REAL is non empty V50() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V50() cardinal limit_cardinal Element of bool REAL
bool REAL is non empty V50() set
COMPLEX is non empty V50() set
omega is non empty epsilon-transitive epsilon-connected ordinal V50() cardinal limit_cardinal set
bool omega is non empty V50() set
bool NAT is non empty V50() set
[:NAT,REAL:] is non empty V50() set
bool [:NAT,REAL:] is non empty V50() set
{} is set
the functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered set is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered set
1 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative V50() cardinal Element of NAT
{{},1} is set
[:1,1:] is non empty set
bool [:1,1:] is non empty set
[:[:1,1:],1:] is non empty set
bool [:[:1,1:],1:] is non empty set
2 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative V50() cardinal Element of NAT
3 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative V50() cardinal Element of NAT
0 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
1r is complex Element of COMPLEX
|.1r.| is complex real ext-real Element of REAL
{{}} is non empty trivial 1 -element 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 non empty set
[:[: the non empty set , the non empty set :], the non empty set :] is non empty set
bool [:[: the non empty set , the non empty set :], the non empty set :] is non empty set
the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued 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 [: the non empty set , the non empty set :] -defined the non empty set -valued 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 :]
[:COMPLEX, the non empty set :] is non empty V50() set
[:[:COMPLEX, the non empty set :], the non empty set :] is non empty V50() set
bool [:[:COMPLEX, the non empty set :], the non empty set :] is non empty V50() set
the Relation-like [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :] is Relation-like [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :]
( the non empty set , the Element of the non empty set , the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued 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 [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, 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 [: the non empty set , the non empty set :] -defined the non empty set -valued 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 [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :]) is set
V is non empty ()
the carrier of V is non empty set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
X is complex set
niltonil is Element of the carrier of V
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is complex Element of COMPLEX
[z,niltonil] is Element of [:COMPLEX, the carrier of V:]
{z,niltonil} is set
{z} is non empty trivial 1 -element set
{{z,niltonil},{z}} is set
the of V . [z,niltonil] is Element of the carrier of V
V is non empty set
[:V,V:] is non empty set
[:[:V,V:],V:] is non empty set
bool [:[:V,V:],V:] is non empty set
[:COMPLEX,V:] is non empty V50() set
[:[:COMPLEX,V:],V:] is non empty V50() set
bool [:[:COMPLEX,V:],V:] is non empty V50() set
niltonil is Element of V
X is Relation-like [:V,V:] -defined V -valued Function-like V18([:V,V:],V) Element of bool [:[:V,V:],V:]
z is Relation-like [:COMPLEX,V:] -defined V -valued Function-like V18([:COMPLEX,V:],V) Element of bool [:[:COMPLEX,V:],V:]
(V,niltonil,X,z) is () ()
op0 is epsilon-transitive epsilon-connected ordinal Element of 1
op2 is Relation-like [:1,1:] -defined 1 -valued Function-like V18([:1,1:],1) Element of bool [:[:1,1:],1:]
pr2 (COMPLEX,1) is Relation-like [:COMPLEX,1:] -defined 1 -valued Function-like V18([:COMPLEX,1:],1) Element of bool [:[:COMPLEX,1:],1:]
[:COMPLEX,1:] is non empty V50() set
[:[:COMPLEX,1:],1:] is non empty V50() set
bool [:[:COMPLEX,1:],1:] is non empty V50() set
(1,op0,op2,(pr2 (COMPLEX,1))) is non empty () ()
() is () ()
the carrier of () is set
{0} is non empty trivial 1 -element Element of bool NAT
V is non empty trivial V68() 1 -element () ()
the carrier of V is non empty trivial V50() 1 -element set
niltonil is Element of the carrier of V
X is Element of the carrier of V
niltonil + X is Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,X) is Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
X + niltonil is Element of the carrier of V
the addF of V . (X,niltonil) is Element of the carrier of V
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the addF of V . [X,niltonil] is set
the carrier of V is non empty trivial V50() 1 -element set
niltonil is Element of the carrier of V
X is Element of the carrier of V
niltonil + X is Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,X) is Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
z is Element of the carrier of V
(niltonil + X) + z is Element of the carrier of V
the addF of V . ((niltonil + X),z) is Element of the carrier of V
[(niltonil + X),z] is set
{(niltonil + X),z} is set
{(niltonil + X)} is non empty trivial 1 -element set
{{(niltonil + X),z},{(niltonil + X)}} is set
the addF of V . [(niltonil + X),z] is set
X + z is Element of the carrier of V
the addF of V . (X,z) is Element of the carrier of V
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the addF of V . [X,z] is set
niltonil + (X + z) is Element of the carrier of V
the addF of V . (niltonil,(X + z)) is Element of the carrier of V
[niltonil,(X + z)] is set
{niltonil,(X + z)} is set
{{niltonil,(X + z)},{niltonil}} is set
the addF of V . [niltonil,(X + z)] is set
the carrier of V is non empty trivial V50() 1 -element set
niltonil is Element of the carrier of V
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
niltonil + (0. V) is Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(0. V)) is Element of the carrier of V
[niltonil,(0. V)] is set
{niltonil,(0. V)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(0. V)},{niltonil}} is set
the addF of V . [niltonil,(0. V)] is set
the carrier of V is non empty trivial V50() 1 -element set
niltonil is Element of the carrier of V
niltonil + niltonil is Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,niltonil) is Element of the carrier of V
[niltonil,niltonil] is set
{niltonil,niltonil} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,niltonil},{niltonil}} is set
the addF of V . [niltonil,niltonil] is set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
the carrier of V is non empty trivial V50() 1 -element set
X is Element of the carrier of V
z is Element of the carrier of V
X + z is Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,z) is Element of the carrier of V
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the addF of V . [X,z] is set
niltonil is complex set
(V,(X + z),niltonil) is Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[niltonil,(X + z)] is set
{niltonil,(X + z)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(X + z)},{niltonil}} is set
the of V . [niltonil,(X + z)] is set
(V,X,niltonil) is Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{{niltonil,X},{niltonil}} is set
the of V . [niltonil,X] is set
(V,z,niltonil) is Element of the carrier of V
[niltonil,z] is set
{niltonil,z} is set
{{niltonil,z},{niltonil}} is set
the of V . [niltonil,z] is set
(V,X,niltonil) + (V,z,niltonil) is Element of the carrier of V
the addF of V . ((V,X,niltonil),(V,z,niltonil)) is Element of the carrier of V
[(V,X,niltonil),(V,z,niltonil)] is set
{(V,X,niltonil),(V,z,niltonil)} is set
{(V,X,niltonil)} is non empty trivial 1 -element set
{{(V,X,niltonil),(V,z,niltonil)},{(V,X,niltonil)}} is set
the addF of V . [(V,X,niltonil),(V,z,niltonil)] is set
z is Element of the carrier of V
niltonil is complex set
X is complex set
niltonil + X is complex set
(V,z,(niltonil + X)) is Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(niltonil + X),z] is set
{(niltonil + X),z} is set
{(niltonil + X)} is non empty trivial 1 -element set
{{(niltonil + X),z},{(niltonil + X)}} is set
the of V . [(niltonil + X),z] is set
(V,z,niltonil) is Element of the carrier of V
[niltonil,z] is set
{niltonil,z} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,z},{niltonil}} is set
the of V . [niltonil,z] is set
(V,z,X) is Element of the carrier of V
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the of V . [X,z] is set
(V,z,niltonil) + (V,z,X) is Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,z,niltonil),(V,z,X)) is Element of the carrier of V
[(V,z,niltonil),(V,z,X)] is set
{(V,z,niltonil),(V,z,X)} is set
{(V,z,niltonil)} is non empty trivial 1 -element set
{{(V,z,niltonil),(V,z,X)},{(V,z,niltonil)}} is set
the addF of V . [(V,z,niltonil),(V,z,X)] is set
z is Element of the carrier of V
niltonil is complex set
X is complex set
niltonil * X is complex set
(V,z,(niltonil * X)) is Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(niltonil * X),z] is set
{(niltonil * X),z} is set
{(niltonil * X)} is non empty trivial 1 -element set
{{(niltonil * X),z},{(niltonil * X)}} is set
the of V . [(niltonil * X),z] is set
(V,z,X) is Element of the carrier of V
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the of V . [X,z] is set
(V,(V,z,X),niltonil) is Element of the carrier of V
[niltonil,(V,z,X)] is set
{niltonil,(V,z,X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(V,z,X)},{niltonil}} is set
the of V . [niltonil,(V,z,X)] is set
niltonil is Element of the carrier of V
(V,niltonil,1r) is Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
0c is complex Element of COMPLEX
(V,niltonil,0c) is right_complementable Element of the carrier of V
[0c,niltonil] is set
{0c,niltonil} is set
{0c} is non empty trivial 1 -element set
{{0c,niltonil},{0c}} is set
the of V . [0c,niltonil] is set
niltonil + (V,niltonil,0c) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(V,niltonil,0c)) is right_complementable Element of the carrier of V
[niltonil,(V,niltonil,0c)] is set
{niltonil,(V,niltonil,0c)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(V,niltonil,0c)},{niltonil}} is set
the addF of V . [niltonil,(V,niltonil,0c)] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,1r) + (V,niltonil,0c) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),(V,niltonil,0c)) is right_complementable Element of the carrier of V
[(V,niltonil,1r),(V,niltonil,0c)] is set
{(V,niltonil,1r),(V,niltonil,0c)} is set
{(V,niltonil,1r)} is non empty trivial 1 -element set
{{(V,niltonil,1r),(V,niltonil,0c)},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),(V,niltonil,0c)] is set
1r + 0c is complex Element of COMPLEX
(V,niltonil,(1r + 0c)) is right_complementable Element of the carrier of V
[(1r + 0c),niltonil] is set
{(1r + 0c),niltonil} is set
{(1r + 0c)} is non empty trivial 1 -element set
{{(1r + 0c),niltonil},{(1r + 0c)}} is set
the of V . [(1r + 0c),niltonil] is set
niltonil + (0. V) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(0. V)) is right_complementable Element of the carrier of V
[niltonil,(0. V)] is set
{niltonil,(0. V)} is set
{{niltonil,(0. V)},{niltonil}} is set
the addF of V . [niltonil,(0. V)] is set
(V,(0. V),X) is right_complementable Element of the carrier of V
[X,(0. V)] is set
{X,(0. V)} is set
{{X,(0. V)},{X}} is set
the of V . [X,(0. V)] is set
(V,(0. V),X) + (V,(0. V),X) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,(0. V),X),(V,(0. V),X)) is right_complementable Element of the carrier of V
[(V,(0. V),X),(V,(0. V),X)] is set
{(V,(0. V),X),(V,(0. V),X)} is set
{(V,(0. V),X)} is non empty trivial 1 -element set
{{(V,(0. V),X),(V,(0. V),X)},{(V,(0. V),X)}} is set
the addF of V . [(V,(0. V),X),(V,(0. V),X)] is set
(0. V) + (0. V) is right_complementable Element of the carrier of V
the addF of V . ((0. V),(0. V)) is right_complementable Element of the carrier of V
[(0. V),(0. V)] is set
{(0. V),(0. V)} is set
{(0. V)} is non empty trivial 1 -element set
{{(0. V),(0. V)},{(0. V)}} is set
the addF of V . [(0. V),(0. V)] is set
(V,((0. V) + (0. V)),X) is right_complementable Element of the carrier of V
[X,((0. V) + (0. V))] is set
{X,((0. V) + (0. V))} is set
{{X,((0. V) + (0. V))},{X}} is set
the of V . [X,((0. V) + (0. V))] is set
(V,(0. V),X) + (0. V) is right_complementable Element of the carrier of V
the addF of V . ((V,(0. V),X),(0. V)) is right_complementable Element of the carrier of V
[(V,(0. V),X),(0. V)] is set
{(V,(0. V),X),(0. V)} is set
{{(V,(0. V),X),(0. V)},{(V,(0. V),X)}} is set
the addF of V . [(V,(0. V),X),(0. V)] is set
0c is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
X " is complex set
(X ") * X is complex set
(V,niltonil,((X ") * X)) is right_complementable Element of the carrier of V
[((X ") * X),niltonil] is set
{((X ") * X),niltonil} is set
{((X ") * X)} is non empty trivial 1 -element set
{{((X ") * X),niltonil},{((X ") * X)}} is set
the of V . [((X ") * X),niltonil] is set
(V,(0. V),(X ")) is right_complementable Element of the carrier of V
[(X "),(0. V)] is set
{(X "),(0. V)} is set
{(X ")} is non empty trivial 1 -element set
{{(X "),(0. V)},{(X ")}} is set
the of V . [(X "),(0. V)] is set
- 1r is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
(V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- 1r),niltonil] is set
{(- 1r),niltonil} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),niltonil},{(- 1r)}} is set
the of V . [(- 1r),niltonil] is set
niltonil + (V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(V,niltonil,(- 1r))) is right_complementable Element of the carrier of V
[niltonil,(V,niltonil,(- 1r))] is set
{niltonil,(V,niltonil,(- 1r))} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(V,niltonil,(- 1r))},{niltonil}} is set
the addF of V . [niltonil,(V,niltonil,(- 1r))] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,1r) + (V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),(V,niltonil,(- 1r))) is right_complementable Element of the carrier of V
[(V,niltonil,1r),(V,niltonil,(- 1r))] is set
{(V,niltonil,1r),(V,niltonil,(- 1r))} is set
{(V,niltonil,1r)} is non empty trivial 1 -element set
{{(V,niltonil,1r),(V,niltonil,(- 1r))},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),(V,niltonil,(- 1r))] is set
1r + (- 1r) is complex Element of COMPLEX
(V,niltonil,(1r + (- 1r))) is right_complementable Element of the carrier of V
[(1r + (- 1r)),niltonil] is set
{(1r + (- 1r)),niltonil} is set
{(1r + (- 1r))} is non empty trivial 1 -element set
{{(1r + (- 1r)),niltonil},{(1r + (- 1r))}} is set
the of V . [(1r + (- 1r)),niltonil] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(- niltonil) + (niltonil + (V,niltonil,(- 1r))) is right_complementable Element of the carrier of V
the addF of V . ((- niltonil),(niltonil + (V,niltonil,(- 1r)))) is right_complementable Element of the carrier of V
[(- niltonil),(niltonil + (V,niltonil,(- 1r)))] is set
{(- niltonil),(niltonil + (V,niltonil,(- 1r)))} is set
{(- niltonil)} is non empty trivial 1 -element set
{{(- niltonil),(niltonil + (V,niltonil,(- 1r)))},{(- niltonil)}} is set
the addF of V . [(- niltonil),(niltonil + (V,niltonil,(- 1r)))] is set
(- niltonil) + niltonil is right_complementable Element of the carrier of V
the addF of V . ((- niltonil),niltonil) is right_complementable Element of the carrier of V
[(- niltonil),niltonil] is set
{(- niltonil),niltonil} is set
{{(- niltonil),niltonil},{(- niltonil)}} is set
the addF of V . [(- niltonil),niltonil] is set
((- niltonil) + niltonil) + (V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the addF of V . (((- niltonil) + niltonil),(V,niltonil,(- 1r))) is right_complementable Element of the carrier of V
[((- niltonil) + niltonil),(V,niltonil,(- 1r))] is set
{((- niltonil) + niltonil),(V,niltonil,(- 1r))} is set
{((- niltonil) + niltonil)} is non empty trivial 1 -element set
{{((- niltonil) + niltonil),(V,niltonil,(- 1r))},{((- niltonil) + niltonil)}} is set
the addF of V . [((- niltonil) + niltonil),(V,niltonil,(- 1r))] is set
(0. V) + (V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the addF of V . ((0. V),(V,niltonil,(- 1r))) is right_complementable Element of the carrier of V
[(0. V),(V,niltonil,(- 1r))] is set
{(0. V),(V,niltonil,(- 1r))} is set
{(0. V)} is non empty trivial 1 -element set
{{(0. V),(V,niltonil,(- 1r))},{(0. V)}} is set
the addF of V . [(0. V),(V,niltonil,(- 1r))] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
niltonil - (- niltonil) is right_complementable Element of the carrier of V
- (- niltonil) is right_complementable Element of the carrier of V
niltonil + (- (- niltonil)) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- (- niltonil))) is right_complementable Element of the carrier of V
[niltonil,(- (- niltonil))] is set
{niltonil,(- (- niltonil))} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- (- niltonil))},{niltonil}} is set
the addF of V . [niltonil,(- (- niltonil))] is set
niltonil + niltonil is right_complementable Element of the carrier of V
the addF of V . (niltonil,niltonil) is right_complementable Element of the carrier of V
[niltonil,niltonil] is set
{niltonil,niltonil} is set
{{niltonil,niltonil},{niltonil}} is set
the addF of V . [niltonil,niltonil] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,1r) + niltonil is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),niltonil) is right_complementable Element of the carrier of V
[(V,niltonil,1r),niltonil] is set
{(V,niltonil,1r),niltonil} is set
{(V,niltonil,1r)} is non empty trivial 1 -element set
{{(V,niltonil,1r),niltonil},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),niltonil] is set
(V,niltonil,1r) + (V,niltonil,1r) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),(V,niltonil,1r)) is right_complementable Element of the carrier of V
[(V,niltonil,1r),(V,niltonil,1r)] is set
{(V,niltonil,1r),(V,niltonil,1r)} is set
{{(V,niltonil,1r),(V,niltonil,1r)},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),(V,niltonil,1r)] is set
1r + 1r is complex Element of COMPLEX
(V,niltonil,(1r + 1r)) is right_complementable Element of the carrier of V
[(1r + 1r),niltonil] is set
{(1r + 1r),niltonil} is set
{(1r + 1r)} is non empty trivial 1 -element set
{{(1r + 1r),niltonil},{(1r + 1r)}} is set
the of V . [(1r + 1r),niltonil] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is right_complementable Element of the carrier of V
niltonil + niltonil is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,niltonil) is right_complementable Element of the carrier of V
[niltonil,niltonil] is set
{niltonil,niltonil} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,niltonil},{niltonil}} is set
the addF of V . [niltonil,niltonil] is set
- niltonil is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is complex set
(V,(- niltonil),X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,(- niltonil)] is set
{X,(- niltonil)} is set
{X} is non empty trivial 1 -element set
{{X,(- niltonil)},{X}} is set
the of V . [X,(- niltonil)] is set
- X is complex set
(V,niltonil,(- X)) is right_complementable Element of the carrier of V
[(- X),niltonil] is set
{(- X),niltonil} is set
{(- X)} is non empty trivial 1 -element set
{{(- X),niltonil},{(- X)}} is set
the of V . [(- X),niltonil] is set
(V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
[(- 1r),niltonil] is set
{(- 1r),niltonil} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),niltonil},{(- 1r)}} is set
the of V . [(- 1r),niltonil] is set
(V,(V,niltonil,(- 1r)),X) is right_complementable Element of the carrier of V
[X,(V,niltonil,(- 1r))] is set
{X,(V,niltonil,(- 1r))} is set
{{X,(V,niltonil,(- 1r))},{X}} is set
the of V . [X,(V,niltonil,(- 1r))] is set
X * (- 1r) is complex set
(V,niltonil,(X * (- 1r))) is right_complementable Element of the carrier of V
[(X * (- 1r)),niltonil] is set
{(X * (- 1r)),niltonil} is set
{(X * (- 1r))} is non empty trivial 1 -element set
{{(X * (- 1r)),niltonil},{(X * (- 1r))}} is set
the of V . [(X * (- 1r)),niltonil] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is complex set
(V,(- niltonil),X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,(- niltonil)] is set
{X,(- niltonil)} is set
{X} is non empty trivial 1 -element set
{{X,(- niltonil)},{X}} is set
the of V . [X,(- niltonil)] is set
(V,niltonil,X) is right_complementable Element of the carrier of V
[X,niltonil] is set
{X,niltonil} is set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
- (V,niltonil,X) is right_complementable Element of the carrier of V
1r * X is complex set
- (1r * X) is complex set
(V,niltonil,(- (1r * X))) is right_complementable Element of the carrier of V
[(- (1r * X)),niltonil] is set
{(- (1r * X)),niltonil} is set
{(- (1r * X))} is non empty trivial 1 -element set
{{(- (1r * X)),niltonil},{(- (1r * X))}} is set
the of V . [(- (1r * X)),niltonil] is set
(- 1r) * X is complex set
(V,niltonil,((- 1r) * X)) is right_complementable Element of the carrier of V
[((- 1r) * X),niltonil] is set
{((- 1r) * X),niltonil} is set
{((- 1r) * X)} is non empty trivial 1 -element set
{{((- 1r) * X),niltonil},{((- 1r) * X)}} is set
the of V . [((- 1r) * X),niltonil] is set
(V,(V,niltonil,X),(- 1r)) is right_complementable Element of the carrier of V
[(- 1r),(V,niltonil,X)] is set
{(- 1r),(V,niltonil,X)} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),(V,niltonil,X)},{(- 1r)}} is set
the of V . [(- 1r),(V,niltonil,X)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is complex set
- X is complex set
(V,(- niltonil),(- X)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- X),(- niltonil)] is set
{(- X),(- niltonil)} is set
{(- X)} is non empty trivial 1 -element set
{{(- X),(- niltonil)},{(- X)}} is set
the of V . [(- X),(- niltonil)] is set
(V,niltonil,X) is right_complementable Element of the carrier of V
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
- (- X) is complex set
(V,niltonil,(- (- X))) is right_complementable Element of the carrier of V
[(- (- X)),niltonil] is set
{(- (- X)),niltonil} is set
{(- (- X))} is non empty trivial 1 -element set
{{(- (- X)),niltonil},{(- (- X))}} is set
the of V . [(- (- X)),niltonil] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
z is complex set
(V,(niltonil - X),z) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[z,(niltonil - X)] is set
{z,(niltonil - X)} is set
{z} is non empty trivial 1 -element set
{{z,(niltonil - X)},{z}} is set
the of V . [z,(niltonil - X)] is set
(V,niltonil,z) is right_complementable Element of the carrier of V
[z,niltonil] is set
{z,niltonil} is set
{{z,niltonil},{z}} is set
the of V . [z,niltonil] is set
(V,X,z) is right_complementable Element of the carrier of V
[z,X] is set
{z,X} is set
{{z,X},{z}} is set
the of V . [z,X] is set
(V,niltonil,z) - (V,X,z) is right_complementable Element of the carrier of V
- (V,X,z) is right_complementable Element of the carrier of V
(V,niltonil,z) + (- (V,X,z)) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,z),(- (V,X,z))) is right_complementable Element of the carrier of V
[(V,niltonil,z),(- (V,X,z))] is set
{(V,niltonil,z),(- (V,X,z))} is set
{(V,niltonil,z)} is non empty trivial 1 -element set
{{(V,niltonil,z),(- (V,X,z))},{(V,niltonil,z)}} is set
the addF of V . [(V,niltonil,z),(- (V,X,z))] is set
(V,(- X),z) is right_complementable Element of the carrier of V
[z,(- X)] is set
{z,(- X)} is set
{{z,(- X)},{z}} is set
the of V . [z,(- X)] is set
(V,niltonil,z) + (V,(- X),z) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,z),(V,(- X),z)) is right_complementable Element of the carrier of V
[(V,niltonil,z),(V,(- X),z)] is set
{(V,niltonil,z),(V,(- X),z)} is set
{{(V,niltonil,z),(V,(- X),z)},{(V,niltonil,z)}} is set
the addF of V . [(V,niltonil,z),(V,(- X),z)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is complex set
X - z is complex set
(V,niltonil,(X - z)) is right_complementable Element of the carrier of V
[(X - z),niltonil] is set
{(X - z),niltonil} is set
{(X - z)} is non empty trivial 1 -element set
{{(X - z),niltonil},{(X - z)}} is set
the of V . [(X - z),niltonil] is set
(V,niltonil,z) is right_complementable Element of the carrier of V
[z,niltonil] is set
{z,niltonil} is set
{z} is non empty trivial 1 -element set
{{z,niltonil},{z}} is set
the of V . [z,niltonil] is set
(V,niltonil,X) - (V,niltonil,z) is right_complementable Element of the carrier of V
- (V,niltonil,z) is right_complementable Element of the carrier of V
(V,niltonil,X) + (- (V,niltonil,z)) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,X),(- (V,niltonil,z))) is right_complementable Element of the carrier of V
[(V,niltonil,X),(- (V,niltonil,z))] is set
{(V,niltonil,X),(- (V,niltonil,z))} is set
{(V,niltonil,X)} is non empty trivial 1 -element set
{{(V,niltonil,X),(- (V,niltonil,z))},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(- (V,niltonil,z))] is set
- z is complex set
X + (- z) is complex set
(V,niltonil,(X + (- z))) is right_complementable Element of the carrier of V
[(X + (- z)),niltonil] is set
{(X + (- z)),niltonil} is set
{(X + (- z))} is non empty trivial 1 -element set
{{(X + (- z)),niltonil},{(X + (- z))}} is set
the of V . [(X + (- z)),niltonil] is set
(V,niltonil,(- z)) is right_complementable Element of the carrier of V
[(- z),niltonil] is set
{(- z),niltonil} is set
{(- z)} is non empty trivial 1 -element set
{{(- z),niltonil},{(- z)}} is set
the of V . [(- z),niltonil] is set
(V,niltonil,X) + (V,niltonil,(- z)) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,X),(V,niltonil,(- z))) is right_complementable Element of the carrier of V
[(V,niltonil,X),(V,niltonil,(- z))] is set
{(V,niltonil,X),(V,niltonil,(- z))} is set
{{(V,niltonil,X),(V,niltonil,(- z))},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(V,niltonil,(- z))] is set
- niltonil is right_complementable Element of the carrier of V
(V,(- niltonil),z) is right_complementable Element of the carrier of V
