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (0,ZS)),(0. AG)] is set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (CA,(ZS + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(ZS + ML)] is set
{CA,(ZS + ML)} is set
{CA} is non empty trivial V42(1) set
{{CA,(ZS + ML)},{CA}} is set
(Nat-mult-left AG) . [CA,(ZS + ML)] is set
(Nat-mult-left AG) . (CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ZS] is set
{CA,ZS} is set
{{CA,ZS},{CA}} is set
(Nat-mult-left AG) . [CA,ZS] is set
(Nat-mult-left AG) . (CA,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ML] is set
{CA,ML} is set
{{CA,ML},{CA}} is set
(Nat-mult-left AG) . [CA,ML] is set
((Nat-mult-left AG) . (CA,ZS)) + ((Nat-mult-left AG) . (CA,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (CA,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (CA,ML))] is set
{((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (CA,ML))} is set
{((Nat-mult-left AG) . (CA,ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (CA,ML))},{((Nat-mult-left AG) . (CA,ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . (CA,ZS)),((Nat-mult-left AG) . (CA,ML))] is set
CA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((CA + 1),(ZS + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + 1),(ZS + ML)] is set
{(CA + 1),(ZS + ML)} is set
{(CA + 1)} is non empty trivial V42(1) set
{{(CA + 1),(ZS + ML)},{(CA + 1)}} is set
(Nat-mult-left AG) . [(CA + 1),(ZS + ML)] is set
(Nat-mult-left AG) . ((CA + 1),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + 1),ZS] is set
{(CA + 1),ZS} is set
{{(CA + 1),ZS},{(CA + 1)}} is set
(Nat-mult-left AG) . [(CA + 1),ZS] is set
(Nat-mult-left AG) . ((CA + 1),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + 1),ML] is set
{(CA + 1),ML} is set
{{(CA + 1),ML},{(CA + 1)}} is set
(Nat-mult-left AG) . [(CA + 1),ML] is set
((Nat-mult-left AG) . ((CA + 1),ZS)) + ((Nat-mult-left AG) . ((CA + 1),ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . ((CA + 1),ZS)),((Nat-mult-left AG) . ((CA + 1),ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . ((CA + 1),ZS)),((Nat-mult-left AG) . ((CA + 1),ML))] is set
{((Nat-mult-left AG) . ((CA + 1),ZS)),((Nat-mult-left AG) . ((CA + 1),ML))} is set
{((Nat-mult-left AG) . ((CA + 1),ZS))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . ((CA + 1),ZS)),((Nat-mult-left AG) . ((CA + 1),ML))},{((Nat-mult-left AG) . ((CA + 1),ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . ((CA + 1),ZS)),((Nat-mult-left AG) . ((CA + 1),ML))] is set
(ZS + ML) + ((Nat-mult-left AG) . (CA,(ZS + ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + ML),((Nat-mult-left AG) . (CA,(ZS + ML)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + ML),((Nat-mult-left AG) . (CA,(ZS + ML)))] is set
{(ZS + ML),((Nat-mult-left AG) . (CA,(ZS + ML)))} is set
{(ZS + ML)} is non empty trivial V42(1) set
{{(ZS + ML),((Nat-mult-left AG) . (CA,(ZS + ML)))},{(ZS + ML)}} is set
the addF of AG . [(ZS + ML),((Nat-mult-left AG) . (CA,(ZS + ML)))] is set
(ZS + ML) + ((Nat-mult-left AG) . (CA,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + ML),((Nat-mult-left AG) . (CA,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + ML),((Nat-mult-left AG) . (CA,ZS))] is set
{(ZS + ML),((Nat-mult-left AG) . (CA,ZS))} is set
{{(ZS + ML),((Nat-mult-left AG) . (CA,ZS))},{(ZS + ML)}} is set
the addF of AG . [(ZS + ML),((Nat-mult-left AG) . (CA,ZS))] is set
((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS))) + ((Nat-mult-left AG) . (CA,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS))),((Nat-mult-left AG) . (CA,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS))),((Nat-mult-left AG) . (CA,ML))] is set
{((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS))),((Nat-mult-left AG) . (CA,ML))} is set
{((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS)))} is non empty trivial V42(1) set
{{((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS))),((Nat-mult-left AG) . (CA,ML))},{((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS)))}} is set
the addF of AG . [((ZS + ML) + ((Nat-mult-left AG) . (CA,ZS))),((Nat-mult-left AG) . (CA,ML))] is set
ZS + ((Nat-mult-left AG) . (CA,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,((Nat-mult-left AG) . (CA,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,((Nat-mult-left AG) . (CA,ZS))] is set
{ZS,((Nat-mult-left AG) . (CA,ZS))} is set
{{ZS,((Nat-mult-left AG) . (CA,ZS))},{ZS}} is set
the addF of AG . [ZS,((Nat-mult-left AG) . (CA,ZS))] is set
(ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + ((Nat-mult-left AG) . (CA,ZS))),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + ((Nat-mult-left AG) . (CA,ZS))),ML] is set
{(ZS + ((Nat-mult-left AG) . (CA,ZS))),ML} is set
{(ZS + ((Nat-mult-left AG) . (CA,ZS)))} is non empty trivial V42(1) set
{{(ZS + ((Nat-mult-left AG) . (CA,ZS))),ML},{(ZS + ((Nat-mult-left AG) . (CA,ZS)))}} is set
the addF of AG . [(ZS + ((Nat-mult-left AG) . (CA,ZS))),ML] is set