[z,(- niltonil)] is set
{z,(- niltonil)} is set
{{z,(- niltonil)},{z}} is set
the of V . [z,(- niltonil)] is set
(V,niltonil,X) + (V,(- niltonil),z) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,X),(V,(- niltonil),z)) is right_complementable Element of the carrier of V
[(V,niltonil,X),(V,(- niltonil),z)] is set
{(V,niltonil,X),(V,(- niltonil),z)} is set
{{(V,niltonil,X),(V,(- niltonil),z)},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(V,(- niltonil),z)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is complex set
(V,niltonil,z) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[z,niltonil] is set
{z,niltonil} is set
{z} is non empty trivial 1 -element set
{{z,niltonil},{z}} is set
the of V . [z,niltonil] is set
(V,X,z) is right_complementable Element of the carrier of V
[z,X] is set
{z,X} is set
{{z,X},{z}} is set
the of V . [z,X] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(V,niltonil,z) - (V,X,z) is right_complementable Element of the carrier of V
- (V,X,z) is right_complementable Element of the carrier of V
(V,niltonil,z) + (- (V,X,z)) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,z),(- (V,X,z))) is right_complementable Element of the carrier of V
[(V,niltonil,z),(- (V,X,z))] is set
{(V,niltonil,z),(- (V,X,z))} is set
{(V,niltonil,z)} is non empty trivial 1 -element set
{{(V,niltonil,z),(- (V,X,z))},{(V,niltonil,z)}} is set
the addF of V . [(V,niltonil,z),(- (V,X,z))] is set
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
(V,(niltonil - X),z) is right_complementable Element of the carrier of V
[z,(niltonil - X)] is set
{z,(niltonil - X)} is set
{{z,(niltonil - X)},{z}} is set
the of V . [z,(niltonil - X)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is complex set
(V,niltonil,z) is right_complementable Element of the carrier of V
[z,niltonil] is set
{z,niltonil} is set
{z} is non empty trivial 1 -element set
{{z,niltonil},{z}} is set
the of V . [z,niltonil] is set
(V,niltonil,X) - (V,niltonil,z) is right_complementable Element of the carrier of V
- (V,niltonil,z) is right_complementable Element of the carrier of V
(V,niltonil,X) + (- (V,niltonil,z)) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,X),(- (V,niltonil,z))) is right_complementable Element of the carrier of V
[(V,niltonil,X),(- (V,niltonil,z))] is set
{(V,niltonil,X),(- (V,niltonil,z))} is set
{(V,niltonil,X)} is non empty trivial 1 -element set
{{(V,niltonil,X),(- (V,niltonil,z))},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(- (V,niltonil,z))] is set
X - z is complex set
(V,niltonil,(X - z)) is right_complementable Element of the carrier of V
[(X - z),niltonil] is set
{(X - z),niltonil} is set
{(X - z)} is non empty trivial 1 -element set
{{(X - z),niltonil},{(X - z)}} is set
the of V . [(X - z),niltonil] is set
- z is complex set
(- z) + X is complex set
V is non empty addLoopStr
the carrier of V is non empty set
<*> the carrier of V is Relation-like NAT -defined the carrier of V -valued Function-like functional empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of V
[:NAT, the carrier of V:] is non empty V50() set
Sum (<*> the carrier of V) is Element of the carrier of V
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
bool [:NAT, the carrier of V:] is non empty V50() set
len (<*> the carrier of V) is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered Element of NAT
X is Relation-like NAT -defined the carrier of V -valued Function-like V18( NAT , the carrier of V) Element of bool [:NAT, the carrier of V:]
X . (len (<*> the carrier of V)) is Element of the carrier of V
X . 0 is Element of the carrier of V
V is non empty addLoopStr
the carrier of V is non empty set
0. V is zero Element of the carrier of V
the ZeroF of V is Element of the carrier of V
niltonil is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len niltonil is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
Sum niltonil is Element of the carrier of V
<*> the carrier of V is Relation-like NAT -defined the carrier of V -valued Function-like functional empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of V
[:NAT, the carrier of V:] is non empty V50() set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is complex set
X is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len X is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
z is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len z is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
dom X is Element of bool NAT
Sum X is right_complementable Element of the carrier of V
Sum z is right_complementable Element of the carrier of V
(V,(Sum z),niltonil) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[niltonil,(Sum z)] is set
{niltonil,(Sum z)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(Sum z)},{niltonil}} is set
the of V . [niltonil,(Sum z)] is set
Seg (len X) is V50() len X -element Element of bool NAT
CNS is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len S is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
g is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len g is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
CNS + 1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
Seg (len S) is V50() len S -element Element of bool NAT
Seg CNS is V50() CNS -element Element of bool NAT
S | (Seg CNS) is Relation-like NAT -defined the carrier of V -valued Function-like FinSubsequence-like Element of bool [:NAT, the carrier of V:]
[:NAT, the carrier of V:] is non empty V50() set
bool [:NAT, the carrier of V:] is non empty V50() set
g | (Seg CNS) is Relation-like NAT -defined the carrier of V -valued Function-like FinSubsequence-like Element of bool [:NAT, the carrier of V:]
r is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len r is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
h is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len h is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
Seg (len h) is V50() len h -element Element of bool NAT
dom h is Element of bool NAT
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is right_complementable Element of the carrier of V
r . m1 is set
dom r is Element of bool NAT
g . m1 is set
S . m1 is set
(V,k,niltonil) is right_complementable Element of the carrier of V
[niltonil,k] is set
{niltonil,k} is set
{{niltonil,k},{niltonil}} is set
the of V . [niltonil,k] is set
h . m1 is set
Seg (CNS + 1) is V50() CNS + 1 -element Element of bool NAT
dom S is Element of bool NAT
dom g is Element of bool NAT
S . (CNS + 1) is set
g . (CNS + 1) is set
m1 is right_complementable Element of the carrier of V
k is right_complementable Element of the carrier of V
(V,k,niltonil) is right_complementable Element of the carrier of V
[niltonil,k] is set
{niltonil,k} is set
{{niltonil,k},{niltonil}} is set
the of V . [niltonil,k] is set
Seg (len r) is V50() len r -element Element of bool NAT
Sum S is right_complementable Element of the carrier of V
Sum h is right_complementable Element of the carrier of V
(Sum h) + m1 is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((Sum h),m1) is right_complementable Element of the carrier of V
[(Sum h),m1] is set
{(Sum h),m1} is set
{(Sum h)} is non empty trivial 1 -element set
{{(Sum h),m1},{(Sum h)}} is set
the addF of V . [(Sum h),m1] is set
Sum r is right_complementable Element of the carrier of V
(V,(Sum r),niltonil) is right_complementable Element of the carrier of V
[niltonil,(Sum r)] is set
{niltonil,(Sum r)} is set
{{niltonil,(Sum r)},{niltonil}} is set
the of V . [niltonil,(Sum r)] is set
(V,(Sum r),niltonil) + (V,k,niltonil) is right_complementable Element of the carrier of V
the addF of V . ((V,(Sum r),niltonil),(V,k,niltonil)) is right_complementable Element of the carrier of V
[(V,(Sum r),niltonil),(V,k,niltonil)] is set
{(V,(Sum r),niltonil),(V,k,niltonil)} is set
{(V,(Sum r),niltonil)} is non empty trivial 1 -element set
{{(V,(Sum r),niltonil),(V,k,niltonil)},{(V,(Sum r),niltonil)}} is set
the addF of V . [(V,(Sum r),niltonil),(V,k,niltonil)] is set
(Sum r) + k is right_complementable Element of the carrier of V
the addF of V . ((Sum r),k) is right_complementable Element of the carrier of V
[(Sum r),k] is set
{(Sum r),k} is set
{(Sum r)} is non empty trivial 1 -element set
{{(Sum r),k},{(Sum r)}} is set
the addF of V . [(Sum r),k] is set
(V,((Sum r) + k),niltonil) is right_complementable Element of the carrier of V
[niltonil,((Sum r) + k)] is set
{niltonil,((Sum r) + k)} is set
{{niltonil,((Sum r) + k)},{niltonil}} is set
the of V . [niltonil,((Sum r) + k)] is set
Sum g is right_complementable Element of the carrier of V
(V,(Sum g),niltonil) is right_complementable Element of the carrier of V
[niltonil,(Sum g)] is set
{niltonil,(Sum g)} is set
{{niltonil,(Sum g)},{niltonil}} is set
the of V . [niltonil,(Sum g)] is set
CNS is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len S is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
g is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len g is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
CNS + 1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
Seg (len S) is V50() len S -element Element of bool NAT
Sum S is right_complementable Element of the carrier of V
Sum g is right_complementable Element of the carrier of V
(V,(Sum g),niltonil) is right_complementable Element of the carrier of V
[niltonil,(Sum g)] is set
{niltonil,(Sum g)} is set
{{niltonil,(Sum g)},{niltonil}} is set
the of V . [niltonil,(Sum g)] is set
CNS is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len CNS is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len S is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
Seg (len CNS) is V50() len CNS -element Element of bool NAT
Sum CNS is right_complementable Element of the carrier of V
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
Sum S is right_complementable Element of the carrier of V
(V,(Sum S),niltonil) is right_complementable Element of the carrier of V
[niltonil,(Sum S)] is set
{niltonil,(Sum S)} is set
{{niltonil,(Sum S)},{niltonil}} is set
the of V . [niltonil,(Sum S)] is set
CNS is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len CNS is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S is Relation-like NAT -defined the carrier of V -valued Function-like V50() FinSequence-like FinSubsequence-like FinSequence of the carrier of V
len S is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
Seg (len CNS) is V50() len CNS -element Element of bool NAT
Sum CNS is right_complementable Element of the carrier of V
Sum S is right_complementable Element of the carrier of V
(V,(Sum S),niltonil) is right_complementable Element of the carrier of V
[niltonil,(Sum S)] is set
{niltonil,(Sum S)} is set
{{niltonil,(Sum S)},{niltonil}} is set
the of V . [niltonil,(Sum S)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
<*> the carrier of V is Relation-like NAT -defined the carrier of V -valued Function-like functional empty proper epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-like FinSubsequence-like FinSequence-membered FinSequence of the carrier of V
[:NAT, the carrier of V:] is non empty V50() set
Sum (<*> the carrier of V) is right_complementable Element of the carrier of V
niltonil is complex set
(V,(Sum (<*> the carrier of V)),niltonil) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[niltonil,(Sum (<*> the carrier of V))] is set
{niltonil,(Sum (<*> the carrier of V))} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(Sum (<*> the carrier of V))},{niltonil}} is set
the of V . [niltonil,(Sum (<*> the carrier of V))] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
<*niltonil,X*> is Relation-like NAT -defined the carrier of V -valued Function-like non empty V50() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of V
Sum <*niltonil,X*> is right_complementable Element of the carrier of V
z is complex set
(V,(Sum <*niltonil,X*>),z) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[z,(Sum <*niltonil,X*>)] is set
{z,(Sum <*niltonil,X*>)} is set
{z} is non empty trivial 1 -element set
{{z,(Sum <*niltonil,X*>)},{z}} is set
the of V . [z,(Sum <*niltonil,X*>)] is set
(V,niltonil,z) is right_complementable Element of the carrier of V
[z,niltonil] is set
{z,niltonil} is set
{{z,niltonil},{z}} is set
the of V . [z,niltonil] is set
(V,X,z) is right_complementable Element of the carrier of V
[z,X] is set
{z,X} is set
{{z,X},{z}} is set
the of V . [z,X] is set
(V,niltonil,z) + (V,X,z) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,z),(V,X,z)) is right_complementable Element of the carrier of V
[(V,niltonil,z),(V,X,z)] is set
{(V,niltonil,z),(V,X,z)} is set
{(V,niltonil,z)} is non empty trivial 1 -element set
{{(V,niltonil,z),(V,X,z)},{(V,niltonil,z)}} is set
the addF of V . [(V,niltonil,z),(V,X,z)] is set
niltonil + X is right_complementable Element of the carrier of V
the addF of V . (niltonil,X) is right_complementable Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
(V,(niltonil + X),z) is right_complementable Element of the carrier of V
[z,(niltonil + X)] is set
{z,(niltonil + X)} is set
{{z,(niltonil + X)},{z}} is set
the of V . [z,(niltonil + X)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is right_complementable Element of the carrier of V
<*niltonil,X,z*> is Relation-like NAT -defined the carrier of V -valued Function-like non empty V50() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of V
Sum <*niltonil,X,z*> is right_complementable Element of the carrier of V
CNS is complex set
(V,(Sum <*niltonil,X,z*>),CNS) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[CNS,(Sum <*niltonil,X,z*>)] is set
{CNS,(Sum <*niltonil,X,z*>)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(Sum <*niltonil,X,z*>)},{CNS}} is set
the of V . [CNS,(Sum <*niltonil,X,z*>)] is set
(V,niltonil,CNS) is right_complementable Element of the carrier of V
[CNS,niltonil] is set
{CNS,niltonil} is set
{{CNS,niltonil},{CNS}} is set
the of V . [CNS,niltonil] is set
(V,X,CNS) is right_complementable Element of the carrier of V
[CNS,X] is set
{CNS,X} is set
{{CNS,X},{CNS}} is set
the of V . [CNS,X] is set
(V,niltonil,CNS) + (V,X,CNS) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,CNS),(V,X,CNS)) is right_complementable Element of the carrier of V
[(V,niltonil,CNS),(V,X,CNS)] is set
{(V,niltonil,CNS),(V,X,CNS)} is set
{(V,niltonil,CNS)} is non empty trivial 1 -element set
{{(V,niltonil,CNS),(V,X,CNS)},{(V,niltonil,CNS)}} is set
the addF of V . [(V,niltonil,CNS),(V,X,CNS)] is set
(V,z,CNS) is right_complementable Element of the carrier of V
[CNS,z] is set
{CNS,z} is set
{{CNS,z},{CNS}} is set
the of V . [CNS,z] is set
((V,niltonil,CNS) + (V,X,CNS)) + (V,z,CNS) is right_complementable Element of the carrier of V
the addF of V . (((V,niltonil,CNS) + (V,X,CNS)),(V,z,CNS)) is right_complementable Element of the carrier of V
[((V,niltonil,CNS) + (V,X,CNS)),(V,z,CNS)] is set
{((V,niltonil,CNS) + (V,X,CNS)),(V,z,CNS)} is set
{((V,niltonil,CNS) + (V,X,CNS))} is non empty trivial 1 -element set
{{((V,niltonil,CNS) + (V,X,CNS)),(V,z,CNS)},{((V,niltonil,CNS) + (V,X,CNS))}} is set
the addF of V . [((V,niltonil,CNS) + (V,X,CNS)),(V,z,CNS)] is set
niltonil + X is right_complementable Element of the carrier of V
the addF of V . (niltonil,X) is right_complementable Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
(niltonil + X) + z is right_complementable Element of the carrier of V
the addF of V . ((niltonil + X),z) is right_complementable Element of the carrier of V
[(niltonil + X),z] is set
{(niltonil + X),z} is set
{(niltonil + X)} is non empty trivial 1 -element set
{{(niltonil + X),z},{(niltonil + X)}} is set
the addF of V . [(niltonil + X),z] is set
(V,((niltonil + X) + z),CNS) is right_complementable Element of the carrier of V
[CNS,((niltonil + X) + z)] is set
{CNS,((niltonil + X) + z)} is set
{{CNS,((niltonil + X) + z)},{CNS}} is set
the of V . [CNS,((niltonil + X) + z)] is set
(V,(niltonil + X),CNS) is right_complementable Element of the carrier of V
[CNS,(niltonil + X)] is set
{CNS,(niltonil + X)} is set
{{CNS,(niltonil + X)},{CNS}} is set
the of V . [CNS,(niltonil + X)] is set
(V,(niltonil + X),CNS) + (V,z,CNS) is right_complementable Element of the carrier of V
the addF of V . ((V,(niltonil + X),CNS),(V,z,CNS)) is right_complementable Element of the carrier of V
[(V,(niltonil + X),CNS),(V,z,CNS)] is set
{(V,(niltonil + X),CNS),(V,z,CNS)} is set
{(V,(niltonil + X),CNS)} is non empty trivial 1 -element set
{{(V,(niltonil + X),CNS),(V,z,CNS)},{(V,(niltonil + X),CNS)}} is set
the addF of V . [(V,(niltonil + X),CNS),(V,z,CNS)] is set
1r + 1r is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
<*niltonil,niltonil*> is Relation-like NAT -defined the carrier of V -valued Function-like non empty V50() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of V
Sum <*niltonil,niltonil*> is right_complementable Element of the carrier of V
(V,niltonil,(1r + 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(1r + 1r),niltonil] is set
{(1r + 1r),niltonil} is set
{(1r + 1r)} is non empty trivial 1 -element set
{{(1r + 1r),niltonil},{(1r + 1r)}} is set
the of V . [(1r + 1r),niltonil] is set
niltonil + niltonil is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,niltonil) is right_complementable Element of the carrier of V
[niltonil,niltonil] is set
{niltonil,niltonil} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,niltonil},{niltonil}} is set
the addF of V . [niltonil,niltonil] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,1r) + niltonil is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),niltonil) is right_complementable Element of the carrier of V
[(V,niltonil,1r),niltonil] is set
{(V,niltonil,1r),niltonil} is set
{(V,niltonil,1r)} is non empty trivial 1 -element set
{{(V,niltonil,1r),niltonil},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),niltonil] is set
(V,niltonil,1r) + (V,niltonil,1r) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),(V,niltonil,1r)) is right_complementable Element of the carrier of V
[(V,niltonil,1r),(V,niltonil,1r)] is set
{(V,niltonil,1r),(V,niltonil,1r)} is set
{{(V,niltonil,1r),(V,niltonil,1r)},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),(V,niltonil,1r)] is set
- (1r + 1r) is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
<*(- niltonil),(- niltonil)*> is Relation-like NAT -defined the carrier of V -valued Function-like non empty V50() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of V
Sum <*(- niltonil),(- niltonil)*> is right_complementable Element of the carrier of V
(V,niltonil,(- (1r + 1r))) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- (1r + 1r)),niltonil] is set
{(- (1r + 1r)),niltonil} is set
{(- (1r + 1r))} is non empty trivial 1 -element set
{{(- (1r + 1r)),niltonil},{(- (1r + 1r))}} is set
the of V . [(- (1r + 1r)),niltonil] is set
<i> is complex Element of COMPLEX
0 * <i> is complex set
2 + (0 * <i>) is complex set
niltonil + niltonil is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,niltonil) is right_complementable Element of the carrier of V
[niltonil,niltonil] is set
{niltonil,niltonil} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,niltonil},{niltonil}} is set
the addF of V . [niltonil,niltonil] is set
- (niltonil + niltonil) is right_complementable Element of the carrier of V
<*niltonil,niltonil*> is Relation-like NAT -defined the carrier of V -valued Function-like non empty V50() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of V
Sum <*niltonil,niltonil*> is right_complementable Element of the carrier of V
- (Sum <*niltonil,niltonil*>) is right_complementable Element of the carrier of V
(V,niltonil,(1r + 1r)) is right_complementable Element of the carrier of V
[(1r + 1r),niltonil] is set
{(1r + 1r),niltonil} is set
{(1r + 1r)} is non empty trivial 1 -element set
{{(1r + 1r),niltonil},{(1r + 1r)}} is set
the of V . [(1r + 1r),niltonil] is set
- (V,niltonil,(1r + 1r)) is right_complementable Element of the carrier of V
X is complex Element of COMPLEX
(V,niltonil,X) is right_complementable Element of the carrier of V
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
(V,(V,niltonil,X),(- 1r)) is right_complementable Element of the carrier of V
[(- 1r),(V,niltonil,X)] is set
{(- 1r),(V,niltonil,X)} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),(V,niltonil,X)},{(- 1r)}} is set
the of V . [(- 1r),(V,niltonil,X)] is set
(- 1r) * X is complex Element of COMPLEX
(V,niltonil,((- 1r) * X)) is right_complementable Element of the carrier of V
[((- 1r) * X),niltonil] is set
{((- 1r) * X),niltonil} is set
{((- 1r) * X)} is non empty trivial 1 -element set
{{((- 1r) * X),niltonil},{((- 1r) * X)}} is set
the of V . [((- 1r) * X),niltonil] is set
(1r + 1r) + 1r is complex Element of COMPLEX
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
<*niltonil,niltonil,niltonil*> is Relation-like NAT -defined the carrier of V -valued Function-like non empty V50() 3 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of V
Sum <*niltonil,niltonil,niltonil*> is right_complementable Element of the carrier of V
(V,niltonil,((1r + 1r) + 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[((1r + 1r) + 1r),niltonil] is set
{((1r + 1r) + 1r),niltonil} is set
{((1r + 1r) + 1r)} is non empty trivial 1 -element set
{{((1r + 1r) + 1r),niltonil},{((1r + 1r) + 1r)}} is set
the of V . [((1r + 1r) + 1r),niltonil] is set
<i> is complex Element of COMPLEX
0 * <i> is complex set
2 + (0 * <i>) is complex set
<*niltonil,niltonil*> is Relation-like NAT -defined the carrier of V -valued Function-like non empty V50() 2 -element FinSequence-like FinSubsequence-like FinSequence of the carrier of V
Sum <*niltonil,niltonil*> is right_complementable Element of the carrier of V
(Sum <*niltonil,niltonil*>) + niltonil is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((Sum <*niltonil,niltonil*>),niltonil) is right_complementable Element of the carrier of V
[(Sum <*niltonil,niltonil*>),niltonil] is set
{(Sum <*niltonil,niltonil*>),niltonil} is set
{(Sum <*niltonil,niltonil*>)} is non empty trivial 1 -element set
{{(Sum <*niltonil,niltonil*>),niltonil},{(Sum <*niltonil,niltonil*>)}} is set
the addF of V . [(Sum <*niltonil,niltonil*>),niltonil] is set
(V,niltonil,(1r + 1r)) is right_complementable Element of the carrier of V
[(1r + 1r),niltonil] is set
{(1r + 1r),niltonil} is set
{(1r + 1r)} is non empty trivial 1 -element set
{{(1r + 1r),niltonil},{(1r + 1r)}} is set
the of V . [(1r + 1r),niltonil] is set
(V,niltonil,(1r + 1r)) + niltonil is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,(1r + 1r)),niltonil) is right_complementable Element of the carrier of V
[(V,niltonil,(1r + 1r)),niltonil] is set
{(V,niltonil,(1r + 1r)),niltonil} is set
{(V,niltonil,(1r + 1r))} is non empty trivial 1 -element set
{{(V,niltonil,(1r + 1r)),niltonil},{(V,niltonil,(1r + 1r))}} is set
the addF of V . [(V,niltonil,(1r + 1r)),niltonil] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,(1r + 1r)) + (V,niltonil,1r) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,(1r + 1r)),(V,niltonil,1r)) is right_complementable Element of the carrier of V
[(V,niltonil,(1r + 1r)),(V,niltonil,1r)] is set
{(V,niltonil,(1r + 1r)),(V,niltonil,1r)} is set
{{(V,niltonil,(1r + 1r)),(V,niltonil,1r)},{(V,niltonil,(1r + 1r))}} is set
the addF of V . [(V,niltonil,(1r + 1r)),(V,niltonil,1r)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is Element of bool the carrier of V
the Element of niltonil is Element of niltonil
z is right_complementable Element of the carrier of V
0c is complex Element of COMPLEX
(V,z,0c) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[0c,z] is set
{0c,z} is set
{0c} is non empty trivial 1 -element set
{{0c,z},{0c}} is set
the of V . [0c,z] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is Element of bool the carrier of V
X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
(V,X,(- 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- 1r),X] is set
{(- 1r),X} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),X},{(- 1r)}} is set
the of V . [(- 1r),X] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is Element of bool the carrier of V
X is right_complementable Element of the carrier of V
z is right_complementable Element of the carrier of V
X - z is right_complementable Element of the carrier of V
- z is right_complementable Element of the carrier of V
X + (- z) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,(- z)) is right_complementable Element of the carrier of V
[X,(- z)] is set
{X,(- z)} is set
{X} is non empty trivial 1 -element set
{{X,(- z)},{X}} is set
the addF of V . [X,(- z)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty trivial 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil + X is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,X) is right_complementable Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
niltonil is complex set
X is right_complementable Element of the carrier of V
(V,X,niltonil) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the of V . [niltonil,X] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is Element of bool the carrier of V
X is right_complementable Element of the carrier of V
z is right_complementable Element of the carrier of V
X + z is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,z) is right_complementable Element of the carrier of V
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the addF of V . [X,z] is set
X is complex set
z is right_complementable Element of the carrier of V
(V,z,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the of V . [X,z] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is Element of bool the carrier of V
X is Element of bool the carrier of V
{ (b1 + b2) where b1, b2 is right_complementable Element of the carrier of V : ( b1 in niltonil & b2 in X ) } is set
z is Element of bool the carrier of V
CNS is right_complementable Element of the carrier of V
S is right_complementable Element of the carrier of V
CNS + S is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (CNS,S) is right_complementable Element of the carrier of V
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the addF of V . [CNS,S] is set
g is right_complementable Element of the carrier of V
h is right_complementable Element of the carrier of V
g + h is right_complementable Element of the carrier of V
the addF of V . (g,h) is right_complementable Element of the carrier of V
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
the addF of V . [g,h] is set
r is right_complementable Element of the carrier of V
m1 is right_complementable Element of the carrier of V
r + m1 is right_complementable Element of the carrier of V
the addF of V . (r,m1) is right_complementable Element of the carrier of V
[r,m1] is set
{r,m1} is set
{r} is non empty trivial 1 -element set
{{r,m1},{r}} is set
the addF of V . [r,m1] is set
(g + h) + r is right_complementable Element of the carrier of V
the addF of V . ((g + h),r) is right_complementable Element of the carrier of V
[(g + h),r] is set
{(g + h),r} is set
{(g + h)} is non empty trivial 1 -element set
{{(g + h),r},{(g + h)}} is set
the addF of V . [(g + h),r] is set
((g + h) + r) + m1 is right_complementable Element of the carrier of V
the addF of V . (((g + h) + r),m1) is right_complementable Element of the carrier of V
[((g + h) + r),m1] is set
{((g + h) + r),m1} is set
{((g + h) + r)} is non empty trivial 1 -element set
{{((g + h) + r),m1},{((g + h) + r)}} is set
the addF of V . [((g + h) + r),m1] is set
g + r is right_complementable Element of the carrier of V
the addF of V . (g,r) is right_complementable Element of the carrier of V
[g,r] is set
{g,r} is set
{{g,r},{g}} is set
the addF of V . [g,r] is set
(g + r) + h is right_complementable Element of the carrier of V
the addF of V . ((g + r),h) is right_complementable Element of the carrier of V
[(g + r),h] is set
{(g + r),h} is set
{(g + r)} is non empty trivial 1 -element set
{{(g + r),h},{(g + r)}} is set
the addF of V . [(g + r),h] is set
((g + r) + h) + m1 is right_complementable Element of the carrier of V
the addF of V . (((g + r) + h),m1) is right_complementable Element of the carrier of V
[((g + r) + h),m1] is set
{((g + r) + h),m1} is set
{((g + r) + h)} is non empty trivial 1 -element set
{{((g + r) + h),m1},{((g + r) + h)}} is set
the addF of V . [((g + r) + h),m1] is set
h + m1 is right_complementable Element of the carrier of V
the addF of V . (h,m1) is right_complementable Element of the carrier of V
[h,m1] is set
{h,m1} is set
{h} is non empty trivial 1 -element set
{{h,m1},{h}} is set
the addF of V . [h,m1] is set
(g + r) + (h + m1) is right_complementable Element of the carrier of V
the addF of V . ((g + r),(h + m1)) is right_complementable Element of the carrier of V
[(g + r),(h + m1)] is set
{(g + r),(h + m1)} is set
{{(g + r),(h + m1)},{(g + r)}} is set
the addF of V . [(g + r),(h + m1)] is set
CNS is complex set
S is right_complementable Element of the carrier of V
(V,S,CNS) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the of V . [CNS,S] is set
g is right_complementable Element of the carrier of V
h is right_complementable Element of the carrier of V
g + h is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (g,h) is right_complementable Element of the carrier of V
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
the addF of V . [g,h] is set
(V,g,CNS) is right_complementable Element of the carrier of V
[CNS,g] is set
{CNS,g} is set
{{CNS,g},{CNS}} is set
the of V . [CNS,g] is set
(V,h,CNS) is right_complementable Element of the carrier of V
[CNS,h] is set
{CNS,h} is set
{{CNS,h},{CNS}} is set
the of V . [CNS,h] is set
(V,g,CNS) + (V,h,CNS) is right_complementable Element of the carrier of V
the addF of V . ((V,g,CNS),(V,h,CNS)) is right_complementable Element of the carrier of V
[(V,g,CNS),(V,h,CNS)] is set
{(V,g,CNS),(V,h,CNS)} is set
{(V,g,CNS)} is non empty trivial 1 -element set
{{(V,g,CNS),(V,h,CNS)},{(V,g,CNS)}} is set
the addF of V . [(V,g,CNS),(V,h,CNS)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is Element of bool the carrier of V
X is Element of bool the carrier of V
niltonil /\ X is Element of bool the carrier of V
z is right_complementable Element of the carrier of V
CNS is right_complementable Element of the carrier of V
z + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (z,CNS) is right_complementable Element of the carrier of V
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of V . [z,CNS] is set
z is complex set
CNS is right_complementable Element of the carrier of V
(V,CNS,z) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the of V . [z,CNS] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
[:COMPLEX, the carrier of V:] is non empty V50() set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
the addF of V || the carrier of V is Relation-like Function-like set
the addF of V | [: the carrier of V, the carrier of V:] is Relation-like set
the of V | [:COMPLEX, the carrier of V:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
z is set
the carrier of niltonil is non empty set
the carrier of X is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
X is set
the carrier of niltonil is non empty set
the carrier of V is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of niltonil is non empty set
X is right_complementable Element of the carrier of niltonil
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
0. niltonil is zero right_complementable Element of the carrier of niltonil
the carrier of niltonil is non empty set
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
0. niltonil is zero right_complementable Element of the carrier of niltonil
the carrier of niltonil is non empty set
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
0. X is zero right_complementable Element of the carrier of X
the carrier of X is non empty set
the ZeroF of X is right_complementable Element of the carrier of X
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil + X is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,X) is right_complementable Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
S is right_complementable Element of the carrier of z
CNS + S is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,S) is right_complementable Element of the carrier of z
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the addF of z . [CNS,S] is set
the addF of V || the carrier of z is Relation-like Function-like set
the addF of V | [: the carrier of z, the carrier of z:] is Relation-like set
[CNS,S] is Element of [: the carrier of z, the carrier of z:]
( the addF of V || the carrier of z) . [CNS,S] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
(z,CNS,X) is right_complementable Element of the carrier of z
the of z is Relation-like [:COMPLEX, the carrier of z:] -defined the carrier of z -valued Function-like V18([:COMPLEX, the carrier of z:], the carrier of z) Element of bool [:[:COMPLEX, the carrier of z:], the carrier of z:]
[:COMPLEX, the carrier of z:] is non empty V50() set
[:[:COMPLEX, the carrier of z:], the carrier of z:] is non empty V50() set
bool [:[:COMPLEX, the carrier of z:], the carrier of z:] is non empty V50() set
[X,CNS] is set
{X,CNS} is set
{{X,CNS},{X}} is set
the of z . [X,CNS] is set
S is complex Element of COMPLEX
(z,CNS,S) is right_complementable Element of the carrier of z
[S,CNS] is set
{S,CNS} is set
{S} is non empty trivial 1 -element set
{{S,CNS},{S}} is set
the of z . [S,CNS] is set
the of V | [:COMPLEX, the carrier of z:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[S,CNS] is Element of [:COMPLEX, the carrier of z:]
( the of V | [:COMPLEX, the carrier of z:]) . [S,CNS] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of X is non empty set
z is right_complementable Element of the carrier of X
- z is right_complementable Element of the carrier of X
(V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- 1r),niltonil] is set
{(- 1r),niltonil} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),niltonil},{(- 1r)}} is set
the of V . [(- 1r),niltonil] is set
(X,z,(- 1r)) is right_complementable Element of the carrier of X
the of X is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like V18([:COMPLEX, the carrier of X:], the carrier of X) Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
[:COMPLEX, the carrier of X:] is non empty V50() set
[:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
bool [:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
[(- 1r),z] is set
{(- 1r),z} is set
{{(- 1r),z},{(- 1r)}} is set
the of X . [(- 1r),z] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
S is right_complementable Element of the carrier of z
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is Element of bool the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of X is non empty set
S is right_complementable Element of the carrier of V
g is right_complementable Element of the carrier of V
S + g is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (S,g) is right_complementable Element of the carrier of V
[S,g] is set
{S,g} is set
{S} is non empty trivial 1 -element set
{{S,g},{S}} is set
the addF of V . [S,g] is set
CNS is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of CNS is non empty set
h is right_complementable Element of the carrier of CNS
r is right_complementable Element of the carrier of CNS
h + r is right_complementable Element of the carrier of CNS
the addF of CNS is Relation-like [: the carrier of CNS, the carrier of CNS:] -defined the carrier of CNS -valued Function-like V18([: the carrier of CNS, the carrier of CNS:], the carrier of CNS) Element of bool [:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:]
[: the carrier of CNS, the carrier of CNS:] is non empty set
[:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:] is non empty set
bool [:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:] is non empty set
the addF of CNS . (h,r) is right_complementable Element of the carrier of CNS
[h,r] is set
{h,r} is set
{h} is non empty trivial 1 -element set
{{h,r},{h}} is set
the addF of CNS . [h,r] is set
m1 is right_complementable Element of the carrier of X
S is complex set
g is right_complementable Element of the carrier of V
(V,g,S) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[S,g] is set
{S,g} is set
{S} is non empty trivial 1 -element set
{{S,g},{S}} is set
the of V . [S,g] is set
CNS is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of CNS is non empty set
h is right_complementable Element of the carrier of CNS
(CNS,h,S) is right_complementable Element of the carrier of CNS
the of CNS is Relation-like [:COMPLEX, the carrier of CNS:] -defined the carrier of CNS -valued Function-like V18([:COMPLEX, the carrier of CNS:], the carrier of CNS) Element of bool [:[:COMPLEX, the carrier of CNS:], the carrier of CNS:]
[:COMPLEX, the carrier of CNS:] is non empty V50() set
[:[:COMPLEX, the carrier of CNS:], the carrier of CNS:] is non empty V50() set
bool [:[:COMPLEX, the carrier of CNS:], the carrier of CNS:] is non empty V50() set
[S,h] is set
{S,h} is set
{{S,h},{S}} is set
the of CNS . [S,h] is set
r is right_complementable Element of the carrier of X
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
0. niltonil is zero right_complementable Element of the carrier of niltonil
the carrier of niltonil is non empty set
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
0. niltonil is zero right_complementable Element of the carrier of niltonil
the carrier of niltonil is non empty set
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
0. niltonil is zero right_complementable Element of the carrier of niltonil
the carrier of niltonil is non empty set
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil + X is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,X) is right_complementable Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
bool the carrier of V is non empty set
the carrier of z is non empty set
CNS is Element of bool the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
bool the carrier of V is non empty set
the carrier of z is non empty set
CNS is Element of bool the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- 1r),niltonil] is set
{(- 1r),niltonil} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),niltonil},{(- 1r)}} is set
the of V . [(- 1r),niltonil] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
X is non empty set
[:X,X:] is non empty set
[:[:X,X:],X:] is non empty set
bool [:[:X,X:],X:] is non empty set
[:COMPLEX,X:] is non empty V50() set
[:[:COMPLEX,X:],X:] is non empty V50() set
bool [:[:COMPLEX,X:],X:] is non empty V50() set
z is Element of X
CNS is Relation-like [:X,X:] -defined X -valued Function-like V18([:X,X:],X) Element of bool [:[:X,X:],X:]
S is Relation-like [:COMPLEX,X:] -defined X -valued Function-like V18([:COMPLEX,X:],X) Element of bool [:[:COMPLEX,X:],X:]
(X,z,CNS,S) is non empty () ()
the carrier of (X,z,CNS,S) is non empty set
niltonil is Element of bool the carrier of V
[:COMPLEX, the carrier of V:] is non empty V50() set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[:COMPLEX,niltonil:] is set
the of V | [:COMPLEX,niltonil:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
h is Element of the carrier of (X,z,CNS,S)
r is right_complementable Element of the carrier of V
g is complex set
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
((X,z,CNS,S),h,g) is Element of the carrier of (X,z,CNS,S)
the of (X,z,CNS,S) is Relation-like [:COMPLEX, the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[:COMPLEX, the carrier of (X,z,CNS,S):] is non empty V50() set
[:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
the of (X,z,CNS,S) . [g,h] is set
(V,r,g) is right_complementable Element of the carrier of V
[g,r] is set
{g,r} is set
{{g,r},{g}} is set
the of V . [g,r] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
[:COMPLEX, the carrier of V:] is non empty V50() set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
niltonil is Element of bool the carrier of V
the addF of V || niltonil is Relation-like Function-like set
[:niltonil,niltonil:] is set
the addF of V | [:niltonil,niltonil:] is Relation-like set
[:COMPLEX,niltonil:] is set
the of V | [:COMPLEX,niltonil:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
X is non empty set
[:X,X:] is non empty set
[:[:X,X:],X:] is non empty set
bool [:[:X,X:],X:] is non empty set
[:COMPLEX,X:] is non empty V50() set
[:[:COMPLEX,X:],X:] is non empty V50() set
bool [:[:COMPLEX,X:],X:] is non empty V50() set
z is Element of X
CNS is Relation-like [:X,X:] -defined X -valued Function-like V18([:X,X:],X) Element of bool [:[:X,X:],X:]
S is Relation-like [:COMPLEX,X:] -defined X -valued Function-like V18([:COMPLEX,X:],X) Element of bool [:[:COMPLEX,X:],X:]
(X,z,CNS,S) is non empty () ()
the carrier of (X,z,CNS,S) is non empty set
h is Element of the carrier of (X,z,CNS,S)
r is Element of the carrier of (X,z,CNS,S)
h + r is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) is Relation-like [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] is non empty set
[:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
the addF of (X,z,CNS,S) . (h,r) is Element of the carrier of (X,z,CNS,S)
[h,r] is set
{h,r} is set
{h} is non empty trivial 1 -element set
{{h,r},{h}} is set
the addF of (X,z,CNS,S) . [h,r] is set
[h,r] is Element of [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):]
the addF of V . [h,r] is set
m1 is Element of the carrier of (X,z,CNS,S)
k is Element of the carrier of (X,z,CNS,S)
m1 + k is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) is Relation-like [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] is non empty set
[:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
the addF of (X,z,CNS,S) . (m1,k) is Element of the carrier of (X,z,CNS,S)
[m1,k] is set
{m1,k} is set
{m1} is non empty trivial 1 -element set
{{m1,k},{m1}} is set
the addF of (X,z,CNS,S) . [m1,k] is set
k + m1 is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) . (k,m1) is Element of the carrier of (X,z,CNS,S)
[k,m1] is set
{k,m1} is set
{k} is non empty trivial 1 -element set
{{k,m1},{k}} is set
the addF of (X,z,CNS,S) . [k,m1] is set
n is right_complementable Element of the carrier of V
k is right_complementable Element of the carrier of V
n + k is right_complementable Element of the carrier of V
the addF of V . (n,k) is right_complementable Element of the carrier of V
[n,k] is set
{n,k} is set
{n} is non empty trivial 1 -element set
{{n,k},{n}} is set
the addF of V . [n,k] is set
k + n is right_complementable Element of the carrier of V
the addF of V . (k,n) is right_complementable Element of the carrier of V
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the addF of V . [k,n] is set
m1 is Element of the carrier of (X,z,CNS,S)
k is Element of the carrier of (X,z,CNS,S)
m1 + k is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) is Relation-like [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] is non empty set
[:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
the addF of (X,z,CNS,S) . (m1,k) is Element of the carrier of (X,z,CNS,S)
[m1,k] is set
{m1,k} is set
{m1} is non empty trivial 1 -element set
{{m1,k},{m1}} is set
the addF of (X,z,CNS,S) . [m1,k] is set
n is Element of the carrier of (X,z,CNS,S)
(m1 + k) + n is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) . ((m1 + k),n) is Element of the carrier of (X,z,CNS,S)
[(m1 + k),n] is set
{(m1 + k),n} is set
{(m1 + k)} is non empty trivial 1 -element set
{{(m1 + k),n},{(m1 + k)}} is set
the addF of (X,z,CNS,S) . [(m1 + k),n] is set
k + n is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) . (k,n) is Element of the carrier of (X,z,CNS,S)
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the addF of (X,z,CNS,S) . [k,n] is set
m1 + (k + n) is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) . (m1,(k + n)) is Element of the carrier of (X,z,CNS,S)
[m1,(k + n)] is set
{m1,(k + n)} is set
{{m1,(k + n)},{m1}} is set
the addF of (X,z,CNS,S) . [m1,(k + n)] is set
z1 is right_complementable Element of the carrier of V
[(m1 + k),z1] is Element of [: the carrier of (X,z,CNS,S), the carrier of V:]
[: the carrier of (X,z,CNS,S), the carrier of V:] is non empty set
{(m1 + k),z1} is set
{{(m1 + k),z1},{(m1 + k)}} is set
the addF of V . [(m1 + k),z1] is set
k is right_complementable Element of the carrier of V
n is right_complementable Element of the carrier of V
k + n is right_complementable Element of the carrier of V
the addF of V . (k,n) is right_complementable Element of the carrier of V
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the addF of V . [k,n] is set
(k + n) + z1 is right_complementable Element of the carrier of V
the addF of V . ((k + n),z1) is right_complementable Element of the carrier of V
[(k + n),z1] is set
{(k + n),z1} is set
{(k + n)} is non empty trivial 1 -element set
{{(k + n),z1},{(k + n)}} is set
the addF of V . [(k + n),z1] is set
n + z1 is right_complementable Element of the carrier of V
the addF of V . (n,z1) is right_complementable Element of the carrier of V
[n,z1] is set
{n,z1} is set
{n} is non empty trivial 1 -element set
{{n,z1},{n}} is set
the addF of V . [n,z1] is set
k + (n + z1) is right_complementable Element of the carrier of V
the addF of V . (k,(n + z1)) is right_complementable Element of the carrier of V
[k,(n + z1)] is set
{k,(n + z1)} is set
{{k,(n + z1)},{k}} is set
the addF of V . [k,(n + z1)] is set
[k,(k + n)] is Element of [: the carrier of V, the carrier of (X,z,CNS,S):]
[: the carrier of V, the carrier of (X,z,CNS,S):] is non empty set
{k,(k + n)} is set
{{k,(k + n)},{k}} is set
the addF of V . [k,(k + n)] is set
0. (X,z,CNS,S) is zero Element of the carrier of (X,z,CNS,S)
the ZeroF of (X,z,CNS,S) is Element of the carrier of (X,z,CNS,S)
m1 is Element of the carrier of (X,z,CNS,S)
m1 + (0. (X,z,CNS,S)) is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) is Relation-like [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] is non empty set
[:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
the addF of (X,z,CNS,S) . (m1,(0. (X,z,CNS,S))) is Element of the carrier of (X,z,CNS,S)
[m1,(0. (X,z,CNS,S))] is set
{m1,(0. (X,z,CNS,S))} is set
{m1} is non empty trivial 1 -element set
{{m1,(0. (X,z,CNS,S))},{m1}} is set
the addF of (X,z,CNS,S) . [m1,(0. (X,z,CNS,S))] is set
k is right_complementable Element of the carrier of V
k + (0. V) is right_complementable Element of the carrier of V
the addF of V . (k,(0. V)) is right_complementable Element of the carrier of V
[k,(0. V)] is set
{k,(0. V)} is set
{k} is non empty trivial 1 -element set
{{k,(0. V)},{k}} is set
the addF of V . [k,(0. V)] is set
m1 is Element of the carrier of (X,z,CNS,S)
k is right_complementable Element of the carrier of V
n is right_complementable Element of the carrier of V
k + n is right_complementable Element of the carrier of V
the addF of V . (k,n) is right_complementable Element of the carrier of V
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the addF of V . [k,n] is set
- k is right_complementable Element of the carrier of V
(V,k,(- 1r)) is right_complementable Element of the carrier of V
[(- 1r),k] is set
{(- 1r),k} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),k},{(- 1r)}} is set
the of V . [(- 1r),k] is set
[(- 1r),m1] is Element of [:COMPLEX, the carrier of (X,z,CNS,S):]
[:COMPLEX, the carrier of (X,z,CNS,S):] is non empty V50() set
{(- 1r),m1} is set
{{(- 1r),m1},{(- 1r)}} is set
the of V . [(- 1r),m1] is set
((X,z,CNS,S),m1,(- 1r)) is Element of the carrier of (X,z,CNS,S)
the of (X,z,CNS,S) is Relation-like [:COMPLEX, the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
[(- 1r),m1] is set
the of (X,z,CNS,S) . [(- 1r),m1] is set
k is Element of the carrier of (X,z,CNS,S)
m1 + k is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) is Relation-like [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] is non empty set
[:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
the addF of (X,z,CNS,S) . (m1,k) is Element of the carrier of (X,z,CNS,S)
[m1,k] is set
{m1,k} is set
{m1} is non empty trivial 1 -element set
{{m1,k},{m1}} is set
the addF of (X,z,CNS,S) . [m1,k] is set
m1 is complex set
k is Element of the carrier of (X,z,CNS,S)
n is Element of the carrier of (X,z,CNS,S)
k + n is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) is Relation-like [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] is non empty set
[:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
the addF of (X,z,CNS,S) . (k,n) is Element of the carrier of (X,z,CNS,S)
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the addF of (X,z,CNS,S) . [k,n] is set
((X,z,CNS,S),(k + n),m1) is Element of the carrier of (X,z,CNS,S)
the of (X,z,CNS,S) is Relation-like [:COMPLEX, the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[:COMPLEX, the carrier of (X,z,CNS,S):] is non empty V50() set
[:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
[m1,(k + n)] is set
{m1,(k + n)} is set
{m1} is non empty trivial 1 -element set
{{m1,(k + n)},{m1}} is set
the of (X,z,CNS,S) . [m1,(k + n)] is set
((X,z,CNS,S),k,m1) is Element of the carrier of (X,z,CNS,S)
[m1,k] is set
{m1,k} is set
{{m1,k},{m1}} is set
the of (X,z,CNS,S) . [m1,k] is set
((X,z,CNS,S),n,m1) is Element of the carrier of (X,z,CNS,S)
[m1,n] is set
{m1,n} is set
{{m1,n},{m1}} is set
the of (X,z,CNS,S) . [m1,n] is set
((X,z,CNS,S),k,m1) + ((X,z,CNS,S),n,m1) is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) . (((X,z,CNS,S),k,m1),((X,z,CNS,S),n,m1)) is Element of the carrier of (X,z,CNS,S)
[((X,z,CNS,S),k,m1),((X,z,CNS,S),n,m1)] is set
{((X,z,CNS,S),k,m1),((X,z,CNS,S),n,m1)} is set
{((X,z,CNS,S),k,m1)} is non empty trivial 1 -element set
{{((X,z,CNS,S),k,m1),((X,z,CNS,S),n,m1)},{((X,z,CNS,S),k,m1)}} is set
the addF of (X,z,CNS,S) . [((X,z,CNS,S),k,m1),((X,z,CNS,S),n,m1)] is set
k is right_complementable Element of the carrier of V
(V,k,m1) is right_complementable Element of the carrier of V
[m1,k] is set
{m1,k} is set
{{m1,k},{m1}} is set
the of V . [m1,k] is set
n is right_complementable Element of the carrier of V
(V,n,m1) is right_complementable Element of the carrier of V
[m1,n] is set
{m1,n} is set
{{m1,n},{m1}} is set
the of V . [m1,n] is set
k + n is right_complementable Element of the carrier of V
the addF of V . (k,n) is right_complementable Element of the carrier of V
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the addF of V . [k,n] is set
(V,(k + n),m1) is right_complementable Element of the carrier of V
[m1,(k + n)] is set
{m1,(k + n)} is set
{{m1,(k + n)},{m1}} is set
the of V . [m1,(k + n)] is set
(V,k,m1) + (V,n,m1) is right_complementable Element of the carrier of V
the addF of V . ((V,k,m1),(V,n,m1)) is right_complementable Element of the carrier of V
[(V,k,m1),(V,n,m1)] is set
{(V,k,m1),(V,n,m1)} is set
{(V,k,m1)} is non empty trivial 1 -element set
{{(V,k,m1),(V,n,m1)},{(V,k,m1)}} is set
the addF of V . [(V,k,m1),(V,n,m1)] is set
m1 is complex set
k is complex set
m1 + k is complex set
n is Element of the carrier of (X,z,CNS,S)
((X,z,CNS,S),n,(m1 + k)) is Element of the carrier of (X,z,CNS,S)
the of (X,z,CNS,S) is Relation-like [:COMPLEX, the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[:COMPLEX, the carrier of (X,z,CNS,S):] is non empty V50() set
[:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
[(m1 + k),n] is set
{(m1 + k),n} is set
{(m1 + k)} is non empty trivial 1 -element set