((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML) + ((Nat-mult-left AG) . (CA,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML),((Nat-mult-left AG) . (CA,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML),((Nat-mult-left AG) . (CA,ML))] is set
{((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML),((Nat-mult-left AG) . (CA,ML))} is set
{((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML)} is non empty trivial V42(1) set
{{((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML),((Nat-mult-left AG) . (CA,ML))},{((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML)}} is set
the addF of AG . [((ZS + ((Nat-mult-left AG) . (CA,ZS))) + ML),((Nat-mult-left AG) . (CA,ML))] is set
((Nat-mult-left AG) . ((CA + 1),ZS)) + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . ((CA + 1),ZS)),ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . ((CA + 1),ZS)),ML] is set
{((Nat-mult-left AG) . ((CA + 1),ZS)),ML} is set
{{((Nat-mult-left AG) . ((CA + 1),ZS)),ML},{((Nat-mult-left AG) . ((CA + 1),ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . ((CA + 1),ZS)),ML] is set
(((Nat-mult-left AG) . ((CA + 1),ZS)) + ML) + ((Nat-mult-left AG) . (CA,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((((Nat-mult-left AG) . ((CA + 1),ZS)) + ML),((Nat-mult-left AG) . (CA,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(((Nat-mult-left AG) . ((CA + 1),ZS)) + ML),((Nat-mult-left AG) . (CA,ML))] is set
{(((Nat-mult-left AG) . ((CA + 1),ZS)) + ML),((Nat-mult-left AG) . (CA,ML))} is set
{(((Nat-mult-left AG) . ((CA + 1),ZS)) + ML)} is non empty trivial V42(1) set
{{(((Nat-mult-left AG) . ((CA + 1),ZS)) + ML),((Nat-mult-left AG) . (CA,ML))},{(((Nat-mult-left AG) . ((CA + 1),ZS)) + ML)}} is set
the addF of AG . [(((Nat-mult-left AG) . ((CA + 1),ZS)) + ML),((Nat-mult-left AG) . (CA,ML))] is set
ML + ((Nat-mult-left AG) . (CA,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,((Nat-mult-left AG) . (CA,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((Nat-mult-left AG) . (CA,ML))] is set
{ML,((Nat-mult-left AG) . (CA,ML))} is set
{ML} is non empty trivial V42(1) set
{{ML,((Nat-mult-left AG) . (CA,ML))},{ML}} is set
the addF of AG . [ML,((Nat-mult-left AG) . (CA,ML))] is set
((Nat-mult-left AG) . ((CA + 1),ZS)) + (ML + ((Nat-mult-left AG) . (CA,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((Nat-mult-left AG) . ((CA + 1),ZS)),(ML + ((Nat-mult-left AG) . (CA,ML)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . ((CA + 1),ZS)),(ML + ((Nat-mult-left AG) . (CA,ML)))] is set
{((Nat-mult-left AG) . ((CA + 1),ZS)),(ML + ((Nat-mult-left AG) . (CA,ML)))} is set
{{((Nat-mult-left AG) . ((CA + 1),ZS)),(ML + ((Nat-mult-left AG) . (CA,ML)))},{((Nat-mult-left AG) . ((CA + 1),ZS))}} is set
the addF of AG . [((Nat-mult-left AG) . ((CA + 1),ZS)),(ML + ((Nat-mult-left AG) . (CA,ML)))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ZS + ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (ZS,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,ML] is set
{ZS,ML} is set
{ZS} is non empty trivial V42(1) set
{{ZS,ML},{ZS}} is set
the addF of AG . [ZS,ML] is set
AD is V31() ext-real V79() integer Element of INT
(AG) . (AD,(ZS + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,(ZS + ML)] is set
{AD,(ZS + ML)} is set
{AD} is non empty trivial V42(1) set
{{AD,(ZS + ML)},{AD}} is set
(AG) . [AD,(ZS + ML)] is set
(AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{{AD,ZS},{AD}} is set
(AG) . [AD,ZS] is set
(AG) . (AD,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ML] is set
{AD,ML} is set
{{AD,ML},{AD}} is set
(AG) . [AD,ML] is set
((AG) . (AD,ZS)) + ((AG) . (AD,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (AD,ZS)),((AG) . (AD,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (AD,ZS)),((AG) . (AD,ML))] is set
{((AG) . (AD,ZS)),((AG) . (AD,ML))} is set
{((AG) . (AD,ZS))} is non empty trivial V42(1) set
{{((AG) . (AD,ZS)),((AG) . (AD,ML))},{((AG) . (AD,ZS))}} is set
the addF of AG . [((AG) . (AD,ZS)),((AG) . (AD,ML))] is set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (CA,(ZS + ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(ZS + ML)] is set
{CA,(ZS + ML)} is set
{CA} is non empty trivial V42(1) set
{{CA,(ZS + ML)},{CA}} is set
(Nat-mult-left AG) . [CA,(ZS + ML)] is set
CA * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ZS] is set
{CA,ZS} is set
{{CA,ZS},{CA}} is set
(Nat-mult-left AG) . [CA,ZS] is set
CA * ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,ML] is set
{CA,ML} is set
{{CA,ML},{CA}} is set
(Nat-mult-left AG) . [CA,ML] is set
(CA * ZS) + (CA * ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((CA * ZS),(CA * ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * ZS),(CA * ML)] is set
{(CA * ZS),(CA * ML)} is set
{(CA * ZS)} is non empty trivial V42(1) set
{{(CA * ZS),(CA * ML)},{(CA * ZS)}} is set
the addF of AG . [(CA * ZS),(CA * ML)] is set
((AG) . (AD,ZS)) + ((Nat-mult-left AG) . (CA,ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ML))] is set
{((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ML))} is set
{{((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ML))},{((AG) . (AD,ZS))}} is set
the addF of AG . [((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,ML))] is set
- AD is V31() ext-real V79() integer set
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ML is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(- ZS) + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((- ZS),(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(- ZS),(- ML)] is set
{(- ZS),(- ML)} is set
{(- ZS)} is non empty trivial V42(1) set
{{(- ZS),(- ML)},{(- ZS)}} is set
the addF of AG . [(- ZS),(- ML)] is set
(ZS + ML) + ((- ZS) + (- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ZS + ML),((- ZS) + (- ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ZS + ML),((- ZS) + (- ML))] is set
{(ZS + ML),((- ZS) + (- ML))} is set
{(ZS + ML)} is non empty trivial V42(1) set
{{(ZS + ML),((- ZS) + (- ML))},{(ZS + ML)}} is set
the addF of AG . [(ZS + ML),((- ZS) + (- ML))] is set
ML + ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,ZS] is set
{ML,ZS} is set
{ML} is non empty trivial V42(1) set
{{ML,ZS},{ML}} is set
the addF of AG . [ML,ZS] is set
(ML + ZS) + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + ZS),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + ZS),(- ZS)] is set
{(ML + ZS),(- ZS)} is set
{(ML + ZS)} is non empty trivial V42(1) set
{{(ML + ZS),(- ZS)},{(ML + ZS)}} is set
the addF of AG . [(ML + ZS),(- ZS)] is set
((ML + ZS) + (- ZS)) + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((ML + ZS) + (- ZS)),(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((ML + ZS) + (- ZS)),(- ML)] is set
{((ML + ZS) + (- ZS)),(- ML)} is set
{((ML + ZS) + (- ZS))} is non empty trivial V42(1) set
{{((ML + ZS) + (- ZS)),(- ML)},{((ML + ZS) + (- ZS))}} is set
the addF of AG . [((ML + ZS) + (- ZS)),(- ML)] is set
ZS + (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ZS,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ZS,(- ZS)] is set
{ZS,(- ZS)} is set
{{ZS,(- ZS)},{ZS}} is set
the addF of AG . [ZS,(- ZS)] is set
ML + (ZS + (- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(ZS + (- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(ZS + (- ZS))] is set
{ML,(ZS + (- ZS))} is set
{{ML,(ZS + (- ZS))},{ML}} is set
the addF of AG . [ML,(ZS + (- ZS))] is set
(ML + (ZS + (- ZS))) + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + (ZS + (- ZS))),(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + (ZS + (- ZS))),(- ML)] is set
{(ML + (ZS + (- ZS))),(- ML)} is set
{(ML + (ZS + (- ZS)))} is non empty trivial V42(1) set
{{(ML + (ZS + (- ZS))),(- ML)},{(ML + (ZS + (- ZS)))}} is set
the addF of AG . [(ML + (ZS + (- ZS))),(- ML)] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{{ML,(0. AG)},{ML}} is set
the addF of AG . [ML,(0. AG)] is set
(ML + (0. AG)) + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((ML + (0. AG)),(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML + (0. AG)),(- ML)] is set
{(ML + (0. AG)),(- ML)} is set
{(ML + (0. AG))} is non empty trivial V42(1) set
{{(ML + (0. AG)),(- ML)},{(ML + (0. AG))}} is set
the addF of AG . [(ML + (0. AG)),(- ML)] is set
ML + (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (ML,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(- ML)] is set
{ML,(- ML)} is set
{{ML,(- ML)},{ML}} is set
the addF of AG . [ML,(- ML)] is set
- (ZS + ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (CA,(- (ZS + ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- (ZS + ML))] is set
{CA,(- (ZS + ML))} is set
{CA} is non empty trivial V42(1) set
{{CA,(- (ZS + ML))},{CA}} is set
(Nat-mult-left AG) . [CA,(- (ZS + ML))] is set
CA * (- ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- ZS)] is set
{CA,(- ZS)} is set
{{CA,(- ZS)},{CA}} is set
(Nat-mult-left AG) . [CA,(- ZS)] is set
CA * (- ML) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,(- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- ML)] is set
{CA,(- ML)} is set
{{CA,(- ML)},{CA}} is set
(Nat-mult-left AG) . [CA,(- ML)] is set
(CA * (- ZS)) + (CA * (- ML)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((CA * (- ZS)),(CA * (- ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * (- ZS)),(CA * (- ML))] is set
{(CA * (- ZS)),(CA * (- ML))} is set
{(CA * (- ZS))} is non empty trivial V42(1) set
{{(CA * (- ZS)),(CA * (- ML))},{(CA * (- ZS))}} is set
the addF of AG . [(CA * (- ZS)),(CA * (- ML))] is set
((AG) . (AD,ZS)) + ((Nat-mult-left AG) . (CA,(- ML))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,(- ML)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,(- ML)))] is set
{((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,(- ML)))} is set
{{((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,(- ML)))},{((AG) . (AD,ZS))}} is set
the addF of AG . [((AG) . (AD,ZS)),((Nat-mult-left AG) . (CA,(- ML)))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
ML * AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((ML * AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(ML * AD),ZS] is set
{(ML * AD),ZS} is set
{(ML * AD)} is non empty trivial V42(1) set
{{(ML * AD),ZS},{(ML * AD)}} is set