{{(m1 + k),n},{(m1 + k)}} is set
the of (X,z,CNS,S) . [(m1 + k),n] is set
((X,z,CNS,S),n,m1) is Element of the carrier of (X,z,CNS,S)
[m1,n] is set
{m1,n} is set
{m1} is non empty trivial 1 -element set
{{m1,n},{m1}} is set
the of (X,z,CNS,S) . [m1,n] is set
((X,z,CNS,S),n,k) is Element of the carrier of (X,z,CNS,S)
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the of (X,z,CNS,S) . [k,n] is set
((X,z,CNS,S),n,m1) + ((X,z,CNS,S),n,k) is Element of the carrier of (X,z,CNS,S)
the addF of (X,z,CNS,S) is Relation-like [: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):] is non empty set
[:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
bool [:[: the carrier of (X,z,CNS,S), the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty set
the addF of (X,z,CNS,S) . (((X,z,CNS,S),n,m1),((X,z,CNS,S),n,k)) is Element of the carrier of (X,z,CNS,S)
[((X,z,CNS,S),n,m1),((X,z,CNS,S),n,k)] is set
{((X,z,CNS,S),n,m1),((X,z,CNS,S),n,k)} is set
{((X,z,CNS,S),n,m1)} is non empty trivial 1 -element set
{{((X,z,CNS,S),n,m1),((X,z,CNS,S),n,k)},{((X,z,CNS,S),n,m1)}} is set
the addF of (X,z,CNS,S) . [((X,z,CNS,S),n,m1),((X,z,CNS,S),n,k)] is set
k is right_complementable Element of the carrier of V
(V,k,m1) is right_complementable Element of the carrier of V
[m1,k] is set
{m1,k} is set
{{m1,k},{m1}} is set
the of V . [m1,k] is set
(V,k,k) is right_complementable Element of the carrier of V
[k,k] is set
{k,k} is set
{{k,k},{k}} is set
the of V . [k,k] is set
(V,k,(m1 + k)) is right_complementable Element of the carrier of V
[(m1 + k),k] is set
{(m1 + k),k} is set
{{(m1 + k),k},{(m1 + k)}} is set
the of V . [(m1 + k),k] is set
(V,k,m1) + (V,k,k) is right_complementable Element of the carrier of V
the addF of V . ((V,k,m1),(V,k,k)) is right_complementable Element of the carrier of V
[(V,k,m1),(V,k,k)] is set
{(V,k,m1),(V,k,k)} is set
{(V,k,m1)} is non empty trivial 1 -element set
{{(V,k,m1),(V,k,k)},{(V,k,m1)}} is set
the addF of V . [(V,k,m1),(V,k,k)] is set
m1 is complex set
k is complex set
m1 * k is complex set
n is Element of the carrier of (X,z,CNS,S)
((X,z,CNS,S),n,(m1 * k)) is Element of the carrier of (X,z,CNS,S)
the of (X,z,CNS,S) is Relation-like [:COMPLEX, the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[:COMPLEX, the carrier of (X,z,CNS,S):] is non empty V50() set
[:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
[(m1 * k),n] is set
{(m1 * k),n} is set
{(m1 * k)} is non empty trivial 1 -element set
{{(m1 * k),n},{(m1 * k)}} is set
the of (X,z,CNS,S) . [(m1 * k),n] is set
((X,z,CNS,S),n,k) is Element of the carrier of (X,z,CNS,S)
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the of (X,z,CNS,S) . [k,n] is set
((X,z,CNS,S),((X,z,CNS,S),n,k),m1) is Element of the carrier of (X,z,CNS,S)
[m1,((X,z,CNS,S),n,k)] is set
{m1,((X,z,CNS,S),n,k)} is set
{m1} is non empty trivial 1 -element set
{{m1,((X,z,CNS,S),n,k)},{m1}} is set
the of (X,z,CNS,S) . [m1,((X,z,CNS,S),n,k)] is set
k is right_complementable Element of the carrier of V
(V,k,k) is right_complementable Element of the carrier of V
[k,k] is set
{k,k} is set
{{k,k},{k}} is set
the of V . [k,k] is set
(V,k,(m1 * k)) is right_complementable Element of the carrier of V
[(m1 * k),k] is set
{(m1 * k),k} is set
{{(m1 * k),k},{(m1 * k)}} is set
the of V . [(m1 * k),k] is set
(V,(V,k,k),m1) is right_complementable Element of the carrier of V
[m1,(V,k,k)] is set
{m1,(V,k,k)} is set
{{m1,(V,k,k)},{m1}} is set
the of V . [m1,(V,k,k)] is set
m1 is Element of the carrier of (X,z,CNS,S)
((X,z,CNS,S),m1,1r) is Element of the carrier of (X,z,CNS,S)
the of (X,z,CNS,S) is Relation-like [:COMPLEX, the carrier of (X,z,CNS,S):] -defined the carrier of (X,z,CNS,S) -valued Function-like V18([:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S)) Element of bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):]
[:COMPLEX, the carrier of (X,z,CNS,S):] is non empty V50() set
[:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
bool [:[:COMPLEX, the carrier of (X,z,CNS,S):], the carrier of (X,z,CNS,S):] is non empty V50() set
[1r,m1] is set
{1r,m1} is set
{1r} is non empty trivial 1 -element set
{{1r,m1},{1r}} is set
the of (X,z,CNS,S) . [1r,m1] is set
k is right_complementable Element of the carrier of V
(V,k,1r) is right_complementable Element of the carrier of V
[1r,k] is set
{1r,k} is set
{{1r,k},{1r}} is set
the of V . [1r,k] is set
0. (X,z,CNS,S) is zero Element of the carrier of (X,z,CNS,S)
the ZeroF of (X,z,CNS,S) is Element of the carrier of (X,z,CNS,S)
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V || the carrier of V is Relation-like Function-like set
the addF of V | [: the carrier of V, the carrier of V:] is Relation-like set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
the of V | [:COMPLEX, the carrier of V:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
V is non empty right_complementable Abelian add-associative right_zeroed () () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () () ()
the carrier of niltonil is non empty set
the carrier of V is non empty set
the addF of niltonil is Relation-like [: the carrier of niltonil, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like V18([: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil) Element of bool [:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:]
[: the carrier of niltonil, the carrier of niltonil:] is non empty set
[:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:] is non empty set
bool [:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:] is non empty set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of niltonil || the carrier of V is Relation-like Function-like set
the addF of niltonil | [: the carrier of V, the carrier of V:] is Relation-like set
the addF of V || the carrier of niltonil is Relation-like Function-like set
the addF of V | [: the carrier of niltonil, the carrier of niltonil:] is Relation-like set
the of niltonil is Relation-like [:COMPLEX, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like V18([:COMPLEX, the carrier of niltonil:], the carrier of niltonil) Element of bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:]
[:COMPLEX, the carrier of niltonil:] is non empty V50() set
[:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:] is non empty V50() set
bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:] is non empty V50() set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
the of V | [:COMPLEX, the carrier of niltonil:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
0. niltonil is zero right_complementable Element of the carrier of niltonil
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
the of niltonil | [:COMPLEX, the carrier of V:] is Relation-like [:COMPLEX, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like Element of bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:]
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
X is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
the carrier of niltonil is non empty set
the carrier of X is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
0. X is zero right_complementable Element of the carrier of X
the ZeroF of X is right_complementable Element of the carrier of X
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V18([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is non empty set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
the addF of X || the carrier of V is Relation-like Function-like set
the addF of X | [: the carrier of V, the carrier of V:] is Relation-like set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[:COMPLEX, the carrier of X:] is non empty V50() set
the of X is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like V18([:COMPLEX, the carrier of X:], the carrier of X) Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
[:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
bool [:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
the of X | [:COMPLEX, the carrier of V:] is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
0. niltonil is zero right_complementable Element of the carrier of niltonil
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
the addF of niltonil is Relation-like [: the carrier of niltonil, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like V18([: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil) Element of bool [:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:]
[: the carrier of niltonil, the carrier of niltonil:] is non empty set
[:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:] is non empty set
bool [:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:] is non empty set
the addF of niltonil || the carrier of V is Relation-like Function-like set
the addF of niltonil | [: the carrier of V, the carrier of V:] is Relation-like set
the addF of X || the carrier of niltonil is Relation-like Function-like set
the addF of X | [: the carrier of niltonil, the carrier of niltonil:] is Relation-like set
( the addF of X || the carrier of niltonil) || the carrier of V is Relation-like Function-like set
( the addF of X || the carrier of niltonil) | [: the carrier of V, the carrier of V:] is Relation-like set
the of niltonil is Relation-like [:COMPLEX, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like V18([:COMPLEX, the carrier of niltonil:], the carrier of niltonil) Element of bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:]
[:COMPLEX, the carrier of niltonil:] is non empty V50() set
[:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:] is non empty V50() set
bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:] is non empty V50() set
the of niltonil | [:COMPLEX, the carrier of V:] is Relation-like [:COMPLEX, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like Element of bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:]
the of X | [:COMPLEX, the carrier of niltonil:] is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
( the of X | [:COMPLEX, the carrier of niltonil:]) | [:COMPLEX, the carrier of V:] is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of niltonil is non empty set
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of X is non empty set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
the carrier of V is non empty set
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[: the carrier of niltonil, the carrier of niltonil:] is non empty set
[: the carrier of X, the carrier of X:] is non empty set
0. niltonil is zero right_complementable Element of the carrier of niltonil
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
0. X is zero right_complementable Element of the carrier of X
the ZeroF of X is right_complementable Element of the carrier of X
the addF of niltonil is Relation-like [: the carrier of niltonil, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like V18([: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil) Element of bool [:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:]
[:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:] is non empty set
bool [:[: the carrier of niltonil, the carrier of niltonil:], the carrier of niltonil:] is non empty set
the addF of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V18([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
the addF of X || the carrier of niltonil is Relation-like Function-like set
the addF of X | [: the carrier of niltonil, the carrier of niltonil:] is Relation-like set
the of niltonil is Relation-like [:COMPLEX, the carrier of niltonil:] -defined the carrier of niltonil -valued Function-like V18([:COMPLEX, the carrier of niltonil:], the carrier of niltonil) Element of bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:]
[:COMPLEX, the carrier of niltonil:] is non empty V50() set
[:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:] is non empty V50() set
bool [:[:COMPLEX, the carrier of niltonil:], the carrier of niltonil:] is non empty V50() set
[:COMPLEX, the carrier of X:] is non empty V50() set
the of X is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like V18([:COMPLEX, the carrier of X:], the carrier of X) Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
[:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
bool [:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
the of X | [:COMPLEX, the carrier of niltonil:] is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
the addF of V || the carrier of niltonil is Relation-like Function-like set
the addF of V | [: the carrier of niltonil, the carrier of niltonil:] is Relation-like set
the addF of V || the carrier of X is Relation-like Function-like set
the addF of V | [: the carrier of X, the carrier of X:] is Relation-like set
the of V | [:COMPLEX, the carrier of niltonil:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
the of V | [:COMPLEX, the carrier of X:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of niltonil is non empty set
the carrier of X is non empty set
z is set
CNS is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
niltonil is Element of bool the carrier of V
the addF of V || niltonil is Relation-like Function-like set
[:niltonil,niltonil:] is set
the addF of V | [:niltonil,niltonil:] is Relation-like set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[:COMPLEX,niltonil:] is set
the of V | [:COMPLEX,niltonil:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
( the carrier of V,(0. V), the addF of V, the of V) is non empty () ()
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the carrier of niltonil is non empty set
X is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the carrier of X is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
X is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the carrier of niltonil is non empty set
the carrier of X is non empty set
z is set
CNS is right_complementable Element of the carrier of V
CNS is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () () ()
the carrier of V is non empty set
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the carrier of niltonil is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () () ()
the carrier of V is non empty set
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of X is non empty set
niltonil is Element of bool the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is Element of bool the carrier of V
[:COMPLEX, the carrier of V:] is non empty V50() set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[:COMPLEX,niltonil:] is set
the of V | [:COMPLEX,niltonil:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
dom the of V is Relation-like set
dom ( the of V | [:COMPLEX,niltonil:]) is Relation-like set
[:COMPLEX, the carrier of V:] /\ [:COMPLEX,niltonil:] is set
X is non empty set
[:COMPLEX,X:] is non empty V50() set
S is set
[1r,S] is set
{1r,S} is set
{1r} is non empty trivial 1 -element set
{{1r,S},{1r}} is set
( the of V | [:COMPLEX,niltonil:]) . [1r,S] is set
g is right_complementable Element of the carrier of V
(V,g,1r) is right_complementable Element of the carrier of V
[1r,g] is set
{1r,g} is set
{{1r,g},{1r}} is set
the of V . [1r,g] is set
g is set
( the of V | [:COMPLEX,niltonil:]) . g is set
h is set
r is set
[h,r] is set
{h,r} is set
{h} is non empty trivial 1 -element set
{{h,r},{h}} is set
k is right_complementable Element of the carrier of V
m1 is complex Element of COMPLEX
(V,k,m1) is right_complementable Element of the carrier of V
[m1,k] is set
{m1,k} is set
{m1} is non empty trivial 1 -element set
{{m1,k},{m1}} is set
the of V . [m1,k] is set
rng ( the of V | [:COMPLEX,niltonil:]) is set
[:[:COMPLEX,X:],X:] is non empty V50() set
bool [:[:COMPLEX,X:],X:] is non empty V50() set
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V || niltonil is Relation-like Function-like set
[:niltonil,niltonil:] is set
the addF of V | [:niltonil,niltonil:] is Relation-like set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
dom the addF of V is Relation-like set
dom ( the addF of V || niltonil) is set
[: the carrier of V, the carrier of V:] /\ [:niltonil,niltonil:] is set
[:X,X:] is non empty set
r is set
h is Element of X
[h,r] is set
{h,r} is set
{h} is non empty trivial 1 -element set
{{h,r},{h}} is set
( the addF of V || niltonil) . [h,r] is set
k is right_complementable Element of the carrier of V
m1 is right_complementable Element of the carrier of V
k + m1 is right_complementable Element of the carrier of V
the addF of V . (k,m1) is right_complementable Element of the carrier of V
[k,m1] is set
{k,m1} is set
{k} is non empty trivial 1 -element set
{{k,m1},{k}} is set
the addF of V . [k,m1] is set
m1 is set
( the addF of V || niltonil) . m1 is set
k is set
n is set
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
k is right_complementable Element of the carrier of V
n is right_complementable Element of the carrier of V
k + n is right_complementable Element of the carrier of V
the addF of V . (k,n) is right_complementable Element of the carrier of V
[k,n] is set
{k,n} is set
{k} is non empty trivial 1 -element set
{{k,n},{k}} is set
the addF of V . [k,n] is set
rng ( the addF of V || niltonil) is set
[:[:X,X:],X:] is non empty set
bool [:[:X,X:],X:] is non empty set
h is Element of X
r is Relation-like [:X,X:] -defined X -valued Function-like V18([:X,X:],X) Element of bool [:[:X,X:],X:]
S is Relation-like [:COMPLEX,X:] -defined X -valued Function-like V18([:COMPLEX,X:],X) Element of bool [:[:COMPLEX,X:],X:]
(X,h,r,S) is non empty () ()
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty trivial 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the carrier of niltonil is non empty set
X is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the carrier of X is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
( the carrier of V, the ZeroF of V, the addF of V, the of V) is non empty () ()
the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is non empty set
X is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
z is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
X + z is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
[:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (X,z) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,z] is set
CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
(X + z) + CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . ((X + z),CNS) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[(X + z),CNS] is set
{(X + z),CNS} is set
{(X + z)} is non empty trivial 1 -element set
{{(X + z),CNS},{(X + z)}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [(X + z),CNS] is set
z + CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (z,CNS) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [z,CNS] is set
X + (z + CNS) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (X,(z + CNS)) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,(z + CNS)] is set
{X,(z + CNS)} is set
{{X,(z + CNS)},{X}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,(z + CNS)] is set
S is right_complementable Element of the carrier of V
g is right_complementable Element of the carrier of V
S + g is right_complementable Element of the carrier of V
the addF of V . (S,g) is right_complementable Element of the carrier of V
[S,g] is set
{S,g} is set
{S} is non empty trivial 1 -element set
{{S,g},{S}} is set
the addF of V . [S,g] is set
h is right_complementable Element of the carrier of V
(S + g) + h is right_complementable Element of the carrier of V
the addF of V . ((S + g),h) is right_complementable Element of the carrier of V
[(S + g),h] is set
{(S + g),h} is set
{(S + g)} is non empty trivial 1 -element set
{{(S + g),h},{(S + g)}} is set
the addF of V . [(S + g),h] is set
g + h is right_complementable Element of the carrier of V
the addF of V . (g,h) is right_complementable Element of the carrier of V
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
the addF of V . [g,h] is set
S + (g + h) is right_complementable Element of the carrier of V
the addF of V . (S,(g + h)) is right_complementable Element of the carrier of V
[S,(g + h)] is set
{S,(g + h)} is set
{{S,(g + h)},{S}} is set
the addF of V . [S,(g + h)] is set
0. ( the carrier of V, the ZeroF of V, the addF of V, the of V) is zero Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the ZeroF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
X is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
X + (0. ( the carrier of V, the ZeroF of V, the addF of V, the of V)) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
[:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (X,(0. ( the carrier of V, the ZeroF of V, the addF of V, the of V))) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,(0. ( the carrier of V, the ZeroF of V, the addF of V, the of V))] is set
{X,(0. ( the carrier of V, the ZeroF of V, the addF of V, the of V))} is set
{X} is non empty trivial 1 -element set
{{X,(0. ( the carrier of V, the ZeroF of V, the addF of V, the of V))},{X}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,(0. ( the carrier of V, the ZeroF of V, the addF of V, the of V))] is set
z is right_complementable Element of the carrier of V
0. V is zero right_complementable Element of the carrier of V
z + (0. V) is right_complementable Element of the carrier of V
the addF of V . (z,(0. V)) is right_complementable Element of the carrier of V
[z,(0. V)] is set
{z,(0. V)} is set
{z} is non empty trivial 1 -element set
{{z,(0. V)},{z}} is set
the addF of V . [z,(0. V)] is set
X is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
z is right_complementable Element of the carrier of V
0. V is zero right_complementable Element of the carrier of V
CNS is right_complementable Element of the carrier of V
z + CNS is right_complementable Element of the carrier of V
the addF of V . (z,CNS) is right_complementable Element of the carrier of V
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of V . [z,CNS] is set
S is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
X + S is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
[:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (X,S) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,S] is set
{X,S} is set
{X} is non empty trivial 1 -element set
{{X,S},{X}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,S] is set
X is complex set
z is complex set
X * z is complex set
CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,(X * z)) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[(X * z),CNS] is set
{(X * z),CNS} is set
{(X * z)} is non empty trivial 1 -element set
{{(X * z),CNS},{(X * z)}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [(X * z),CNS] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [z,CNS] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z),X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)] is set
{X,(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)} is set
{X} is non empty trivial 1 -element set
{{X,(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)},{X}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)] is set
S is right_complementable Element of the carrier of V
(V,S,(X * z)) is right_complementable Element of the carrier of V
[(X * z),S] is set
{(X * z),S} is set
{{(X * z),S},{(X * z)}} is set
the of V . [(X * z),S] is set
(V,S,z) is right_complementable Element of the carrier of V
[z,S] is set
{z,S} is set
{{z,S},{z}} is set
the of V . [z,S] is set
(V,(V,S,z),X) is right_complementable Element of the carrier of V
[X,(V,S,z)] is set
{X,(V,S,z)} is set
{{X,(V,S,z)},{X}} is set
the of V . [X,(V,S,z)] is set
X is complex set
z is complex set
X + z is complex set
CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,(X + z)) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[(X + z),CNS] is set
{(X + z),CNS} is set
{(X + z)} is non empty trivial 1 -element set
{{(X + z),CNS},{(X + z)}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [(X + z),CNS] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,CNS] is set
{X,CNS} is set
{X} is non empty trivial 1 -element set
{{X,CNS},{X}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,CNS] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [z,CNS] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X) + (( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
[:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . ((( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)] is set
{(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)} is set
{(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X)} is non empty trivial 1 -element set
{{(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)},{(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X)}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,z)] is set
S is right_complementable Element of the carrier of V
(V,S,(X + z)) is right_complementable Element of the carrier of V
[(X + z),S] is set
{(X + z),S} is set
{{(X + z),S},{(X + z)}} is set
the of V . [(X + z),S] is set
(V,S,X) is right_complementable Element of the carrier of V
[X,S] is set
{X,S} is set
{{X,S},{X}} is set
the of V . [X,S] is set
(V,S,z) is right_complementable Element of the carrier of V
[z,S] is set
{z,S} is set
{{z,S},{z}} is set
the of V . [z,S] is set
(V,S,X) + (V,S,z) is right_complementable Element of the carrier of V
the addF of V . ((V,S,X),(V,S,z)) is right_complementable Element of the carrier of V
[(V,S,X),(V,S,z)] is set
{(V,S,X),(V,S,z)} is set
{(V,S,X)} is non empty trivial 1 -element set
{{(V,S,X),(V,S,z)},{(V,S,X)}} is set
the addF of V . [(V,S,X),(V,S,z)] is set
X is complex set
z is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
z + CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
[:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (z,CNS) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [z,CNS] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),(z + CNS),X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[X,(z + CNS)] is set
{X,(z + CNS)} is set
{X} is non empty trivial 1 -element set
{{X,(z + CNS)},{X}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,(z + CNS)] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,z] is set
{X,z} is set
{{X,z},{X}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,z] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,CNS] is set
{X,CNS} is set
{{X,CNS},{X}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,CNS] is set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X) + (( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . ((( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X)) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X)] is set
{(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X)} is set
{(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X)} is non empty trivial 1 -element set
{{(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X)},{(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X)}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X),(( the carrier of V, the ZeroF of V, the addF of V, the of V),CNS,X)] is set
S is right_complementable Element of the carrier of V
g is right_complementable Element of the carrier of V
S + g is right_complementable Element of the carrier of V
the addF of V . (S,g) is right_complementable Element of the carrier of V
[S,g] is set
{S,g} is set
{S} is non empty trivial 1 -element set
{{S,g},{S}} is set
the addF of V . [S,g] is set
(V,(S + g),X) is right_complementable Element of the carrier of V
[X,(S + g)] is set
{X,(S + g)} is set
{{X,(S + g)},{X}} is set
the of V . [X,(S + g)] is set
(V,S,X) is right_complementable Element of the carrier of V
[X,S] is set
{X,S} is set
{{X,S},{X}} is set
the of V . [X,S] is set
(V,g,X) is right_complementable Element of the carrier of V
[X,g] is set
{X,g} is set
{{X,g},{X}} is set
the of V . [X,g] is set
(V,S,X) + (V,g,X) is right_complementable Element of the carrier of V
the addF of V . ((V,S,X),(V,g,X)) is right_complementable Element of the carrier of V
[(V,S,X),(V,g,X)] is set
{(V,S,X),(V,g,X)} is set
{(V,S,X)} is non empty trivial 1 -element set
{{(V,S,X),(V,g,X)},{(V,S,X)}} is set
the addF of V . [(V,S,X),(V,g,X)] is set
z is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
S is right_complementable Element of the carrier of V
CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
g is right_complementable Element of the carrier of V
z + CNS is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
[:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (z,CNS) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [z,CNS] is set
S + g is right_complementable Element of the carrier of V
the addF of V . (S,g) is right_complementable Element of the carrier of V
[S,g] is set
{S,g} is set
{S} is non empty trivial 1 -element set
{{S,g},{S}} is set
the addF of V . [S,g] is set
X is complex set
(( the carrier of V, the ZeroF of V, the addF of V, the of V),z,X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,z] is set
(V,S,X) is right_complementable Element of the carrier of V
[X,S] is set
{X,S} is set
{{X,S},{X}} is set
the of V . [X,S] is set
X is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
z is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
X + z is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
[:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
bool [:[: the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V), the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (X,z) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [X,z] is set
z + X is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . (z,X) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
[z,X] is set
{z,X} is set
{z} is non empty trivial 1 -element set
{{z,X},{z}} is set
the addF of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [z,X] is set
S is right_complementable Element of the carrier of V
CNS is right_complementable Element of the carrier of V
S + CNS is right_complementable Element of the carrier of V
the addF of V . (S,CNS) is right_complementable Element of the carrier of V
[S,CNS] is set
{S,CNS} is set
{S} is non empty trivial 1 -element set
{{S,CNS},{S}} is set
the addF of V . [S,CNS] is set
X is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
(( the carrier of V, the ZeroF of V, the addF of V, the of V),X,1r) is Element of the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) is Relation-like [:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] -defined the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V) -valued Function-like V18([:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V)) Element of bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):]
[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
bool [:[:COMPLEX, the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):], the carrier of ( the carrier of V, the ZeroF of V, the addF of V, the of V):] is non empty V50() set
[1r,X] is set
{1r,X} is set
{1r} is non empty trivial 1 -element set
{{1r,X},{1r}} is set
the of ( the carrier of V, the ZeroF of V, the addF of V, the of V) . [1r,X] is set
z is right_complementable Element of the carrier of V
(V,z,1r) is right_complementable Element of the carrier of V
[1r,z] is set
{1r,z} is set
{{1r,z},{1r}} is set
the of V . [1r,z] is set
X is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the of X is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like V18([:COMPLEX, the carrier of X:], the carrier of X) Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
the carrier of X is non empty set
[:COMPLEX, the carrier of X:] is non empty V50() set
[:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
bool [:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
the of V | [:COMPLEX, the carrier of X:] is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
0. X is zero right_complementable Element of the carrier of X
the ZeroF of X is right_complementable Element of the carrier of X
0. V is zero right_complementable Element of the carrier of V
the addF of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V18([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is non empty set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
the addF of V || the carrier of X is Relation-like Function-like set
the addF of V | [: the carrier of X, the carrier of X:] is Relation-like set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(niltonil) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (niltonil)
the carrier of (niltonil) is non empty set
the carrier of niltonil is non empty set
0. niltonil is zero right_complementable Element of the carrier of niltonil
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
{(0. niltonil)} is non empty trivial 1 -element Element of bool the carrier of niltonil
bool the carrier of niltonil is non empty set
the carrier of (V) is non empty set
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty trivial 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(niltonil) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (niltonil)
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(X) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (X)
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(niltonil) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (niltonil)
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of (V) is non empty set
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty trivial 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
the carrier of niltonil is non empty set
0. niltonil is zero right_complementable Element of the carrier of niltonil
the ZeroF of niltonil is right_complementable Element of the carrier of niltonil
{(0. niltonil)} is non empty trivial 1 -element Element of bool the carrier of niltonil
bool the carrier of niltonil is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(niltonil) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (niltonil)
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(X) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (X)
V is non empty right_complementable Abelian add-associative right_zeroed () () () () () ()
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
( the carrier of V, the ZeroF of V, the addF of V, the of V) is non empty () ()
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
bool the carrier of V is non empty set
CNS is set
S is set
S is Element of bool the carrier of V
g is set
h is right_complementable Element of the carrier of V
niltonil + h is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,h) is right_complementable Element of the carrier of V
[niltonil,h] is set
{niltonil,h} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,h},{niltonil}} is set
the addF of V . [niltonil,h] is set
g is set
h is right_complementable Element of the carrier of V
niltonil + h is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,h) is right_complementable Element of the carrier of V
[niltonil,h] is set
{niltonil,h} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,h},{niltonil}} is set
the addF of V . [niltonil,h] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,(0. V),niltonil) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((0. V) + b1) where b1 is right_complementable Element of the carrier of V : b1 in niltonil } is set
the carrier of niltonil is non empty set
z is set
CNS is right_complementable Element of the carrier of V
(0. V) + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((0. V),CNS) is right_complementable Element of the carrier of V
[(0. V),CNS] is set
{(0. V),CNS} is set
{(0. V)} is non empty trivial 1 -element set
{{(0. V),CNS},{(0. V)}} is set
the addF of V . [(0. V),CNS] is set
z is set
CNS is right_complementable Element of the carrier of V
(0. V) + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((0. V),CNS) is right_complementable Element of the carrier of V
[(0. V),CNS] is set
{(0. V),CNS} is set
{(0. V)} is non empty trivial 1 -element set
{{(0. V),CNS},{(0. V)}} is set
the addF of V . [(0. V),CNS] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of niltonil is non empty set
X is Element of bool the carrier of V
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(V,(0. V),niltonil) is Element of bool the carrier of V
{ ((0. V) + b1) where b1 is right_complementable Element of the carrier of V : b1 in niltonil } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
z is right_complementable Element of the carrier of V
niltonil + z is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,z) is right_complementable Element of the carrier of V
[niltonil,z] is set
{niltonil,z} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,z},{niltonil}} is set
the addF of V . [niltonil,z] is set
- z is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
niltonil - niltonil is right_complementable Element of the carrier of V
niltonil + (- niltonil) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- niltonil)) is right_complementable Element of the carrier of V
[niltonil,(- niltonil)] is set
{niltonil,(- niltonil)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- niltonil)},{niltonil}} is set
the addF of V . [niltonil,(- niltonil)] is set
niltonil + (- niltonil) is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(0. V)) is right_complementable Element of the carrier of V
[niltonil,(0. V)] is set
{niltonil,(0. V)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(0. V)},{niltonil}} is set
the addF of V . [niltonil,(0. V)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,(0. V),niltonil) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((0. V) + b1) where b1 is right_complementable Element of the carrier of V : b1 in niltonil } is set
the carrier of niltonil is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
niltonil is right_complementable Element of the carrier of V
(V,niltonil,(V)) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in (V) } is set
{niltonil} is non empty trivial 1 -element Element of bool the carrier of V
X is set
z is right_complementable Element of the carrier of V
niltonil + z is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,z) is right_complementable Element of the carrier of V
[niltonil,z] is set
{niltonil,z} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,z},{niltonil}} is set
the addF of V . [niltonil,z] is set
the carrier of (V) is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
{(0. V)} is non empty trivial 1 -element Element of bool the carrier of V
X is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(0. V)) is right_complementable Element of the carrier of V
[niltonil,(0. V)] is set
{niltonil,(0. V)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(0. V)},{niltonil}} is set
the addF of V . [niltonil,(0. V)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
the carrier of X is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(0. V)) is right_complementable Element of the carrier of V
[niltonil,(0. V)] is set
{niltonil,(0. V)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(0. V)},{niltonil}} is set
the addF of V . [niltonil,(0. V)] is set
z is set
CNS is right_complementable Element of the carrier of V
niltonil + CNS is right_complementable Element of the carrier of V
the addF of V . (niltonil,CNS) is right_complementable Element of the carrier of V
[niltonil,CNS] is set
{niltonil,CNS} is set
{{niltonil,CNS},{niltonil}} is set
the addF of V . [niltonil,CNS] is set
z is set
CNS is right_complementable Element of the carrier of X
S is right_complementable Element of the carrier of X
CNS - S is right_complementable Element of the carrier of X
- S is right_complementable Element of the carrier of X
CNS + (- S) is right_complementable Element of the carrier of X
the addF of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V18([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is non empty set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
the addF of X . (CNS,(- S)) is right_complementable Element of the carrier of X
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of X . [CNS,(- S)] is set
S + (CNS - S) is right_complementable Element of the carrier of X
the addF of X . (S,(CNS - S)) is right_complementable Element of the carrier of X
[S,(CNS - S)] is set
{S,(CNS - S)} is set
{S} is non empty trivial 1 -element set
{{S,(CNS - S)},{S}} is set
the addF of X . [S,(CNS - S)] is set
CNS + S is right_complementable Element of the carrier of X
the addF of X . (CNS,S) is right_complementable Element of the carrier of X
[CNS,S] is set
{CNS,S} is set
{{CNS,S},{CNS}} is set
the addF of X . [CNS,S] is set
(CNS + S) - S is right_complementable Element of the carrier of X
(CNS + S) + (- S) is right_complementable Element of the carrier of X
the addF of X . ((CNS + S),(- S)) is right_complementable Element of the carrier of X
[(CNS + S),(- S)] is set
{(CNS + S),(- S)} is set
{(CNS + S)} is non empty trivial 1 -element set
{{(CNS + S),(- S)},{(CNS + S)}} is set
the addF of X . [(CNS + S),(- S)] is set
S - S is right_complementable Element of the carrier of X
S + (- S) is right_complementable Element of the carrier of X
the addF of X . (S,(- S)) is right_complementable Element of the carrier of X
[S,(- S)] is set
{S,(- S)} is set
{{S,(- S)},{S}} is set
the addF of X . [S,(- S)] is set
CNS + (S - S) is right_complementable Element of the carrier of X
the addF of X . (CNS,(S - S)) is right_complementable Element of the carrier of X
[CNS,(S - S)] is set
{CNS,(S - S)} is set
{{CNS,(S - S)},{CNS}} is set
the addF of X . [CNS,(S - S)] is set
0. X is zero right_complementable Element of the carrier of X
the ZeroF of X is right_complementable Element of the carrier of X
CNS + (0. X) is right_complementable Element of the carrier of X
the addF of X . (CNS,(0. X)) is right_complementable Element of the carrier of X
[CNS,(0. X)] is set
{CNS,(0. X)} is set
{{CNS,(0. X)},{CNS}} is set
the addF of X . [CNS,(0. X)] is set
g is right_complementable Element of the carrier of V
h is right_complementable Element of the carrier of V
g - h is right_complementable Element of the carrier of V
- h is right_complementable Element of the carrier of V
g + (- h) is right_complementable Element of the carrier of V
the addF of V . (g,(- h)) is right_complementable Element of the carrier of V
[g,(- h)] is set
{g,(- h)} is set
{g} is non empty trivial 1 -element set
{{g,(- h)},{g}} is set
the addF of V . [g,(- h)] is set
h + (g - h) is right_complementable Element of the carrier of V
the addF of V . (h,(g - h)) is right_complementable Element of the carrier of V
[h,(g - h)] is set
{h,(g - h)} is set
{h} is non empty trivial 1 -element set
{{h,(g - h)},{h}} is set
the addF of V . [h,(g - h)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
( the carrier of V, the ZeroF of V, the addF of V, the of V) is non empty () ()
niltonil is right_complementable Element of the carrier of V
(V,niltonil,(V)) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in (V) } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
the carrier of X is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of z is non empty set
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
niltonil is right_complementable Element of the carrier of V
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
the carrier of X is non empty set
CNS is right_complementable Element of the carrier of z
S is non empty right_complementable Abelian add-associative right_zeroed () () () () (z)
(z,CNS,S) is Element of bool the carrier of z
bool the carrier of z is non empty set
{ (CNS + b1) where b1 is right_complementable Element of the carrier of z : b1 in S } is set
the carrier of S is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,(V,niltonil,X),z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((V,niltonil,X) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
the carrier of z is non empty set
CNS is set
S is right_complementable Element of the carrier of V
(V,niltonil,X) + S is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,X),S) is right_complementable Element of the carrier of V
[(V,niltonil,X),S] is set
{(V,niltonil,X),S} is set
{(V,niltonil,X)} is non empty trivial 1 -element set
{{(V,niltonil,X),S},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),S] is set
CNS is set
S is right_complementable Element of the carrier of V
S - (V,niltonil,X) is right_complementable Element of the carrier of V
- (V,niltonil,X) is right_complementable Element of the carrier of V
S + (- (V,niltonil,X)) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (S,(- (V,niltonil,X))) is right_complementable Element of the carrier of V
[S,(- (V,niltonil,X))] is set
{S,(- (V,niltonil,X))} is set
{S} is non empty trivial 1 -element set
{{S,(- (V,niltonil,X))},{S}} is set
the addF of V . [S,(- (V,niltonil,X))] is set
(V,niltonil,X) + (S - (V,niltonil,X)) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,X),(S - (V,niltonil,X))) is right_complementable Element of the carrier of V
[(V,niltonil,X),(S - (V,niltonil,X))] is set
{(V,niltonil,X),(S - (V,niltonil,X))} is set
{(V,niltonil,X)} is non empty trivial 1 -element set
{{(V,niltonil,X),(S - (V,niltonil,X))},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(S - (V,niltonil,X))] is set
S + (V,niltonil,X) is right_complementable Element of the carrier of V
the addF of V . (S,(V,niltonil,X)) is right_complementable Element of the carrier of V
[S,(V,niltonil,X)] is set
{S,(V,niltonil,X)} is set
{{S,(V,niltonil,X)},{S}} is set
the addF of V . [S,(V,niltonil,X)] is set
(S + (V,niltonil,X)) - (V,niltonil,X) is right_complementable Element of the carrier of V
(S + (V,niltonil,X)) + (- (V,niltonil,X)) is right_complementable Element of the carrier of V
the addF of V . ((S + (V,niltonil,X)),(- (V,niltonil,X))) is right_complementable Element of the carrier of V
[(S + (V,niltonil,X)),(- (V,niltonil,X))] is set
{(S + (V,niltonil,X)),(- (V,niltonil,X))} is set
{(S + (V,niltonil,X))} is non empty trivial 1 -element set
{{(S + (V,niltonil,X)),(- (V,niltonil,X))},{(S + (V,niltonil,X))}} is set
the addF of V . [(S + (V,niltonil,X)),(- (V,niltonil,X))] is set
(V,niltonil,X) - (V,niltonil,X) is right_complementable Element of the carrier of V
(V,niltonil,X) + (- (V,niltonil,X)) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,X),(- (V,niltonil,X))) is right_complementable Element of the carrier of V
[(V,niltonil,X),(- (V,niltonil,X))] is set
{(V,niltonil,X),(- (V,niltonil,X))} is set
{{(V,niltonil,X),(- (V,niltonil,X))},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(- (V,niltonil,X))] is set
S + ((V,niltonil,X) - (V,niltonil,X)) is right_complementable Element of the carrier of V
the addF of V . (S,((V,niltonil,X) - (V,niltonil,X))) is right_complementable Element of the carrier of V
[S,((V,niltonil,X) - (V,niltonil,X))] is set
{S,((V,niltonil,X) - (V,niltonil,X))} is set
{{S,((V,niltonil,X) - (V,niltonil,X))},{S}} is set
the addF of V . [S,((V,niltonil,X) - (V,niltonil,X))] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
S + (0. V) is right_complementable Element of the carrier of V
the addF of V . (S,(0. V)) is right_complementable Element of the carrier of V
[S,(0. V)] is set
{S,(0. V)} is set
{{S,(0. V)},{S}} is set
the addF of V . [S,(0. V)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,(V,niltonil,X),z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((V,niltonil,X) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
the carrier of z is non empty set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
X " is complex set
(X ") * X is complex set
(V,niltonil,((X ") * X)) is right_complementable Element of the carrier of V
[((X ") * X),niltonil] is set
{((X ") * X),niltonil} is set
{((X ") * X)} is non empty trivial 1 -element set
{{((X ") * X),niltonil},{((X ") * X)}} is set
the of V . [((X ") * X),niltonil] is set
(V,(V,niltonil,X),(X ")) is right_complementable Element of the carrier of V
[(X "),(V,niltonil,X)] is set
{(X "),(V,niltonil,X)} is set
{(X ")} is non empty trivial 1 -element set
{{(X "),(V,niltonil,X)},{(X ")}} is set
the of V . [(X "),(V,niltonil,X)] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(V,niltonil,X) + (0. V) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,X),(0. V)) is right_complementable Element of the carrier of V
[(V,niltonil,X),(0. V)] is set
{(V,niltonil,X),(0. V)} is set
{(V,niltonil,X)} is non empty trivial 1 -element set
{{(V,niltonil,X),(0. V)},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(0. V)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,(- niltonil),X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((- niltonil) + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
the carrier of X is non empty set
(V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- 1r),niltonil] is set
{(- 1r),niltonil} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),niltonil},{(- 1r)}} is set
the of V . [(- 1r),niltonil] is set
(V,(V,niltonil,(- 1r)),X) is Element of bool the carrier of V
{ ((V,niltonil,(- 1r)) + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
X + niltonil is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,niltonil) is right_complementable Element of the carrier of V
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the addF of V . [X,niltonil] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,(X + niltonil),z) is Element of bool the carrier of V
{ ((X + niltonil) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is set
S is right_complementable Element of the carrier of V
X + S is right_complementable Element of the carrier of V
the addF of V . (X,S) is right_complementable Element of the carrier of V
[X,S] is set
{X,S} is set
{{X,S},{X}} is set
the addF of V . [X,S] is set
S - niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
S + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (S,(- niltonil)) is right_complementable Element of the carrier of V
[S,(- niltonil)] is set
{S,(- niltonil)} is set
{S} is non empty trivial 1 -element set
{{S,(- niltonil)},{S}} is set
the addF of V . [S,(- niltonil)] is set
(X + niltonil) + (S - niltonil) is right_complementable Element of the carrier of V
the addF of V . ((X + niltonil),(S - niltonil)) is right_complementable Element of the carrier of V
[(X + niltonil),(S - niltonil)] is set
{(X + niltonil),(S - niltonil)} is set
{(X + niltonil)} is non empty trivial 1 -element set
{{(X + niltonil),(S - niltonil)},{(X + niltonil)}} is set
the addF of V . [(X + niltonil),(S - niltonil)] is set
niltonil + (S - niltonil) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(S - niltonil)) is right_complementable Element of the carrier of V
[niltonil,(S - niltonil)] is set
{niltonil,(S - niltonil)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(S - niltonil)},{niltonil}} is set
the addF of V . [niltonil,(S - niltonil)] is set
X + (niltonil + (S - niltonil)) is right_complementable Element of the carrier of V
the addF of V . (X,(niltonil + (S - niltonil))) is right_complementable Element of the carrier of V
[X,(niltonil + (S - niltonil))] is set
{X,(niltonil + (S - niltonil))} is set
{{X,(niltonil + (S - niltonil))},{X}} is set
the addF of V . [X,(niltonil + (S - niltonil))] is set
S + niltonil is right_complementable Element of the carrier of V
the addF of V . (S,niltonil) is right_complementable Element of the carrier of V
[S,niltonil] is set
{S,niltonil} is set
{{S,niltonil},{S}} is set
the addF of V . [S,niltonil] is set
(S + niltonil) - niltonil is right_complementable Element of the carrier of V