(Nat-mult-left AG) . [(ML * AD),ZS] is set
(Nat-mult-left AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(Nat-mult-left AG) . [AD,ZS] is set
(Nat-mult-left AG) . (ML,((Nat-mult-left AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((Nat-mult-left AG) . (AD,ZS))] is set
{ML,((Nat-mult-left AG) . (AD,ZS))} is set
{ML} is non empty trivial V42(1) set
{{ML,((Nat-mult-left AG) . (AD,ZS))},{ML}} is set
(Nat-mult-left AG) . [ML,((Nat-mult-left AG) . (AD,ZS))] is set
0 * AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((0 * AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(0 * AD),ZS] is set
{(0 * AD),ZS} is set
{(0 * AD)} is non empty trivial V42(1) set
{{(0 * AD),ZS},{(0 * AD)}} is set
(Nat-mult-left AG) . [(0 * AD),ZS] is set
(Nat-mult-left AG) . (0,((Nat-mult-left AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[0,((Nat-mult-left AG) . (AD,ZS))] is set
{0,((Nat-mult-left AG) . (AD,ZS))} is set
{0} is non empty trivial V42(1) set
{{0,((Nat-mult-left AG) . (AD,ZS))},{0}} is set
(Nat-mult-left AG) . [0,((Nat-mult-left AG) . (AD,ZS))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA * AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((CA * AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * AD),ZS] is set
{(CA * AD),ZS} is set
{(CA * AD)} is non empty trivial V42(1) set
{{(CA * AD),ZS},{(CA * AD)}} is set
(Nat-mult-left AG) . [(CA * AD),ZS] is set
(Nat-mult-left AG) . (CA,((Nat-mult-left AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,((Nat-mult-left AG) . (AD,ZS))] is set
{CA,((Nat-mult-left AG) . (AD,ZS))} is set
{CA} is non empty trivial V42(1) set
{{CA,((Nat-mult-left AG) . (AD,ZS))},{CA}} is set
(Nat-mult-left AG) . [CA,((Nat-mult-left AG) . (AD,ZS))] is set
CA + 1 is non empty epsilon-transitive epsilon-connected ordinal natural V31() ext-real positive non negative V35() V40() V79() integer Element of NAT
(CA + 1) * AD is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (((CA + 1) * AD),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((CA + 1) * AD),ZS] is set
{((CA + 1) * AD),ZS} is set
{((CA + 1) * AD)} is non empty trivial V42(1) set
{{((CA + 1) * AD),ZS},{((CA + 1) * AD)}} is set
(Nat-mult-left AG) . [((CA + 1) * AD),ZS] is set
(Nat-mult-left AG) . ((CA + 1),((Nat-mult-left AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + 1),((Nat-mult-left AG) . (AD,ZS))] is set
{(CA + 1),((Nat-mult-left AG) . (AD,ZS))} is set
{(CA + 1)} is non empty trivial V42(1) set
{{(CA + 1),((Nat-mult-left AG) . (AD,ZS))},{(CA + 1)}} is set
(Nat-mult-left AG) . [(CA + 1),((Nat-mult-left AG) . (AD,ZS))] is set
AD + (CA * AD) is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(AD + (CA * AD)) * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . ((AD + (CA * AD)),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AD + (CA * AD)),ZS] is set
{(AD + (CA * AD)),ZS} is set
{(AD + (CA * AD))} is non empty trivial V42(1) set
{{(AD + (CA * AD)),ZS},{(AD + (CA * AD))}} is set
(Nat-mult-left AG) . [(AD + (CA * AD)),ZS] is set
AD * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(CA * AD) * ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AD * ZS) + ((CA * AD) * ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . ((AD * ZS),((CA * AD) * ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(AD * ZS),((CA * AD) * ZS)] is set
{(AD * ZS),((CA * AD) * ZS)} is set
{(AD * ZS)} is non empty trivial V42(1) set
{{(AD * ZS),((CA * AD) * ZS)},{(AD * ZS)}} is set
the addF of AG . [(AD * ZS),((CA * AD) * ZS)] is set
(Nat-mult-left AG) . ((CA + 1),(AD * ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA + 1),(AD * ZS)] is set
{(CA + 1),(AD * ZS)} is set
{{(CA + 1),(AD * ZS)},{(CA + 1)}} is set
(Nat-mult-left AG) . [(CA + 1),(AD * ZS)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer Element of INT
AD is V31() ext-real V79() integer Element of INT
ML * AD is V31() ext-real V79() integer set
(AG) . ((ML * AD),ZS) is set
[(ML * AD),ZS] is set
{(ML * AD),ZS} is set
{(ML * AD)} is non empty trivial V42(1) set
{{(ML * AD),ZS},{(ML * AD)}} is set
(AG) . [(ML * AD),ZS] is set
(AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(AG) . [AD,ZS] is set
(AG) . (ML,((AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((AG) . (AD,ZS))] is set
{ML,((AG) . (AD,ZS))} is set
{ML} is non empty trivial V42(1) set
{{ML,((AG) . (AD,ZS))},{ML}} is set
(AG) . [ML,((AG) . (AD,ZS))] is set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA * Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((CA * Z0),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * Z0),ZS] is set
{(CA * Z0),ZS} is set
{(CA * Z0)} is non empty trivial V42(1) set
{{(CA * Z0),ZS},{(CA * Z0)}} is set
(Nat-mult-left AG) . [(CA * Z0),ZS] is set
(Nat-mult-left AG) . (Z0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,ZS] is set
{Z0,ZS} is set
{Z0} is non empty trivial V42(1) set
{{Z0,ZS},{Z0}} is set
(Nat-mult-left AG) . [Z0,ZS] is set
(Nat-mult-left AG) . (CA,((Nat-mult-left AG) . (Z0,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,((Nat-mult-left AG) . (Z0,ZS))] is set