(S + niltonil) + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . ((S + niltonil),(- niltonil)) is right_complementable Element of the carrier of V
[(S + niltonil),(- niltonil)] is set
{(S + niltonil),(- niltonil)} is set
{(S + niltonil)} is non empty trivial 1 -element set
{{(S + niltonil),(- niltonil)},{(S + niltonil)}} is set
the addF of V . [(S + niltonil),(- niltonil)] is set
X + ((S + niltonil) - niltonil) is right_complementable Element of the carrier of V
the addF of V . (X,((S + niltonil) - niltonil)) is right_complementable Element of the carrier of V
[X,((S + niltonil) - niltonil)] is set
{X,((S + niltonil) - niltonil)} is set
{{X,((S + niltonil) - niltonil)},{X}} is set
the addF of V . [X,((S + niltonil) - niltonil)] is set
niltonil - niltonil is right_complementable Element of the carrier of V
niltonil + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- niltonil)) is right_complementable Element of the carrier of V
[niltonil,(- niltonil)] is set
{niltonil,(- niltonil)} is set
{{niltonil,(- niltonil)},{niltonil}} is set
the addF of V . [niltonil,(- niltonil)] is set
S + (niltonil - niltonil) is right_complementable Element of the carrier of V
the addF of V . (S,(niltonil - niltonil)) is right_complementable Element of the carrier of V
[S,(niltonil - niltonil)] is set
{S,(niltonil - niltonil)} is set
{{S,(niltonil - niltonil)},{S}} is set
the addF of V . [S,(niltonil - niltonil)] is set
X + (S + (niltonil - niltonil)) is right_complementable Element of the carrier of V
the addF of V . (X,(S + (niltonil - niltonil))) is right_complementable Element of the carrier of V
[X,(S + (niltonil - niltonil))] is set
{X,(S + (niltonil - niltonil))} is set
{{X,(S + (niltonil - niltonil))},{X}} is set
the addF of V . [X,(S + (niltonil - niltonil))] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
S + (0. V) is right_complementable Element of the carrier of V
the addF of V . (S,(0. V)) is right_complementable Element of the carrier of V
[S,(0. V)] is set
{S,(0. V)} is set
{{S,(0. V)},{S}} is set
the addF of V . [S,(0. V)] is set
X + (S + (0. V)) is right_complementable Element of the carrier of V
the addF of V . (X,(S + (0. V))) is right_complementable Element of the carrier of V
[X,(S + (0. V))] is set
{X,(S + (0. V))} is set
{{X,(S + (0. V))},{X}} is set
the addF of V . [X,(S + (0. V))] is set
CNS is set
S is right_complementable Element of the carrier of V
(X + niltonil) + S is right_complementable Element of the carrier of V
the addF of V . ((X + niltonil),S) is right_complementable Element of the carrier of V
[(X + niltonil),S] is set
{(X + niltonil),S} is set
{(X + niltonil)} is non empty trivial 1 -element set
{{(X + niltonil),S},{(X + niltonil)}} is set
the addF of V . [(X + niltonil),S] is set
niltonil + S is right_complementable Element of the carrier of V
the addF of V . (niltonil,S) is right_complementable Element of the carrier of V
[niltonil,S] is set
{niltonil,S} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,S},{niltonil}} is set
the addF of V . [niltonil,S] is set
X + (niltonil + S) is right_complementable Element of the carrier of V
the addF of V . (X,(niltonil + S)) is right_complementable Element of the carrier of V
[X,(niltonil + S)] is set
{X,(niltonil + S)} is set
{{X,(niltonil + S)},{X}} is set
the addF of V . [X,(niltonil + S)] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
X + (0. V) is right_complementable Element of the carrier of V
the addF of V . (X,(0. V)) is right_complementable Element of the carrier of V
[X,(0. V)] is set
{X,(0. V)} is set
{{X,(0. V)},{X}} is set
the addF of V . [X,(0. V)] is set
CNS is right_complementable Element of the carrier of V
(X + niltonil) + CNS is right_complementable Element of the carrier of V
the addF of V . ((X + niltonil),CNS) is right_complementable Element of the carrier of V
[(X + niltonil),CNS] is set
{(X + niltonil),CNS} is set
{(X + niltonil)} is non empty trivial 1 -element set
{{(X + niltonil),CNS},{(X + niltonil)}} is set
the addF of V . [(X + niltonil),CNS] is set
niltonil + CNS is right_complementable Element of the carrier of V
the addF of V . (niltonil,CNS) is right_complementable Element of the carrier of V
[niltonil,CNS] is set
{niltonil,CNS} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,CNS},{niltonil}} is set
the addF of V . [niltonil,CNS] is set
X + (niltonil + CNS) is right_complementable Element of the carrier of V
the addF of V . (X,(niltonil + CNS)) is right_complementable Element of the carrier of V
[X,(niltonil + CNS)] is set
{X,(niltonil + CNS)} is set
{{X,(niltonil + CNS)},{X}} is set
the addF of V . [X,(niltonil + CNS)] is set
- CNS is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
X - niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X + (- niltonil) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,(- niltonil)) is right_complementable Element of the carrier of V
[X,(- niltonil)] is set
{X,(- niltonil)} is set
{X} is non empty trivial 1 -element set
{{X,(- niltonil)},{X}} is set
the addF of V . [X,(- niltonil)] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,(X - niltonil),z) is Element of bool the carrier of V
{ ((X - niltonil) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
- (- niltonil) is right_complementable Element of the carrier of V
X + (- niltonil) is right_complementable Element of the carrier of V
(V,(X + (- niltonil)),z) is Element of bool the carrier of V
{ ((X + (- niltonil)) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,niltonil,z) is Element of bool the carrier of V
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is right_complementable Element of the carrier of V
X + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,CNS) is right_complementable Element of the carrier of V
[X,CNS] is set
{X,CNS} is set
{X} is non empty trivial 1 -element set
{{X,CNS},{X}} is set
the addF of V . [X,CNS] is set
S is set
g is right_complementable Element of the carrier of V
X + g is right_complementable Element of the carrier of V
the addF of V . (X,g) is right_complementable Element of the carrier of V
[X,g] is set
{X,g} is set
{{X,g},{X}} is set
the addF of V . [X,g] is set
niltonil - CNS is right_complementable Element of the carrier of V
- CNS is right_complementable Element of the carrier of V
niltonil + (- CNS) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- CNS)) is right_complementable Element of the carrier of V
[niltonil,(- CNS)] is set
{niltonil,(- CNS)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- CNS)},{niltonil}} is set
the addF of V . [niltonil,(- CNS)] is set
CNS - CNS is right_complementable Element of the carrier of V
CNS + (- CNS) is right_complementable Element of the carrier of V
the addF of V . (CNS,(- CNS)) is right_complementable Element of the carrier of V
[CNS,(- CNS)] is set
{CNS,(- CNS)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- CNS)},{CNS}} is set
the addF of V . [CNS,(- CNS)] is set
X + (CNS - CNS) is right_complementable Element of the carrier of V
the addF of V . (X,(CNS - CNS)) is right_complementable Element of the carrier of V
[X,(CNS - CNS)] is set
{X,(CNS - CNS)} is set
{{X,(CNS - CNS)},{X}} is set
the addF of V . [X,(CNS - CNS)] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
X + (0. V) is right_complementable Element of the carrier of V
the addF of V . (X,(0. V)) is right_complementable Element of the carrier of V
[X,(0. V)] is set
{X,(0. V)} is set
{{X,(0. V)},{X}} is set
the addF of V . [X,(0. V)] is set
g + (- CNS) is right_complementable Element of the carrier of V
the addF of V . (g,(- CNS)) is right_complementable Element of the carrier of V
[g,(- CNS)] is set
{g,(- CNS)} is set
{g} is non empty trivial 1 -element set
{{g,(- CNS)},{g}} is set
the addF of V . [g,(- CNS)] is set
niltonil + (g + (- CNS)) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(g + (- CNS))) is right_complementable Element of the carrier of V
[niltonil,(g + (- CNS))] is set
{niltonil,(g + (- CNS))} is set
{{niltonil,(g + (- CNS))},{niltonil}} is set
the addF of V . [niltonil,(g + (- CNS))] is set
g - CNS is right_complementable Element of the carrier of V
g + (- CNS) is right_complementable Element of the carrier of V
niltonil + (g - CNS) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(g - CNS)) is right_complementable Element of the carrier of V
[niltonil,(g - CNS)] is set
{niltonil,(g - CNS)} is set
{{niltonil,(g - CNS)},{niltonil}} is set
the addF of V . [niltonil,(g - CNS)] is set
S is set
g is right_complementable Element of the carrier of V
niltonil + g is right_complementable Element of the carrier of V
the addF of V . (niltonil,g) is right_complementable Element of the carrier of V
[niltonil,g] is set
{niltonil,g} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,g},{niltonil}} is set
the addF of V . [niltonil,g] is set
CNS + g is right_complementable Element of the carrier of V
the addF of V . (CNS,g) is right_complementable Element of the carrier of V
[CNS,g] is set
{CNS,g} is set
{CNS} is non empty trivial 1 -element set
{{CNS,g},{CNS}} is set
the addF of V . [CNS,g] is set
X + (CNS + g) is right_complementable Element of the carrier of V
the addF of V . (X,(CNS + g)) is right_complementable Element of the carrier of V
[X,(CNS + g)] is set
{X,(CNS + g)} is set
{{X,(CNS + g)},{X}} is set
the addF of V . [X,(CNS + g)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
(V,(- niltonil),X) is Element of bool the carrier of V
{ ((- niltonil) + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
z is right_complementable Element of the carrier of V
(- niltonil) + z is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((- niltonil),z) is right_complementable Element of the carrier of V
[(- niltonil),z] is set
{(- niltonil),z} is set
{(- niltonil)} is non empty trivial 1 -element set
{{(- niltonil),z},{(- niltonil)}} is set
the addF of V . [(- niltonil),z] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
niltonil - ((- niltonil) + z) is right_complementable Element of the carrier of V
- ((- niltonil) + z) is right_complementable Element of the carrier of V
niltonil + (- ((- niltonil) + z)) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- ((- niltonil) + z))) is right_complementable Element of the carrier of V
[niltonil,(- ((- niltonil) + z))] is set
{niltonil,(- ((- niltonil) + z))} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- ((- niltonil) + z))},{niltonil}} is set
the addF of V . [niltonil,(- ((- niltonil) + z))] is set
niltonil - (- niltonil) is right_complementable Element of the carrier of V
- (- niltonil) is right_complementable Element of the carrier of V
niltonil + (- (- niltonil)) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- (- niltonil))) is right_complementable Element of the carrier of V
[niltonil,(- (- niltonil))] is set
{niltonil,(- (- niltonil))} is set
{{niltonil,(- (- niltonil))},{niltonil}} is set
the addF of V . [niltonil,(- (- niltonil))] is set
(niltonil - (- niltonil)) - z is right_complementable Element of the carrier of V
- z is right_complementable Element of the carrier of V
(niltonil - (- niltonil)) + (- z) is right_complementable Element of the carrier of V
the addF of V . ((niltonil - (- niltonil)),(- z)) is right_complementable Element of the carrier of V
[(niltonil - (- niltonil)),(- z)] is set
{(niltonil - (- niltonil)),(- z)} is set
{(niltonil - (- niltonil))} is non empty trivial 1 -element set
{{(niltonil - (- niltonil)),(- z)},{(niltonil - (- niltonil))}} is set
the addF of V . [(niltonil - (- niltonil)),(- z)] is set
niltonil + niltonil is right_complementable Element of the carrier of V
the addF of V . (niltonil,niltonil) is right_complementable Element of the carrier of V
[niltonil,niltonil] is set
{niltonil,niltonil} is set
{{niltonil,niltonil},{niltonil}} is set
the addF of V . [niltonil,niltonil] is set
(niltonil + niltonil) - z is right_complementable Element of the carrier of V
(niltonil + niltonil) + (- z) is right_complementable Element of the carrier of V
the addF of V . ((niltonil + niltonil),(- z)) is right_complementable Element of the carrier of V
[(niltonil + niltonil),(- z)] is set
{(niltonil + niltonil),(- z)} is set
{(niltonil + niltonil)} is non empty trivial 1 -element set
{{(niltonil + niltonil),(- z)},{(niltonil + niltonil)}} is set
the addF of V . [(niltonil + niltonil),(- z)] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,1r) + niltonil is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),niltonil) is right_complementable Element of the carrier of V
[(V,niltonil,1r),niltonil] is set
{(V,niltonil,1r),niltonil} is set
{(V,niltonil,1r)} is non empty trivial 1 -element set
{{(V,niltonil,1r),niltonil},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),niltonil] is set
((V,niltonil,1r) + niltonil) - z is right_complementable Element of the carrier of V
((V,niltonil,1r) + niltonil) + (- z) is right_complementable Element of the carrier of V
the addF of V . (((V,niltonil,1r) + niltonil),(- z)) is right_complementable Element of the carrier of V
[((V,niltonil,1r) + niltonil),(- z)] is set
{((V,niltonil,1r) + niltonil),(- z)} is set
{((V,niltonil,1r) + niltonil)} is non empty trivial 1 -element set
{{((V,niltonil,1r) + niltonil),(- z)},{((V,niltonil,1r) + niltonil)}} is set
the addF of V . [((V,niltonil,1r) + niltonil),(- z)] is set
(V,niltonil,1r) + (V,niltonil,1r) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,1r),(V,niltonil,1r)) is right_complementable Element of the carrier of V
[(V,niltonil,1r),(V,niltonil,1r)] is set
{(V,niltonil,1r),(V,niltonil,1r)} is set
{{(V,niltonil,1r),(V,niltonil,1r)},{(V,niltonil,1r)}} is set
the addF of V . [(V,niltonil,1r),(V,niltonil,1r)] is set
((V,niltonil,1r) + (V,niltonil,1r)) - z is right_complementable Element of the carrier of V
((V,niltonil,1r) + (V,niltonil,1r)) + (- z) is right_complementable Element of the carrier of V
the addF of V . (((V,niltonil,1r) + (V,niltonil,1r)),(- z)) is right_complementable Element of the carrier of V
[((V,niltonil,1r) + (V,niltonil,1r)),(- z)] is set
{((V,niltonil,1r) + (V,niltonil,1r)),(- z)} is set
{((V,niltonil,1r) + (V,niltonil,1r))} is non empty trivial 1 -element set
{{((V,niltonil,1r) + (V,niltonil,1r)),(- z)},{((V,niltonil,1r) + (V,niltonil,1r))}} is set
the addF of V . [((V,niltonil,1r) + (V,niltonil,1r)),(- z)] is set
(V,niltonil,(1r + 1r)) is right_complementable Element of the carrier of V
[(1r + 1r),niltonil] is set
{(1r + 1r),niltonil} is set
{(1r + 1r)} is non empty trivial 1 -element set
{{(1r + 1r),niltonil},{(1r + 1r)}} is set
the of V . [(1r + 1r),niltonil] is set
(V,niltonil,(1r + 1r)) - z is right_complementable Element of the carrier of V
(V,niltonil,(1r + 1r)) + (- z) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,(1r + 1r)),(- z)) is right_complementable Element of the carrier of V
[(V,niltonil,(1r + 1r)),(- z)] is set
{(V,niltonil,(1r + 1r)),(- z)} is set
{(V,niltonil,(1r + 1r))} is non empty trivial 1 -element set
{{(V,niltonil,(1r + 1r)),(- z)},{(V,niltonil,(1r + 1r))}} is set
the addF of V . [(V,niltonil,(1r + 1r)),(- z)] is set
(1r + 1r) " is complex Element of COMPLEX
(V,(V,niltonil,(1r + 1r)),((1r + 1r) ")) is right_complementable Element of the carrier of V
[((1r + 1r) "),(V,niltonil,(1r + 1r))] is set
{((1r + 1r) "),(V,niltonil,(1r + 1r))} is set
{((1r + 1r) ")} is non empty trivial 1 -element set
{{((1r + 1r) "),(V,niltonil,(1r + 1r))},{((1r + 1r) ")}} is set
the of V . [((1r + 1r) "),(V,niltonil,(1r + 1r))] is set
(V,z,((1r + 1r) ")) is right_complementable Element of the carrier of V
[((1r + 1r) "),z] is set
{((1r + 1r) "),z} is set
{{((1r + 1r) "),z},{((1r + 1r) ")}} is set
the of V . [((1r + 1r) "),z] is set
((1r + 1r) ") * (1r + 1r) is complex Element of COMPLEX
(V,niltonil,(((1r + 1r) ") * (1r + 1r))) is right_complementable Element of the carrier of V
[(((1r + 1r) ") * (1r + 1r)),niltonil] is set
{(((1r + 1r) ") * (1r + 1r)),niltonil} is set
{(((1r + 1r) ") * (1r + 1r))} is non empty trivial 1 -element set
{{(((1r + 1r) ") * (1r + 1r)),niltonil},{(((1r + 1r) ") * (1r + 1r))}} is set
the of V . [(((1r + 1r) ") * (1r + 1r)),niltonil] is set
the carrier of X is non empty set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is right_complementable Element of the carrier of V
CNS is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,CNS) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in CNS } is set
(V,z,CNS) is Element of bool the carrier of V
{ (z + b1) where b1 is right_complementable Element of the carrier of V : b1 in CNS } is set
S is right_complementable Element of the carrier of V
X + S is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,S) is right_complementable Element of the carrier of V
[X,S] is set
{X,S} is set
{X} is non empty trivial 1 -element set
{{X,S},{X}} is set
the addF of V . [X,S] is set
g is right_complementable Element of the carrier of V
z + g is right_complementable Element of the carrier of V
the addF of V . (z,g) is right_complementable Element of the carrier of V
[z,g] is set
{z,g} is set
{z} is non empty trivial 1 -element set
{{z,g},{z}} is set
the addF of V . [z,g] is set
h is set
r is right_complementable Element of the carrier of V
X + r is right_complementable Element of the carrier of V
the addF of V . (X,r) is right_complementable Element of the carrier of V
[X,r] is set
{X,r} is set
{{X,r},{X}} is set
the addF of V . [X,r] is set
g - S is right_complementable Element of the carrier of V
- S is right_complementable Element of the carrier of V
g + (- S) is right_complementable Element of the carrier of V
the addF of V . (g,(- S)) is right_complementable Element of the carrier of V
[g,(- S)] is set
{g,(- S)} is set
{g} is non empty trivial 1 -element set
{{g,(- S)},{g}} is set
the addF of V . [g,(- S)] is set
(g - S) + r is right_complementable Element of the carrier of V
the addF of V . ((g - S),r) is right_complementable Element of the carrier of V
[(g - S),r] is set
{(g - S),r} is set
{(g - S)} is non empty trivial 1 -element set
{{(g - S),r},{(g - S)}} is set
the addF of V . [(g - S),r] is set
niltonil - S is right_complementable Element of the carrier of V
niltonil + (- S) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- S)) is right_complementable Element of the carrier of V
[niltonil,(- S)] is set
{niltonil,(- S)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- S)},{niltonil}} is set
the addF of V . [niltonil,(- S)] is set
S - S is right_complementable Element of the carrier of V
S + (- S) is right_complementable Element of the carrier of V
the addF of V . (S,(- S)) is right_complementable Element of the carrier of V
[S,(- S)] is set
{S,(- S)} is set
{S} is non empty trivial 1 -element set
{{S,(- S)},{S}} is set
the addF of V . [S,(- S)] is set
X + (S - S) is right_complementable Element of the carrier of V
the addF of V . (X,(S - S)) is right_complementable Element of the carrier of V
[X,(S - S)] is set
{X,(S - S)} is set
{{X,(S - S)},{X}} is set
the addF of V . [X,(S - S)] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
X + (0. V) is right_complementable Element of the carrier of V
the addF of V . (X,(0. V)) is right_complementable Element of the carrier of V
[X,(0. V)] is set
{X,(0. V)} is set
{{X,(0. V)},{X}} is set
the addF of V . [X,(0. V)] is set
z + (g - S) is right_complementable Element of the carrier of V
the addF of V . (z,(g - S)) is right_complementable Element of the carrier of V
[z,(g - S)] is set
{z,(g - S)} is set
{{z,(g - S)},{z}} is set
the addF of V . [z,(g - S)] is set
(z + (g - S)) + r is right_complementable Element of the carrier of V
the addF of V . ((z + (g - S)),r) is right_complementable Element of the carrier of V
[(z + (g - S)),r] is set
{(z + (g - S)),r} is set
{(z + (g - S))} is non empty trivial 1 -element set
{{(z + (g - S)),r},{(z + (g - S))}} is set
the addF of V . [(z + (g - S)),r] is set
z + ((g - S) + r) is right_complementable Element of the carrier of V
the addF of V . (z,((g - S) + r)) is right_complementable Element of the carrier of V
[z,((g - S) + r)] is set
{z,((g - S) + r)} is set
{{z,((g - S) + r)},{z}} is set
the addF of V . [z,((g - S) + r)] is set
h is set
r is right_complementable Element of the carrier of V
z + r is right_complementable Element of the carrier of V
the addF of V . (z,r) is right_complementable Element of the carrier of V
[z,r] is set
{z,r} is set
{{z,r},{z}} is set
the addF of V . [z,r] is set
S - g is right_complementable Element of the carrier of V
- g is right_complementable Element of the carrier of V
S + (- g) is right_complementable Element of the carrier of V
the addF of V . (S,(- g)) is right_complementable Element of the carrier of V
[S,(- g)] is set
{S,(- g)} is set
{S} is non empty trivial 1 -element set
{{S,(- g)},{S}} is set
the addF of V . [S,(- g)] is set
(S - g) + r is right_complementable Element of the carrier of V
the addF of V . ((S - g),r) is right_complementable Element of the carrier of V
[(S - g),r] is set
{(S - g),r} is set
{(S - g)} is non empty trivial 1 -element set
{{(S - g),r},{(S - g)}} is set
the addF of V . [(S - g),r] is set
niltonil - g is right_complementable Element of the carrier of V
niltonil + (- g) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- g)) is right_complementable Element of the carrier of V
[niltonil,(- g)] is set
{niltonil,(- g)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- g)},{niltonil}} is set
the addF of V . [niltonil,(- g)] is set
g - g is right_complementable Element of the carrier of V
g + (- g) is right_complementable Element of the carrier of V
the addF of V . (g,(- g)) is right_complementable Element of the carrier of V
[g,(- g)] is set
{g,(- g)} is set
{g} is non empty trivial 1 -element set
{{g,(- g)},{g}} is set
the addF of V . [g,(- g)] is set
z + (g - g) is right_complementable Element of the carrier of V
the addF of V . (z,(g - g)) is right_complementable Element of the carrier of V
[z,(g - g)] is set
{z,(g - g)} is set
{{z,(g - g)},{z}} is set
the addF of V . [z,(g - g)] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
z + (0. V) is right_complementable Element of the carrier of V
the addF of V . (z,(0. V)) is right_complementable Element of the carrier of V
[z,(0. V)] is set
{z,(0. V)} is set
{{z,(0. V)},{z}} is set
the addF of V . [z,(0. V)] is set
X + (S - g) is right_complementable Element of the carrier of V
the addF of V . (X,(S - g)) is right_complementable Element of the carrier of V
[X,(S - g)] is set
{X,(S - g)} is set
{{X,(S - g)},{X}} is set
the addF of V . [X,(S - g)] is set
(X + (S - g)) + r is right_complementable Element of the carrier of V
the addF of V . ((X + (S - g)),r) is right_complementable Element of the carrier of V
[(X + (S - g)),r] is set
{(X + (S - g)),r} is set
{(X + (S - g))} is non empty trivial 1 -element set
{{(X + (S - g)),r},{(X + (S - g))}} is set
the addF of V . [(X + (S - g)),r] is set
X + ((S - g) + r) is right_complementable Element of the carrier of V
the addF of V . (X,((S - g) + r)) is right_complementable Element of the carrier of V
[X,((S - g) + r)] is set
{X,((S - g) + r)} is set
{{X,((S - g) + r)},{X}} is set
the addF of V . [X,((S - g) + r)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,(- X),z) is Element of bool the carrier of V
{ ((- X) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
X - 1r is complex set
CNS is right_complementable Element of the carrier of V
niltonil + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,CNS) is right_complementable Element of the carrier of V
[niltonil,CNS] is set
{niltonil,CNS} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,CNS},{niltonil}} is set
the addF of V . [niltonil,CNS] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
CNS + (0. V) is right_complementable Element of the carrier of V
the addF of V . (CNS,(0. V)) is right_complementable Element of the carrier of V
[CNS,(0. V)] is set
{CNS,(0. V)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(0. V)},{CNS}} is set
the addF of V . [CNS,(0. V)] is set
niltonil - niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
niltonil + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- niltonil)) is right_complementable Element of the carrier of V
[niltonil,(- niltonil)] is set
{niltonil,(- niltonil)} is set
{{niltonil,(- niltonil)},{niltonil}} is set
the addF of V . [niltonil,(- niltonil)] is set
CNS + (niltonil - niltonil) is right_complementable Element of the carrier of V
the addF of V . (CNS,(niltonil - niltonil)) is right_complementable Element of the carrier of V
[CNS,(niltonil - niltonil)] is set
{CNS,(niltonil - niltonil)} is set
{{CNS,(niltonil - niltonil)},{CNS}} is set
the addF of V . [CNS,(niltonil - niltonil)] is set
(V,niltonil,X) - niltonil is right_complementable Element of the carrier of V
(V,niltonil,X) + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,X),(- niltonil)) is right_complementable Element of the carrier of V
[(V,niltonil,X),(- niltonil)] is set
{(V,niltonil,X),(- niltonil)} is set
{(V,niltonil,X)} is non empty trivial 1 -element set
{{(V,niltonil,X),(- niltonil)},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(- niltonil)] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,X) - (V,niltonil,1r) is right_complementable Element of the carrier of V
- (V,niltonil,1r) is right_complementable Element of the carrier of V
(V,niltonil,X) + (- (V,niltonil,1r)) is right_complementable Element of the carrier of V
the addF of V . ((V,niltonil,X),(- (V,niltonil,1r))) is right_complementable Element of the carrier of V
[(V,niltonil,X),(- (V,niltonil,1r))] is set
{(V,niltonil,X),(- (V,niltonil,1r))} is set
{{(V,niltonil,X),(- (V,niltonil,1r))},{(V,niltonil,X)}} is set
the addF of V . [(V,niltonil,X),(- (V,niltonil,1r))] is set
(V,niltonil,(X - 1r)) is right_complementable Element of the carrier of V
[(X - 1r),niltonil] is set
{(X - 1r),niltonil} is set
{(X - 1r)} is non empty trivial 1 -element set
{{(X - 1r),niltonil},{(X - 1r)}} is set
the of V . [(X - 1r),niltonil] is set
(X - 1r) " is complex set
(V,CNS,((X - 1r) ")) is right_complementable Element of the carrier of V
[((X - 1r) "),CNS] is set
{((X - 1r) "),CNS} is set
{((X - 1r) ")} is non empty trivial 1 -element set
{{((X - 1r) "),CNS},{((X - 1r) ")}} is set
the of V . [((X - 1r) "),CNS] is set
((X - 1r) ") * (X - 1r) is complex set
(V,niltonil,(((X - 1r) ") * (X - 1r))) is right_complementable Element of the carrier of V
[(((X - 1r) ") * (X - 1r)),niltonil] is set
{(((X - 1r) ") * (X - 1r)),niltonil} is set
{(((X - 1r) ") * (X - 1r))} is non empty trivial 1 -element set
{{(((X - 1r) ") * (X - 1r)),niltonil},{(((X - 1r) ") * (X - 1r))}} is set
the of V . [(((X - 1r) ") * (X - 1r)),niltonil] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is complex set
(V,niltonil,X) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[X,niltonil] is set
{X,niltonil} is set
{X} is non empty trivial 1 -element set
{{X,niltonil},{X}} is set
the of V . [X,niltonil] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
X - 1r is complex set
(V,niltonil,(X - 1r)) is right_complementable Element of the carrier of V
[(X - 1r),niltonil] is set
{(X - 1r),niltonil} is set
{(X - 1r)} is non empty trivial 1 -element set
{{(X - 1r),niltonil},{(X - 1r)}} is set
the of V . [(X - 1r),niltonil] is set
(X - 1r) + 1r is complex set
(V,niltonil,((X - 1r) + 1r)) is right_complementable Element of the carrier of V
[((X - 1r) + 1r),niltonil] is set
{((X - 1r) + 1r),niltonil} is set
{((X - 1r) + 1r)} is non empty trivial 1 -element set
{{((X - 1r) + 1r),niltonil},{((X - 1r) + 1r)}} is set
the of V . [((X - 1r) + 1r),niltonil] is set
(V,niltonil,1r) is right_complementable Element of the carrier of V
[1r,niltonil] is set
{1r,niltonil} is set
{1r} is non empty trivial 1 -element set
{{1r,niltonil},{1r}} is set
the of V . [1r,niltonil] is set
(V,niltonil,(X - 1r)) + (V,niltonil,1r) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . ((V,niltonil,(X - 1r)),(V,niltonil,1r)) is right_complementable Element of the carrier of V
[(V,niltonil,(X - 1r)),(V,niltonil,1r)] is set
{(V,niltonil,(X - 1r)),(V,niltonil,1r)} is set
{(V,niltonil,(X - 1r))} is non empty trivial 1 -element set
{{(V,niltonil,(X - 1r)),(V,niltonil,1r)},{(V,niltonil,(X - 1r))}} is set
the addF of V . [(V,niltonil,(X - 1r)),(V,niltonil,1r)] is set
niltonil + (V,niltonil,(X - 1r)) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(V,niltonil,(X - 1r))) is right_complementable Element of the carrier of V
[niltonil,(V,niltonil,(X - 1r))] is set
{niltonil,(V,niltonil,(X - 1r))} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(V,niltonil,(X - 1r))},{niltonil}} is set
the addF of V . [niltonil,(V,niltonil,(X - 1r))] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
(V,niltonil,(- 1r)) is right_complementable Element of the carrier of V
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
[(- 1r),niltonil] is set
{(- 1r),niltonil} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),niltonil},{(- 1r)}} is set
the of V . [(- 1r),niltonil] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil + X is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,X) is right_complementable Element of the carrier of V
[niltonil,X] is set
{niltonil,X} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,X},{niltonil}} is set
the addF of V . [niltonil,X] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is right_complementable Element of the carrier of V
X + CNS is right_complementable Element of the carrier of V
the addF of V . (X,CNS) is right_complementable Element of the carrier of V
[X,CNS] is set
{X,CNS} is set
{X} is non empty trivial 1 -element set
{{X,CNS},{X}} is set
the addF of V . [X,CNS] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(- X) + niltonil is right_complementable Element of the carrier of V
the addF of V . ((- X),niltonil) is right_complementable Element of the carrier of V
[(- X),niltonil] is set
{(- X),niltonil} is set
{(- X)} is non empty trivial 1 -element set
{{(- X),niltonil},{(- X)}} is set
the addF of V . [(- X),niltonil] is set
- (- X) is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is right_complementable Element of the carrier of V
X + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,CNS) is right_complementable Element of the carrier of V
[X,CNS] is set
{X,CNS} is set
{X} is non empty trivial 1 -element set
{{X,CNS},{X}} is set
the addF of V . [X,CNS] is set
CNS is right_complementable Element of the carrier of V
X + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,CNS) is right_complementable Element of the carrier of V
[X,CNS] is set
{X,CNS} is set
{X} is non empty trivial 1 -element set
{{X,CNS},{X}} is set
the addF of V . [X,CNS] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,X,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is right_complementable Element of the carrier of V
X + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,CNS) is right_complementable Element of the carrier of V
[X,CNS] is set
{X,CNS} is set
{X} is non empty trivial 1 -element set
{{X,CNS},{X}} is set
the addF of V . [X,CNS] is set
- CNS is right_complementable Element of the carrier of V
S is right_complementable Element of the carrier of V
X - S is right_complementable Element of the carrier of V
- S is right_complementable Element of the carrier of V
X + (- S) is right_complementable Element of the carrier of V
the addF of V . (X,(- S)) is right_complementable Element of the carrier of V
[X,(- S)] is set
{X,(- S)} is set
{{X,(- S)},{X}} is set
the addF of V . [X,(- S)] is set
CNS is right_complementable Element of the carrier of V
X - CNS is right_complementable Element of the carrier of V
- CNS is right_complementable Element of the carrier of V
X + (- CNS) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,(- CNS)) is right_complementable Element of the carrier of V
[X,(- CNS)] is set
{X,(- CNS)} is set
{X} is non empty trivial 1 -element set
{{X,(- CNS)},{X}} is set
the addF of V . [X,(- CNS)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
CNS is right_complementable Element of the carrier of V
(V,CNS,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (CNS + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
S is right_complementable Element of the carrier of V
CNS + S is right_complementable Element of the carrier of V
the addF of V . (CNS,S) is right_complementable Element of the carrier of V
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the addF of V . [CNS,S] is set
g is right_complementable Element of the carrier of V
CNS + g is right_complementable Element of the carrier of V
the addF of V . (CNS,g) is right_complementable Element of the carrier of V
[CNS,g] is set
{CNS,g} is set
{{CNS,g},{CNS}} is set
the addF of V . [CNS,g] is set
g + CNS is right_complementable Element of the carrier of V
the addF of V . (g,CNS) is right_complementable Element of the carrier of V
[g,CNS] is set
{g,CNS} is set
{g} is non empty trivial 1 -element set
{{g,CNS},{g}} is set
the addF of V . [g,CNS] is set
- CNS is right_complementable Element of the carrier of V
(- CNS) - S is right_complementable Element of the carrier of V
- S is right_complementable Element of the carrier of V
(- CNS) + (- S) is right_complementable Element of the carrier of V
the addF of V . ((- CNS),(- S)) is right_complementable Element of the carrier of V
[(- CNS),(- S)] is set
{(- CNS),(- S)} is set
{(- CNS)} is non empty trivial 1 -element set
{{(- CNS),(- S)},{(- CNS)}} is set
the addF of V . [(- CNS),(- S)] is set
(g + CNS) + ((- CNS) - S) is right_complementable Element of the carrier of V
the addF of V . ((g + CNS),((- CNS) - S)) is right_complementable Element of the carrier of V
[(g + CNS),((- CNS) - S)] is set
{(g + CNS),((- CNS) - S)} is set
{(g + CNS)} is non empty trivial 1 -element set
{{(g + CNS),((- CNS) - S)},{(g + CNS)}} is set
the addF of V . [(g + CNS),((- CNS) - S)] is set
(g + CNS) + (- CNS) is right_complementable Element of the carrier of V
the addF of V . ((g + CNS),(- CNS)) is right_complementable Element of the carrier of V
[(g + CNS),(- CNS)] is set
{(g + CNS),(- CNS)} is set
{{(g + CNS),(- CNS)},{(g + CNS)}} is set
the addF of V . [(g + CNS),(- CNS)] is set
((g + CNS) + (- CNS)) - S is right_complementable Element of the carrier of V
((g + CNS) + (- CNS)) + (- S) is right_complementable Element of the carrier of V
the addF of V . (((g + CNS) + (- CNS)),(- S)) is right_complementable Element of the carrier of V
[((g + CNS) + (- CNS)),(- S)] is set
{((g + CNS) + (- CNS)),(- S)} is set
{((g + CNS) + (- CNS))} is non empty trivial 1 -element set
{{((g + CNS) + (- CNS)),(- S)},{((g + CNS) + (- CNS))}} is set
the addF of V . [((g + CNS) + (- CNS)),(- S)] is set
CNS + (- CNS) is right_complementable Element of the carrier of V
the addF of V . (CNS,(- CNS)) is right_complementable Element of the carrier of V
[CNS,(- CNS)] is set
{CNS,(- CNS)} is set
{{CNS,(- CNS)},{CNS}} is set
the addF of V . [CNS,(- CNS)] is set
g + (CNS + (- CNS)) is right_complementable Element of the carrier of V
the addF of V . (g,(CNS + (- CNS))) is right_complementable Element of the carrier of V
[g,(CNS + (- CNS))] is set
{g,(CNS + (- CNS))} is set
{{g,(CNS + (- CNS))},{g}} is set
the addF of V . [g,(CNS + (- CNS))] is set
(g + (CNS + (- CNS))) - S is right_complementable Element of the carrier of V
(g + (CNS + (- CNS))) + (- S) is right_complementable Element of the carrier of V
the addF of V . ((g + (CNS + (- CNS))),(- S)) is right_complementable Element of the carrier of V
[(g + (CNS + (- CNS))),(- S)] is set
{(g + (CNS + (- CNS))),(- S)} is set
{(g + (CNS + (- CNS)))} is non empty trivial 1 -element set
{{(g + (CNS + (- CNS))),(- S)},{(g + (CNS + (- CNS)))}} is set
the addF of V . [(g + (CNS + (- CNS))),(- S)] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
g + (0. V) is right_complementable Element of the carrier of V
the addF of V . (g,(0. V)) is right_complementable Element of the carrier of V
[g,(0. V)] is set
{g,(0. V)} is set
{{g,(0. V)},{g}} is set
the addF of V . [g,(0. V)] is set
(g + (0. V)) - S is right_complementable Element of the carrier of V
(g + (0. V)) + (- S) is right_complementable Element of the carrier of V
the addF of V . ((g + (0. V)),(- S)) is right_complementable Element of the carrier of V
[(g + (0. V)),(- S)] is set
{(g + (0. V)),(- S)} is set
{(g + (0. V))} is non empty trivial 1 -element set
{{(g + (0. V)),(- S)},{(g + (0. V))}} is set
the addF of V . [(g + (0. V)),(- S)] is set
g - S is right_complementable Element of the carrier of V
g + (- S) is right_complementable Element of the carrier of V
the addF of V . (g,(- S)) is right_complementable Element of the carrier of V
[g,(- S)] is set
{g,(- S)} is set
{{g,(- S)},{g}} is set
the addF of V . [g,(- S)] is set
- (niltonil - X) is right_complementable Element of the carrier of V
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
niltonil + (- (niltonil - X)) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- (niltonil - X))) is right_complementable Element of the carrier of V
[niltonil,(- (niltonil - X))] is set
{niltonil,(- (niltonil - X))} is set
{{niltonil,(- (niltonil - X))},{niltonil}} is set
the addF of V . [niltonil,(- (niltonil - X))] is set
- niltonil is right_complementable Element of the carrier of V
(- niltonil) + X is right_complementable Element of the carrier of V
the addF of V . ((- niltonil),X) is right_complementable Element of the carrier of V
[(- niltonil),X] is set
{(- niltonil),X} is set
{(- niltonil)} is non empty trivial 1 -element set
{{(- niltonil),X},{(- niltonil)}} is set
the addF of V . [(- niltonil),X] is set
niltonil + ((- niltonil) + X) is right_complementable Element of the carrier of V
the addF of V . (niltonil,((- niltonil) + X)) is right_complementable Element of the carrier of V
[niltonil,((- niltonil) + X)] is set
{niltonil,((- niltonil) + X)} is set
{{niltonil,((- niltonil) + X)},{niltonil}} is set
the addF of V . [niltonil,((- niltonil) + X)] is set
niltonil + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- niltonil)) is right_complementable Element of the carrier of V
[niltonil,(- niltonil)] is set
{niltonil,(- niltonil)} is set
{{niltonil,(- niltonil)},{niltonil}} is set
the addF of V . [niltonil,(- niltonil)] is set
(niltonil + (- niltonil)) + X is right_complementable Element of the carrier of V
the addF of V . ((niltonil + (- niltonil)),X) is right_complementable Element of the carrier of V
[(niltonil + (- niltonil)),X] is set
{(niltonil + (- niltonil)),X} is set
{(niltonil + (- niltonil))} is non empty trivial 1 -element set
{{(niltonil + (- niltonil)),X},{(niltonil + (- niltonil))}} is set
the addF of V . [(niltonil + (- niltonil)),X] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(0. V) + X is right_complementable Element of the carrier of V
the addF of V . ((0. V),X) is right_complementable Element of the carrier of V
[(0. V),X] is set
{(0. V),X} is set
{(0. V)} is non empty trivial 1 -element set
{{(0. V),X},{(0. V)}} is set
the addF of V . [(0. V),X] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,X,z) is Element of bool the carrier of V
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is right_complementable Element of the carrier of V
X + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (X,CNS) is right_complementable Element of the carrier of V
[X,CNS] is set
{X,CNS} is set
{X} is non empty trivial 1 -element set
{{X,CNS},{X}} is set
the addF of V . [X,CNS] is set
X - niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
X + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (X,(- niltonil)) is right_complementable Element of the carrier of V
[X,(- niltonil)] is set
{X,(- niltonil)} is set
{{X,(- niltonil)},{X}} is set
the addF of V . [X,(- niltonil)] is set
S is right_complementable Element of the carrier of V
niltonil + S is right_complementable Element of the carrier of V
the addF of V . (niltonil,S) is right_complementable Element of the carrier of V
[niltonil,S] is set
{niltonil,S} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,S},{niltonil}} is set
the addF of V . [niltonil,S] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(X + CNS) - niltonil is right_complementable Element of the carrier of V
(X + CNS) + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . ((X + CNS),(- niltonil)) is right_complementable Element of the carrier of V
[(X + CNS),(- niltonil)] is set
{(X + CNS),(- niltonil)} is set
{(X + CNS)} is non empty trivial 1 -element set
{{(X + CNS),(- niltonil)},{(X + CNS)}} is set
the addF of V . [(X + CNS),(- niltonil)] is set
CNS + (X - niltonil) is right_complementable Element of the carrier of V
the addF of V . (CNS,(X - niltonil)) is right_complementable Element of the carrier of V
[CNS,(X - niltonil)] is set
{CNS,(X - niltonil)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(X - niltonil)},{CNS}} is set
the addF of V . [CNS,(X - niltonil)] is set
- CNS is right_complementable Element of the carrier of V
X + niltonil is right_complementable Element of the carrier of V
the addF of V . (X,niltonil) is right_complementable Element of the carrier of V
[X,niltonil] is set
{X,niltonil} is set
{{X,niltonil},{X}} is set
the addF of V . [X,niltonil] is set
(X + niltonil) - niltonil is right_complementable Element of the carrier of V
(X + niltonil) + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . ((X + niltonil),(- niltonil)) is right_complementable Element of the carrier of V
[(X + niltonil),(- niltonil)] is set
{(X + niltonil),(- niltonil)} is set
{(X + niltonil)} is non empty trivial 1 -element set
{{(X + niltonil),(- niltonil)},{(X + niltonil)}} is set
the addF of V . [(X + niltonil),(- niltonil)] is set
niltonil - niltonil is right_complementable Element of the carrier of V
niltonil + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- niltonil)) is right_complementable Element of the carrier of V
[niltonil,(- niltonil)] is set
{niltonil,(- niltonil)} is set
{{niltonil,(- niltonil)},{niltonil}} is set
the addF of V . [niltonil,(- niltonil)] is set
X + (niltonil - niltonil) is right_complementable Element of the carrier of V
the addF of V . (X,(niltonil - niltonil)) is right_complementable Element of the carrier of V
[X,(niltonil - niltonil)] is set
{X,(niltonil - niltonil)} is set
{{X,(niltonil - niltonil)},{X}} is set
the addF of V . [X,(niltonil - niltonil)] is set
X + (0. V) is right_complementable Element of the carrier of V
the addF of V . (X,(0. V)) is right_complementable Element of the carrier of V
[X,(0. V)] is set
{X,(0. V)} is set
{{X,(0. V)},{X}} is set
the addF of V . [X,(0. V)] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,X,z) is Element of bool the carrier of V
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is right_complementable Element of the carrier of V
niltonil + CNS is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,CNS) is right_complementable Element of the carrier of V
[niltonil,CNS] is set
{niltonil,CNS} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,CNS},{niltonil}} is set
the addF of V . [niltonil,CNS] is set
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
S is right_complementable Element of the carrier of V
niltonil - S is right_complementable Element of the carrier of V
- S is right_complementable Element of the carrier of V
niltonil + (- S) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- S)) is right_complementable Element of the carrier of V
[niltonil,(- S)] is set
{niltonil,(- S)} is set
{{niltonil,(- S)},{niltonil}} is set
the addF of V . [niltonil,(- S)] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(niltonil + CNS) - X is right_complementable Element of the carrier of V
(niltonil + CNS) + (- X) is right_complementable Element of the carrier of V
the addF of V . ((niltonil + CNS),(- X)) is right_complementable Element of the carrier of V
[(niltonil + CNS),(- X)] is set
{(niltonil + CNS),(- X)} is set
{(niltonil + CNS)} is non empty trivial 1 -element set
{{(niltonil + CNS),(- X)},{(niltonil + CNS)}} is set
the addF of V . [(niltonil + CNS),(- X)] is set
CNS + (niltonil - X) is right_complementable Element of the carrier of V
the addF of V . (CNS,(niltonil - X)) is right_complementable Element of the carrier of V
[CNS,(niltonil - X)] is set
{CNS,(niltonil - X)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(niltonil - X)},{CNS}} is set
the addF of V . [CNS,(niltonil - X)] is set
- CNS is right_complementable Element of the carrier of V
niltonil - niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
niltonil + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- niltonil)) is right_complementable Element of the carrier of V
[niltonil,(- niltonil)] is set
{niltonil,(- niltonil)} is set
{{niltonil,(- niltonil)},{niltonil}} is set
the addF of V . [niltonil,(- niltonil)] is set
(niltonil - niltonil) + X is right_complementable Element of the carrier of V
the addF of V . ((niltonil - niltonil),X) is right_complementable Element of the carrier of V
[(niltonil - niltonil),X] is set
{(niltonil - niltonil),X} is set
{(niltonil - niltonil)} is non empty trivial 1 -element set
{{(niltonil - niltonil),X},{(niltonil - niltonil)}} is set
the addF of V . [(niltonil - niltonil),X] is set
(0. V) + X is right_complementable Element of the carrier of V
the addF of V . ((0. V),X) is right_complementable Element of the carrier of V
[(0. V),X] is set
{(0. V),X} is set
{(0. V)} is non empty trivial 1 -element set
{{(0. V),X},{(0. V)}} is set
the addF of V . [(0. V),X] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
(V,niltonil,z) is Element of bool the carrier of V
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
the carrier of X is non empty set
the carrier of z is non empty set
CNS is set
S is right_complementable Element of the carrier of V
niltonil + S is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,S) is right_complementable Element of the carrier of V
[niltonil,S] is set
{niltonil,S} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,S},{niltonil}} is set
the addF of V . [niltonil,S] is set
h is right_complementable Element of the carrier of V
niltonil + h is right_complementable Element of the carrier of V
the addF of V . (niltonil,h) is right_complementable Element of the carrier of V
[niltonil,h] is set
{niltonil,h} is set
{{niltonil,h},{niltonil}} is set
the addF of V . [niltonil,h] is set
CNS is set
S is right_complementable Element of the carrier of V
niltonil + S is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,S) is right_complementable Element of the carrier of V
[niltonil,S] is set
{niltonil,S} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,S},{niltonil}} is set
the addF of V . [niltonil,S] is set
h is right_complementable Element of the carrier of V
niltonil + h is right_complementable Element of the carrier of V
the addF of V . (niltonil,h) is right_complementable Element of the carrier of V
[niltonil,h] is set
{niltonil,h} is set
{{niltonil,h},{niltonil}} is set
the addF of V . [niltonil,h] is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
(V,X,CNS) is Element of bool the carrier of V
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in CNS } is set
the carrier of CNS is non empty set
the carrier of z is non empty set
the carrier of z \ the carrier of CNS is Element of bool the carrier of z
bool the carrier of z is non empty set
the Element of the carrier of z \ the carrier of CNS is Element of the carrier of z \ the carrier of CNS
r is right_complementable Element of the carrier of V
niltonil + r is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,r) is right_complementable Element of the carrier of V
[niltonil,r] is set
{niltonil,r} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,r},{niltonil}} is set
the addF of V . [niltonil,r] is set
k is right_complementable Element of the carrier of V
X + k is right_complementable Element of the carrier of V
the addF of V . (X,k) is right_complementable Element of the carrier of V
[X,k] is set
{X,k} is set
{X} is non empty trivial 1 -element set
{{X,k},{X}} is set
the addF of V . [X,k] is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
(0. V) + r is right_complementable Element of the carrier of V
the addF of V . ((0. V),r) is right_complementable Element of the carrier of V
[(0. V),r] is set
{(0. V),r} is set
{(0. V)} is non empty trivial 1 -element set
{{(0. V),r},{(0. V)}} is set
the addF of V . [(0. V),r] is set
niltonil - niltonil is right_complementable Element of the carrier of V
- niltonil is right_complementable Element of the carrier of V
niltonil + (- niltonil) is right_complementable Element of the carrier of V
the addF of V . (niltonil,(- niltonil)) is right_complementable Element of the carrier of V
[niltonil,(- niltonil)] is set
{niltonil,(- niltonil)} is set
{{niltonil,(- niltonil)},{niltonil}} is set
the addF of V . [niltonil,(- niltonil)] is set
(niltonil - niltonil) + r is right_complementable Element of the carrier of V
the addF of V . ((niltonil - niltonil),r) is right_complementable Element of the carrier of V
[(niltonil - niltonil),r] is set
{(niltonil - niltonil),r} is set
{(niltonil - niltonil)} is non empty trivial 1 -element set
{{(niltonil - niltonil),r},{(niltonil - niltonil)}} is set
the addF of V . [(niltonil - niltonil),r] is set
(- niltonil) + (X + k) is right_complementable Element of the carrier of V
the addF of V . ((- niltonil),(X + k)) is right_complementable Element of the carrier of V
[(- niltonil),(X + k)] is set
{(- niltonil),(X + k)} is set
{(- niltonil)} is non empty trivial 1 -element set
{{(- niltonil),(X + k)},{(- niltonil)}} is set
the addF of V . [(- niltonil),(X + k)] is set
niltonil + ((- niltonil) + (X + k)) is right_complementable Element of the carrier of V
the addF of V . (niltonil,((- niltonil) + (X + k))) is right_complementable Element of the carrier of V
[niltonil,((- niltonil) + (X + k))] is set
{niltonil,((- niltonil) + (X + k))} is set
{{niltonil,((- niltonil) + (X + k))},{niltonil}} is set
the addF of V . [niltonil,((- niltonil) + (X + k))] is set
(V,(niltonil + ((- niltonil) + (X + k))),z) is Element of bool the carrier of V
{ ((niltonil + ((- niltonil) + (X + k))) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(niltonil - niltonil) + (X + k) is right_complementable Element of the carrier of V
the addF of V . ((niltonil - niltonil),(X + k)) is right_complementable Element of the carrier of V
[(niltonil - niltonil),(X + k)] is set
{(niltonil - niltonil),(X + k)} is set
{{(niltonil - niltonil),(X + k)},{(niltonil - niltonil)}} is set
the addF of V . [(niltonil - niltonil),(X + k)] is set
(0. V) + (X + k) is right_complementable Element of the carrier of V
the addF of V . ((0. V),(X + k)) is right_complementable Element of the carrier of V
[(0. V),(X + k)] is set
{(0. V),(X + k)} is set
{{(0. V),(X + k)},{(0. V)}} is set
the addF of V . [(0. V),(X + k)] is set
(V,(X + k),CNS) is Element of bool the carrier of V
{ ((X + k) + b1) where b1 is right_complementable Element of the carrier of V : b1 in CNS } is set
(V,(X + k),z) is Element of bool the carrier of V
{ ((X + k) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
the carrier of CNS \ the carrier of z is Element of bool the carrier of CNS
bool the carrier of CNS is non empty set
the Element of the carrier of CNS \ the carrier of z is Element of the carrier of CNS \ the carrier of z
r is right_complementable Element of the carrier of V
X + r is right_complementable Element of the carrier of V
the addF of V . (X,r) is right_complementable Element of the carrier of V
[X,r] is set
{X,r} is set