{CA,((Nat-mult-left AG) . (Z0,ZS))} is set
{CA} is non empty trivial V42(1) set
{{CA,((Nat-mult-left AG) . (Z0,ZS))},{CA}} is set
(Nat-mult-left AG) . [CA,((Nat-mult-left AG) . (Z0,ZS))] is set
(Nat-mult-left AG) . (CA,((AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,((AG) . (AD,ZS))] is set
{CA,((AG) . (AD,ZS))} is set
{{CA,((AG) . (AD,ZS))},{CA}} is set
(Nat-mult-left AG) . [CA,((AG) . (AD,ZS))] is set
- AD is V31() ext-real V79() integer set
- (ML * AD) is V31() ext-real V79() integer set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA * Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
0 * ML is V31() ext-real V79() integer set
AD * ML is V31() ext-real V79() integer set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . ((CA * Z0),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * Z0),(- ZS)] is set
{(CA * Z0),(- ZS)} is set
{(CA * Z0)} is non empty trivial V42(1) set
{{(CA * Z0),(- ZS)},{(CA * Z0)}} is set
(Nat-mult-left AG) . [(CA * Z0),(- ZS)] is set
(Nat-mult-left AG) . (Z0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- ZS)] is set
{Z0,(- ZS)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- ZS)},{Z0}} is set
(Nat-mult-left AG) . [Z0,(- ZS)] is set
(Nat-mult-left AG) . (CA,((Nat-mult-left AG) . (Z0,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,((Nat-mult-left AG) . (Z0,(- ZS)))] is set
{CA,((Nat-mult-left AG) . (Z0,(- ZS)))} is set
{CA} is non empty trivial V42(1) set
{{CA,((Nat-mult-left AG) . (Z0,(- ZS)))},{CA}} is set
(Nat-mult-left AG) . [CA,((Nat-mult-left AG) . (Z0,(- ZS)))] is set
(Nat-mult-left AG) . (CA,((AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,((AG) . (AD,ZS))] is set
{CA,((AG) . (AD,ZS))} is set
{{CA,((AG) . (AD,ZS))},{CA}} is set
(Nat-mult-left AG) . [CA,((AG) . (AD,ZS))] is set
- ML is V31() ext-real V79() integer set
- (ML * AD) is V31() ext-real V79() integer set
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA * Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
0 * AD is V31() ext-real V79() integer set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . ((CA * Z0),(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * Z0),(- ZS)] is set
{(CA * Z0),(- ZS)} is set
{(CA * Z0)} is non empty trivial V42(1) set
{{(CA * Z0),(- ZS)},{(CA * Z0)}} is set
(Nat-mult-left AG) . [(CA * Z0),(- ZS)] is set
(Nat-mult-left AG) . (Z0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- ZS)] is set
{Z0,(- ZS)} is set
{Z0} is non empty trivial V42(1) set
{{Z0,(- ZS)},{Z0}} is set
(Nat-mult-left AG) . [Z0,(- ZS)] is set
(Nat-mult-left AG) . (CA,((Nat-mult-left AG) . (Z0,(- ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,((Nat-mult-left AG) . (Z0,(- ZS)))] is set
{CA,((Nat-mult-left AG) . (Z0,(- ZS)))} is set
{CA} is non empty trivial V42(1) set
{{CA,((Nat-mult-left AG) . (Z0,(- ZS)))},{CA}} is set
(Nat-mult-left AG) . [CA,((Nat-mult-left AG) . (Z0,(- ZS)))] is set
(Nat-mult-left AG) . (Z0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,ZS] is set
{Z0,ZS} is set
{{Z0,ZS},{Z0}} is set
(Nat-mult-left AG) . [Z0,ZS] is set
- ((Nat-mult-left AG) . (Z0,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,(- ((Nat-mult-left AG) . (Z0,ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- ((Nat-mult-left AG) . (Z0,ZS)))] is set
{CA,(- ((Nat-mult-left AG) . (Z0,ZS)))} is set
{{CA,(- ((Nat-mult-left AG) . (Z0,ZS)))},{CA}} is set
(Nat-mult-left AG) . [CA,(- ((Nat-mult-left AG) . (Z0,ZS)))] is set
- ((AG) . (AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,(- ((AG) . (AD,ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- ((AG) . (AD,ZS)))] is set
{CA,(- ((AG) . (AD,ZS)))} is set
{{CA,(- ((AG) . (AD,ZS)))},{CA}} is set
(Nat-mult-left AG) . [CA,(- ((AG) . (AD,ZS)))] is set
- ML is V31() ext-real V79() integer set
- AD is V31() ext-real V79() integer set
Nat-mult-left AG is Relation-like Function-like V18([:NAT, the carrier of AG:], the carrier of AG) Element of bool [:[:NAT, the carrier of AG:], the carrier of AG:]
[:NAT, the carrier of AG:] is Relation-like non empty V35() set
[:[:NAT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:NAT, the carrier of AG:], the carrier of AG:] is non empty V35() set
Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . (Z0,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,ZS] is set
{Z0,ZS} is set
{Z0} is non empty trivial V42(1) set
{{Z0,ZS},{Z0}} is set
(Nat-mult-left AG) . [Z0,ZS] is set
- ((Nat-mult-left AG) . (Z0,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (Z0,(- ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[Z0,(- ZS)] is set
{Z0,(- ZS)} is set
{{Z0,(- ZS)},{Z0}} is set
(Nat-mult-left AG) . [Z0,(- ZS)] is set
((Nat-mult-left AG) . (Z0,(- ZS))) + ((Nat-mult-left AG) . (Z0,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
the addF of AG . (((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (Z0,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (Z0,ZS))] is set
{((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (Z0,ZS))} is set
{((Nat-mult-left AG) . (Z0,(- ZS)))} is non empty trivial V42(1) set
{{((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (Z0,ZS))},{((Nat-mult-left AG) . (Z0,(- ZS)))}} is set
the addF of AG . [((Nat-mult-left AG) . (Z0,(- ZS))),((Nat-mult-left AG) . (Z0,ZS))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
- ((Nat-mult-left AG) . (Z0,(- ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
CA is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
CA * Z0 is epsilon-transitive epsilon-connected ordinal natural V31() ext-real non negative V35() V40() V79() integer Element of NAT
(Nat-mult-left AG) . ((CA * Z0),ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(CA * Z0),ZS] is set
{(CA * Z0),ZS} is set
{(CA * Z0)} is non empty trivial V42(1) set
{{(CA * Z0),ZS},{(CA * Z0)}} is set
(Nat-mult-left AG) . [(CA * Z0),ZS] is set
(Nat-mult-left AG) . (CA,((Nat-mult-left AG) . (Z0,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,((Nat-mult-left AG) . (Z0,ZS))] is set
{CA,((Nat-mult-left AG) . (Z0,ZS))} is set
{CA} is non empty trivial V42(1) set
{{CA,((Nat-mult-left AG) . (Z0,ZS))},{CA}} is set
(Nat-mult-left AG) . [CA,((Nat-mult-left AG) . (Z0,ZS))] is set
- ((AG) . (AD,ZS)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(Nat-mult-left AG) . (CA,(- ((AG) . (AD,ZS)))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[CA,(- ((AG) . (AD,ZS)))] is set
{CA,(- ((AG) . (AD,ZS)))} is set
{{CA,(- ((AG) . (AD,ZS)))},{CA}} is set
(Nat-mult-left AG) . [CA,(- ((AG) . (AD,ZS)))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer Element of INT
AD is V31() ext-real V79() integer Element of INT
ML * AD is V31() ext-real V79() integer set
(AG) . ((ML * AD),ZS) is set
[(ML * AD),ZS] is set
{(ML * AD),ZS} is set
{(ML * AD)} is non empty trivial V42(1) set
{{(ML * AD),ZS},{(ML * AD)}} is set
(AG) . [(ML * AD),ZS] is set
(AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(AG) . [AD,ZS] is set
(AG) . (ML,((AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((AG) . (AD,ZS))] is set
{ML,((AG) . (AD,ZS))} is set
{ML} is non empty trivial V42(1) set
{{ML,((AG) . (AD,ZS))},{ML}} is set
(AG) . [ML,((AG) . (AD,ZS))] is set
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG) . (ML,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,(0. AG)] is set
{ML,(0. AG)} is set
{{ML,(0. AG)},{ML}} is set
(AG) . [ML,(0. AG)] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
ZS is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
ML is V31() ext-real V79() integer Element of INT
AD is V31() ext-real V79() integer Element of INT
ML * AD is V31() ext-real V79() integer set
(AG) . ((ML * AD),ZS) is set
[(ML * AD),ZS] is set
{(ML * AD),ZS} is set
{(ML * AD)} is non empty trivial V42(1) set
{{(ML * AD),ZS},{(ML * AD)}} is set
(AG) . [(ML * AD),ZS] is set
(AG) . (AD,ZS) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[AD,ZS] is set
{AD,ZS} is set
{AD} is non empty trivial V42(1) set
{{AD,ZS},{AD}} is set
(AG) . [AD,ZS] is set
(AG) . (ML,((AG) . (AD,ZS))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[ML,((AG) . (AD,ZS))] is set
{ML,((AG) . (AD,ZS))} is set
{ML} is non empty trivial V42(1) set
{{ML,((AG) . (AD,ZS))},{ML}} is set
(AG) . [ML,((AG) . (AD,ZS))] is set
AG is non empty left_add-cancelable right_add-cancelable add-cancelable right_complementable Abelian add-associative right_zeroed V129() V130() V131() V132() addLoopStr
the carrier of AG is non empty set
the ZeroF of AG is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG is Relation-like Function-like V18([: the carrier of AG, the carrier of AG:], the carrier of AG) Element of bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:]
[: the carrier of AG, the carrier of AG:] is Relation-like non empty set
[:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is Relation-like non empty set
bool [:[: the carrier of AG, the carrier of AG:], the carrier of AG:] is non empty set
(AG) is Relation-like Function-like V18([:INT, the carrier of AG:], the carrier of AG) Element of bool [:[:INT, the carrier of AG:], the carrier of AG:]
[:INT, the carrier of AG:] is Relation-like non empty V35() set
[:[:INT, the carrier of AG:], the carrier of AG:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of AG:], the carrier of AG:] is non empty V35() set
( the carrier of AG, the ZeroF of AG, the addF of AG,(AG)) is non empty () ()
ZS is non empty ()
the of ZS is Relation-like Function-like V18([:INT, the carrier of ZS:], the carrier of ZS) Element of bool [:[:INT, the carrier of ZS:], the carrier of ZS:]
the carrier of ZS is non empty set
[:INT, the carrier of ZS:] is Relation-like non empty V35() set
[:[:INT, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty V35() set
bool [:[:INT, the carrier of ZS:], the carrier of ZS:] is non empty V35() set
the addF of ZS is Relation-like Function-like V18([: the carrier of ZS, the carrier of ZS:], the carrier of ZS) Element of bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:]
[: the carrier of ZS, the carrier of ZS:] is Relation-like non empty set
[:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is Relation-like non empty set
bool [:[: the carrier of ZS, the carrier of ZS:], the carrier of ZS:] is non empty set
the ZeroF of ZS is Element of the carrier of ZS
v is Element of the carrier of ZS
i is Element of the carrier of ZS
v + i is Element of the carrier of ZS
the addF of ZS . (v,i) is Element of the carrier of ZS
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
the addF of ZS . [v,i] is set
i + v is Element of the carrier of ZS
the addF of ZS . (i,v) is Element of the carrier of ZS
[i,v] is set
{i,v} is set
{i} is non empty trivial V42(1) set
{{i,v},{i}} is set
the addF of ZS . [i,v] is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 + a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (v1,a1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[v1,a1] is set
{v1,a1} is set
{v1} is non empty trivial V42(1) set
{{v1,a1},{v1}} is set
the addF of AG . [v1,a1] is set
a1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (a1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,v1] is set
{a1,v1} is set
{a1} is non empty trivial V42(1) set
{{a1,v1},{a1}} is set
the addF of AG . [a1,v1] is set
v is Element of the carrier of ZS
i is Element of the carrier of ZS
v + i is Element of the carrier of ZS
the addF of ZS . (v,i) is Element of the carrier of ZS
[v,i] is set
{v,i} is set
{v} is non empty trivial V42(1) set
{{v,i},{v}} is set
the addF of ZS . [v,i] is set
v1 is Element of the carrier of ZS
(v + i) + v1 is Element of the carrier of ZS
the addF of ZS . ((v + i),v1) is Element of the carrier of ZS
[(v + i),v1] is set
{(v + i),v1} is set
{(v + i)} is non empty trivial V42(1) set
{{(v + i),v1},{(v + i)}} is set
the addF of ZS . [(v + i),v1] is set
i + v1 is Element of the carrier of ZS
the addF of ZS . (i,v1) is Element of the carrier of ZS
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the addF of ZS . [i,v1] is set
v + (i + v1) is Element of the carrier of ZS
the addF of ZS . (v,(i + v1)) is Element of the carrier of ZS
[v,(i + v1)] is set
{v,(i + v1)} is set
{{v,(i + v1)},{v}} is set
the addF of ZS . [v,(i + v1)] is set
a1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
a1 + b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (a1,b1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,b1] is set
{a1,b1} is set
{a1} is non empty trivial V42(1) set
{{a1,b1},{a1}} is set
the addF of AG . [a1,b1] is set
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(a1 + b1) + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . ((a1 + b1),v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[(a1 + b1),v1] is set
{(a1 + b1),v1} is set
{(a1 + b1)} is non empty trivial V42(1) set
{{(a1 + b1),v1},{(a1 + b1)}} is set
the addF of AG . [(a1 + b1),v1] is set
b1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
the addF of AG . [b1,v1] is set
a1 + (b1 + v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (a1,(b1 + v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,(b1 + v1)] is set
{a1,(b1 + v1)} is set
{{a1,(b1 + v1)},{a1}} is set
the addF of AG . [a1,(b1 + v1)] is set
0. ZS is V51(ZS) Element of the carrier of ZS
v is Element of the carrier of ZS
v + (0. ZS) is Element of the carrier of ZS
the addF of ZS . (v,(0. ZS)) is Element of the carrier of ZS
[v,(0. ZS)] is set
{v,(0. ZS)} is set
{v} is non empty trivial V42(1) set
{{v,(0. ZS)},{v}} is set
the addF of ZS . [v,(0. ZS)] is set
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
i + (0. AG) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (i,(0. AG)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,(0. AG)] is set
{i,(0. AG)} is set
{i} is non empty trivial V42(1) set
{{i,(0. AG)},{i}} is set
the addF of AG . [i,(0. AG)] is set
v is Element of the carrier of ZS
i is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
0. AG is V51(AG) left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
i + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (i,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the addF of AG . [i,v1] is set
a1 is Element of the carrier of ZS
v + a1 is Element of the carrier of ZS
the addF of ZS . (v,a1) is Element of the carrier of ZS
[v,a1] is set
{v,a1} is set
{v} is non empty trivial V42(1) set
{{v,a1},{v}} is set
the addF of ZS . [v,a1] is set
v is V31() ext-real V79() integer set
i is V31() ext-real V79() integer set
v + i is V31() ext-real V79() integer set
v1 is Element of the carrier of ZS
(ZS,v1,(v + i)) is Element of the carrier of ZS
the of ZS . ((v + i),v1) is set
[(v + i),v1] is set
{(v + i),v1} is set
{(v + i)} is non empty trivial V42(1) set
{{(v + i),v1},{(v + i)}} is set
the of ZS . [(v + i),v1] is set
(ZS,v1,v) is Element of the carrier of ZS
the of ZS . (v,v1) is set
[v,v1] is set
{v,v1} is set
{v} is non empty trivial V42(1) set
{{v,v1},{v}} is set
the of ZS . [v,v1] is set
(ZS,v1,i) is Element of the carrier of ZS
the of ZS . (i,v1) is set
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the of ZS . [i,v1] is set
(ZS,v1,v) + (ZS,v1,i) is Element of the carrier of ZS
the addF of ZS . ((ZS,v1,v),(ZS,v1,i)) is Element of the carrier of ZS
[(ZS,v1,v),(ZS,v1,i)] is set
{(ZS,v1,v),(ZS,v1,i)} is set
{(ZS,v1,v)} is non empty trivial V42(1) set
{{(ZS,v1,v),(ZS,v1,i)},{(ZS,v1,v)}} is set
the addF of ZS . [(ZS,v1,v),(ZS,v1,i)] is set
a1 is V31() ext-real V79() integer Element of INT
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG) . (a1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,v1] is set
{a1,v1} is set
{a1} is non empty trivial V42(1) set
{{a1,v1},{a1}} is set
(AG) . [a1,v1] is set
b1 is V31() ext-real V79() integer Element of INT
(AG) . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
(AG) . [b1,v1] is set
((AG) . (a1,v1)) + ((AG) . (b1,v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (a1,v1)),((AG) . (b1,v1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (a1,v1)),((AG) . (b1,v1))] is set
{((AG) . (a1,v1)),((AG) . (b1,v1))} is set
{((AG) . (a1,v1))} is non empty trivial V42(1) set
{{((AG) . (a1,v1)),((AG) . (b1,v1))},{((AG) . (a1,v1))}} is set
the addF of AG . [((AG) . (a1,v1)),((AG) . (b1,v1))] is set
v is V31() ext-real V79() integer set
i is Element of the carrier of ZS
v1 is Element of the carrier of ZS
i + v1 is Element of the carrier of ZS
the addF of ZS . (i,v1) is Element of the carrier of ZS
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the addF of ZS . [i,v1] is set
(ZS,(i + v1),v) is Element of the carrier of ZS
the of ZS . (v,(i + v1)) is set
[v,(i + v1)] is set
{v,(i + v1)} is set
{v} is non empty trivial V42(1) set
{{v,(i + v1)},{v}} is set
the of ZS . [v,(i + v1)] is set
(ZS,i,v) is Element of the carrier of ZS
the of ZS . (v,i) is set
[v,i] is set
{v,i} is set
{{v,i},{v}} is set
the of ZS . [v,i] is set
(ZS,v1,v) is Element of the carrier of ZS
the of ZS . (v,v1) is set
[v,v1] is set
{v,v1} is set
{{v,v1},{v}} is set
the of ZS . [v,v1] is set
(ZS,i,v) + (ZS,v1,v) is Element of the carrier of ZS
the addF of ZS . ((ZS,i,v),(ZS,v1,v)) is Element of the carrier of ZS
[(ZS,i,v),(ZS,v1,v)] is set
{(ZS,i,v),(ZS,v1,v)} is set
{(ZS,i,v)} is non empty trivial V42(1) set
{{(ZS,i,v),(ZS,v1,v)},{(ZS,i,v)}} is set
the addF of ZS . [(ZS,i,v),(ZS,v1,v)] is set
a1 is V31() ext-real V79() integer Element of INT
b1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
b1 + v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
the addF of AG . [b1,v1] is set
(AG) . (a1,(b1 + v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,(b1 + v1)] is set
{a1,(b1 + v1)} is set
{a1} is non empty trivial V42(1) set
{{a1,(b1 + v1)},{a1}} is set
(AG) . [a1,(b1 + v1)] is set
(AG) . (a1,b1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,b1] is set
{a1,b1} is set
{{a1,b1},{a1}} is set
(AG) . [a1,b1] is set
(AG) . (a1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,v1] is set
{a1,v1} is set
{{a1,v1},{a1}} is set
(AG) . [a1,v1] is set
((AG) . (a1,b1)) + ((AG) . (a1,v1)) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
the addF of AG . (((AG) . (a1,b1)),((AG) . (a1,v1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[((AG) . (a1,b1)),((AG) . (a1,v1))] is set
{((AG) . (a1,b1)),((AG) . (a1,v1))} is set
{((AG) . (a1,b1))} is non empty trivial V42(1) set
{{((AG) . (a1,b1)),((AG) . (a1,v1))},{((AG) . (a1,b1))}} is set
the addF of AG . [((AG) . (a1,b1)),((AG) . (a1,v1))] is set
v is V31() ext-real V79() integer set
i is V31() ext-real V79() integer set
v * i is V31() ext-real V79() integer set
v1 is Element of the carrier of ZS
(ZS,v1,(v * i)) is Element of the carrier of ZS
the of ZS . ((v * i),v1) is set
[(v * i),v1] is set
{(v * i),v1} is set
{(v * i)} is non empty trivial V42(1) set
{{(v * i),v1},{(v * i)}} is set
the of ZS . [(v * i),v1] is set
(ZS,v1,i) is Element of the carrier of ZS
the of ZS . (i,v1) is set
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
the of ZS . [i,v1] is set
(ZS,(ZS,v1,i),v) is Element of the carrier of ZS
the of ZS . (v,(ZS,v1,i)) is set
[v,(ZS,v1,i)] is set
{v,(ZS,v1,i)} is set
{v} is non empty trivial V42(1) set
{{v,(ZS,v1,i)},{v}} is set
the of ZS . [v,(ZS,v1,i)] is set
a1 is V31() ext-real V79() integer Element of INT
b1 is V31() ext-real V79() integer Element of INT
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG) . (b1,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[b1,v1] is set
{b1,v1} is set
{b1} is non empty trivial V42(1) set
{{b1,v1},{b1}} is set
(AG) . [b1,v1] is set
(AG) . (a1,((AG) . (b1,v1))) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[a1,((AG) . (b1,v1))] is set
{a1,((AG) . (b1,v1))} is set
{a1} is non empty trivial V42(1) set
{{a1,((AG) . (b1,v1))},{a1}} is set
(AG) . [a1,((AG) . (b1,v1))] is set
v is Element of the carrier of ZS
(ZS,v,1) is Element of the carrier of ZS
the of ZS . (1,v) is set
[1,v] is set
{1,v} is set
{1} is non empty trivial V42(1) set
{{1,v},{1}} is set
the of ZS . [1,v] is set
i is V31() ext-real V79() integer Element of INT
v1 is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
(AG) . (i,v1) is left_add-cancelable right_add-cancelable add-cancelable right_complementable Element of the carrier of AG
[i,v1] is set
{i,v1} is set
{i} is non empty trivial V42(1) set
{{i,v1},{i}} is set
(AG) . [i,v1] is set