{{X,r},{X}} is set
the addF of V . [X,r] is set
k is right_complementable Element of the carrier of V
niltonil + k is right_complementable Element of the carrier of V
the addF of V . (niltonil,k) is right_complementable Element of the carrier of V
[niltonil,k] is set
{niltonil,k} is set
{{niltonil,k},{niltonil}} is set
the addF of V . [niltonil,k] is set
(0. V) + r is right_complementable Element of the carrier of V
the addF of V . ((0. V),r) is right_complementable Element of the carrier of V
[(0. V),r] is set
{(0. V),r} is set
{{(0. V),r},{(0. V)}} is set
the addF of V . [(0. V),r] is set
X - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
X + (- X) is right_complementable Element of the carrier of V
the addF of V . (X,(- X)) is right_complementable Element of the carrier of V
[X,(- X)] is set
{X,(- X)} is set
{{X,(- X)},{X}} is set
the addF of V . [X,(- X)] is set
(X - X) + r is right_complementable Element of the carrier of V
the addF of V . ((X - X),r) is right_complementable Element of the carrier of V
[(X - X),r] is set
{(X - X),r} is set
{(X - X)} is non empty trivial 1 -element set
{{(X - X),r},{(X - X)}} is set
the addF of V . [(X - X),r] is set
(- X) + (niltonil + k) is right_complementable Element of the carrier of V
the addF of V . ((- X),(niltonil + k)) is right_complementable Element of the carrier of V
[(- X),(niltonil + k)] is set
{(- X),(niltonil + k)} is set
{(- X)} is non empty trivial 1 -element set
{{(- X),(niltonil + k)},{(- X)}} is set
the addF of V . [(- X),(niltonil + k)] is set
X + ((- X) + (niltonil + k)) is right_complementable Element of the carrier of V
the addF of V . (X,((- X) + (niltonil + k))) is right_complementable Element of the carrier of V
[X,((- X) + (niltonil + k))] is set
{X,((- X) + (niltonil + k))} is set
{{X,((- X) + (niltonil + k))},{X}} is set
the addF of V . [X,((- X) + (niltonil + k))] is set
(V,(X + ((- X) + (niltonil + k))),CNS) is Element of bool the carrier of V
{ ((X + ((- X) + (niltonil + k))) + b1) where b1 is right_complementable Element of the carrier of V : b1 in CNS } is set
(X - X) + (niltonil + k) is right_complementable Element of the carrier of V
the addF of V . ((X - X),(niltonil + k)) is right_complementable Element of the carrier of V
[(X - X),(niltonil + k)] is set
{(X - X),(niltonil + k)} is set
{{(X - X),(niltonil + k)},{(X - X)}} is set
the addF of V . [(X - X),(niltonil + k)] is set
(0. V) + (niltonil + k) is right_complementable Element of the carrier of V
the addF of V . ((0. V),(niltonil + k)) is right_complementable Element of the carrier of V
[(0. V),(niltonil + k)] is set
{(0. V),(niltonil + k)} is set
{{(0. V),(niltonil + k)},{(0. V)}} is set
the addF of V . [(0. V),(niltonil + k)] is set
(V,(niltonil + k),z) is Element of bool the carrier of V
{ ((niltonil + k) + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,(niltonil + k),CNS) is Element of bool the carrier of V
{ ((niltonil + k) + b1) where b1 is right_complementable Element of the carrier of V : b1 in CNS } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of niltonil is non empty set
X is (V,niltonil)
the carrier of V is non empty set
z is right_complementable Element of the carrier of V
(V,z,niltonil) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (z + b1) where b1 is right_complementable Element of the carrier of V : b1 in niltonil } is set
0. V is zero right_complementable Element of the carrier of V
the ZeroF of V is right_complementable Element of the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
X is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
z is (V,niltonil)
CNS is (V,X)
the carrier of V is non empty set
S is right_complementable Element of the carrier of V
(V,S,niltonil) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (S + b1) where b1 is right_complementable Element of the carrier of V : b1 in niltonil } is set
g is right_complementable Element of the carrier of V
(V,g,X) is Element of bool the carrier of V
{ (g + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
niltonil is right_complementable Element of the carrier of V
{niltonil} is non empty trivial 1 -element Element of bool the carrier of V
bool the carrier of V is non empty set
(V,niltonil,(V)) is Element of bool the carrier of V
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in (V) } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
niltonil is Element of bool the carrier of V
X is right_complementable Element of the carrier of V
(V,X,(V)) is Element of bool the carrier of V
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in (V) } is set
{X} is non empty trivial 1 -element Element of bool the carrier of V
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of niltonil is non empty set
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
(V,(0. V),niltonil) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ ((0. V) + b1) where b1 is right_complementable Element of the carrier of V : b1 in niltonil } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
( the carrier of V, the ZeroF of V, the addF of V, the of V) is non empty () ()
the right_complementable Element of the carrier of V is right_complementable Element of the carrier of V
bool the carrier of V is non empty set
X is Element of bool the carrier of V
(V, the right_complementable Element of the carrier of V,(V)) is Element of bool the carrier of V
{ ( the right_complementable Element of the carrier of V + b1) where b1 is right_complementable Element of the carrier of V : b1 in (V) } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
bool the carrier of V is non empty set
(V) is non empty right_complementable Abelian add-associative right_zeroed () () () () () (V)
the ZeroF of V is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the of V is Relation-like [:COMPLEX, the carrier of V:] -defined the carrier of V -valued Function-like V18([:COMPLEX, the carrier of V:], the carrier of V) Element of bool [:[:COMPLEX, the carrier of V:], the carrier of V:]
[:COMPLEX, the carrier of V:] is non empty V50() set
[:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
bool [:[:COMPLEX, the carrier of V:], the carrier of V:] is non empty V50() set
( the carrier of V, the ZeroF of V, the addF of V, the of V) is non empty () ()
niltonil is Element of bool the carrier of V
X is right_complementable Element of the carrier of V
(V,X,(V)) is Element of bool the carrier of V
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in (V) } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
0. V is zero right_complementable Element of the carrier of V
the carrier of V is non empty set
the ZeroF of V is right_complementable Element of the carrier of V
niltonil is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
the carrier of niltonil is non empty set
X is (V,niltonil)
z is right_complementable Element of the carrier of V
(V,z,niltonil) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (z + b1) where b1 is right_complementable Element of the carrier of V : b1 in niltonil } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
(V,niltonil,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
z is (V,X)
CNS is right_complementable Element of the carrier of V
(V,CNS,X) is Element of bool the carrier of V
{ (CNS + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
CNS is (V,z)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,X,z) is Element of bool the carrier of V
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
CNS is (V,z)
(V,niltonil,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (niltonil + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
(V,X,z) is Element of bool the carrier of V
{ (X + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is right_complementable Element of the carrier of V
niltonil - X is right_complementable Element of the carrier of V
- X is right_complementable Element of the carrier of V
niltonil + (- X) is right_complementable Element of the carrier of V
the addF of V is Relation-like [: the carrier of V, the carrier of V:] -defined the carrier of V -valued Function-like V18([: the carrier of V, the carrier of V:], the carrier of V) Element of bool [:[: the carrier of V, the carrier of V:], the carrier of V:]
[: the carrier of V, the carrier of V:] is non empty set
[:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
bool [:[: the carrier of V, the carrier of V:], the carrier of V:] is non empty set
the addF of V . (niltonil,(- X)) is right_complementable Element of the carrier of V
[niltonil,(- X)] is set
{niltonil,(- X)} is set
{niltonil} is non empty trivial 1 -element set
{{niltonil,(- X)},{niltonil}} is set
the addF of V . [niltonil,(- X)] is set
z is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
CNS is (V,z)
S is right_complementable Element of the carrier of V
(V,S,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (S + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
CNS is right_complementable Element of the carrier of V
(V,CNS,z) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (CNS + b1) where b1 is right_complementable Element of the carrier of V : b1 in z } is set
S is (V,z)
V is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of V is non empty set
niltonil is right_complementable Element of the carrier of V
X is non empty right_complementable Abelian add-associative right_zeroed () () () () (V)
z is (V,X)
CNS is (V,X)
S is right_complementable Element of the carrier of V
(V,S,X) is Element of bool the carrier of V
bool the carrier of V is non empty set
{ (S + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is set
g is right_complementable Element of the carrier of V
(V,g,X) is Element of bool the carrier of V
{ (g + b1) where b1 is right_complementable Element of the carrier of V : b1 in X } is 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 non empty set
[:[: the non empty set , the non empty set :], the non empty set :] is non empty set
bool [:[: the non empty set , the non empty set :], the non empty set :] is non empty set
the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued 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 [: the non empty set , the non empty set :] -defined the non empty set -valued 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 :]
[:COMPLEX, the non empty set :] is non empty V50() set
[:[:COMPLEX, the non empty set :], the non empty set :] is non empty V50() set
bool [:[:COMPLEX, the non empty set :], the non empty set :] is non empty V50() set
the Relation-like [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :] is Relation-like [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :]
[: the non empty set ,REAL:] is non empty V50() set
bool [: the non empty set ,REAL:] is non empty V50() set
the Relation-like the non empty set -defined REAL -valued Function-like V18( the non empty set , REAL ) Element of bool [: the non empty set ,REAL:] is Relation-like the non empty set -defined REAL -valued Function-like V18( the non empty set , REAL ) Element of bool [: the non empty set ,REAL:]
( the non empty set , the Element of the non empty set , the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued 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 [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :], the Relation-like the non empty set -defined REAL -valued Function-like V18( the non empty set , REAL ) Element of bool [: the non empty set ,REAL:]) is () ()
the carrier of ( the non empty set , the Element of the non empty set , the Relation-like [: the non empty set , the non empty set :] -defined the non empty set -valued 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 [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like V18([:COMPLEX, the non empty set :], the non empty set ) Element of bool [:[:COMPLEX, the non empty set :], the non empty set :], the Relation-like the non empty set -defined REAL -valued Function-like V18( the non empty set , REAL ) Element of bool [: the non empty set ,REAL:]) is set
the non empty right_complementable Abelian add-associative right_zeroed () () () () () is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is non empty right_complementable Abelian add-associative right_zeroed () () () () () ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is non empty set
the carrier of the non empty right_complementable Abelian add-associative right_zeroed () () () () () is non empty set
0. the non empty right_complementable Abelian add-associative right_zeroed () () () () () is zero right_complementable Element of the carrier of the non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the ZeroF of the non empty right_complementable Abelian add-associative right_zeroed () () () () () is right_complementable Element of the carrier of the non empty right_complementable Abelian add-associative right_zeroed () () () () ()
{(0. the non empty right_complementable Abelian add-associative right_zeroed () () () () ())} is non empty trivial 1 -element Element of bool the carrier of the non empty right_complementable Abelian add-associative right_zeroed () () () () ()
bool the carrier of the non empty right_complementable Abelian add-associative right_zeroed () () () () () is non empty set
[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),REAL:] is non empty V50() set
bool [: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),REAL:] is non empty V50() set
the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) --> 0 is Relation-like the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) -defined NAT -valued Function-like V18( the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), NAT ) Element of bool [: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),NAT:]
[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),NAT:] is non empty V50() set
bool [: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),NAT:] is non empty V50() set
niltonil is Relation-like the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) -defined REAL -valued Function-like V18( the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), REAL ) Element of bool [: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),REAL:]
niltonil . (0. the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is set
X is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
niltonil . X is complex real ext-real Element of REAL
z is complex set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),X,z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is Relation-like [:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] -defined the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) -valued Function-like V18([:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())) Element of bool [:[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):]
[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty V50() set
[:[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty V50() set
bool [:[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty V50() set
[z,X] is set
{z,X} is set
{z} is non empty trivial 1 -element set
{{z,X},{z}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [z,X] is set
niltonil . (( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),X,z) is complex real ext-real Element of REAL
|.z.| is complex real ext-real Element of REAL
|.z.| * (niltonil . X) is complex real ext-real Element of REAL
X is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
z is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
X + z is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is Relation-like [: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] -defined the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) -valued Function-like V18([: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())) Element of bool [:[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):]
[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty set
[:[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty set
bool [:[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (X,z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[X,z] is set
{X,z} is set
{X} is non empty trivial 1 -element set
{{X,z},{X}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [X,z] is set
niltonil . (X + z) is complex real ext-real Element of REAL
niltonil . X is complex real ext-real Element of REAL
niltonil . z is complex real ext-real Element of REAL
(niltonil . X) + (niltonil . z) is complex real ext-real Element of REAL
0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is zero right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the ZeroF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is Relation-like [: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] -defined the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) -valued Function-like V18([: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())) Element of bool [:[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):]
[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty set
[:[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty set
bool [:[: the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) is Relation-like [:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] -defined the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) -valued Function-like V18([:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())) Element of bool [:[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):]
[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty V50() set
[:[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty V50() set
bool [:[:COMPLEX, the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):], the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()):] is non empty V50() set
( the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),(0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())), the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()), the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),niltonil) is () ()
X is non empty ()
the carrier of X is non empty set
z is Element of the carrier of X
CNS is Element of the carrier of X
0. X is zero Element of the carrier of X
the ZeroF of X is Element of the carrier of X
||.z.|| is complex real ext-real Element of REAL
the normF of X is Relation-like the carrier of X -defined REAL -valued Function-like V18( the carrier of X, REAL ) Element of bool [: the carrier of X,REAL:]
[: the carrier of X,REAL:] is non empty V50() set
bool [: the carrier of X,REAL:] is non empty V50() set
the normF of X . z is complex real ext-real Element of REAL
S is complex set
(X,z,S) is Element of the carrier of X
the of X is Relation-like [:COMPLEX, the carrier of X:] -defined the carrier of X -valued Function-like V18([:COMPLEX, the carrier of X:], the carrier of X) Element of bool [:[:COMPLEX, the carrier of X:], the carrier of X:]
[:COMPLEX, the carrier of X:] is non empty V50() set
[:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
bool [:[:COMPLEX, the carrier of X:], the carrier of X:] is non empty V50() set
[S,z] is set
{S,z} is set
{S} is non empty trivial 1 -element set
{{S,z},{S}} is set
the of X . [S,z] is set
g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,S) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[S,g] is set
{S,g} is set
{{S,g},{S}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [S,g] is set
||.(X,z,S).|| is complex real ext-real Element of REAL
the normF of X . (X,z,S) is complex real ext-real Element of REAL
|.S.| is complex real ext-real Element of REAL
|.S.| * ||.z.|| is complex real ext-real Element of REAL
z + CNS is Element of the carrier of X
the addF of X is Relation-like [: the carrier of X, the carrier of X:] -defined the carrier of X -valued Function-like V18([: the carrier of X, the carrier of X:], the carrier of X) Element of bool [:[: the carrier of X, the carrier of X:], the carrier of X:]
[: the carrier of X, the carrier of X:] is non empty set
[:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
bool [:[: the carrier of X, the carrier of X:], the carrier of X:] is non empty set
the addF of X . (z,CNS) is Element of the carrier of X
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of X . [z,CNS] is set
h is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
g + h is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (g,h) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [g,h] is set
||.(z + CNS).|| is complex real ext-real Element of REAL
the normF of X . (z + CNS) is complex real ext-real Element of REAL
||.CNS.|| is complex real ext-real Element of REAL
the normF of X . CNS is complex real ext-real Element of REAL
||.z.|| + ||.CNS.|| is complex real ext-real Element of REAL
||.(0. X).|| is complex real ext-real Element of REAL
the normF of X . (0. X) is complex real ext-real Element of REAL
z is complex set
CNS is Element of the carrier of X
S is Element of the carrier of X
CNS + S is Element of the carrier of X
the addF of X . (CNS,S) is Element of the carrier of X
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the addF of X . [CNS,S] is set
(X,(CNS + S),z) is Element of the carrier of X
[z,(CNS + S)] is set
{z,(CNS + S)} is set
{z} is non empty trivial 1 -element set
{{z,(CNS + S)},{z}} is set
the of X . [z,(CNS + S)] is set
(X,CNS,z) is Element of the carrier of X
[z,CNS] is set
{z,CNS} is set
{{z,CNS},{z}} is set
the of X . [z,CNS] is set
(X,S,z) is Element of the carrier of X
[z,S] is set
{z,S} is set
{{z,S},{z}} is set
the of X . [z,S] is set
(X,CNS,z) + (X,S,z) is Element of the carrier of X
the addF of X . ((X,CNS,z),(X,S,z)) is Element of the carrier of X
[(X,CNS,z),(X,S,z)] is set
{(X,CNS,z),(X,S,z)} is set
{(X,CNS,z)} is non empty trivial 1 -element set
{{(X,CNS,z),(X,S,z)},{(X,CNS,z)}} is set
the addF of X . [(X,CNS,z),(X,S,z)] is set
g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
h is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
g + h is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (g,h) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [g,h] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),(g + h),z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[z,(g + h)] is set
{z,(g + h)} is set
{{z,(g + h)},{z}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [z,(g + h)] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[z,g] is set
{z,g} is set
{{z,g},{z}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [z,g] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),h,z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[z,h] is set
{z,h} is set
{{z,h},{z}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [z,h] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z) + (( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),h,z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . ((( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),h,z)) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),h,z)] is set
{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),h,z)} is set
{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z)} is non empty trivial 1 -element set
{{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),h,z)},{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z)}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),h,z)] is set
z is complex set
CNS is complex set
z + CNS is complex set
S is Element of the carrier of X
(X,S,(z + CNS)) is Element of the carrier of X
[(z + CNS),S] is set
{(z + CNS),S} is set
{(z + CNS)} is non empty trivial 1 -element set
{{(z + CNS),S},{(z + CNS)}} is set
the of X . [(z + CNS),S] is set
(X,S,z) is Element of the carrier of X
[z,S] is set
{z,S} is set
{z} is non empty trivial 1 -element set
{{z,S},{z}} is set
the of X . [z,S] is set
(X,S,CNS) is Element of the carrier of X
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the of X . [CNS,S] is set
(X,S,z) + (X,S,CNS) is Element of the carrier of X
the addF of X . ((X,S,z),(X,S,CNS)) is Element of the carrier of X
[(X,S,z),(X,S,CNS)] is set
{(X,S,z),(X,S,CNS)} is set
{(X,S,z)} is non empty trivial 1 -element set
{{(X,S,z),(X,S,CNS)},{(X,S,z)}} is set
the addF of X . [(X,S,z),(X,S,CNS)] is set
g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,(z + CNS)) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[(z + CNS),g] is set
{(z + CNS),g} is set
{{(z + CNS),g},{(z + CNS)}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [(z + CNS),g] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[z,g] is set
{z,g} is set
{{z,g},{z}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [z,g] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[CNS,g] is set
{CNS,g} is set
{{CNS,g},{CNS}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [CNS,g] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z) + (( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . ((( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)] is set
{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)} is set
{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z)} is non empty trivial 1 -element set
{{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)},{(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z)}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,z),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)] is set
z is complex set
CNS is complex set
z * CNS is complex set
S is Element of the carrier of X
(X,S,(z * CNS)) is Element of the carrier of X
[(z * CNS),S] is set
{(z * CNS),S} is set
{(z * CNS)} is non empty trivial 1 -element set
{{(z * CNS),S},{(z * CNS)}} is set
the of X . [(z * CNS),S] is set
(X,S,CNS) is Element of the carrier of X
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the of X . [CNS,S] is set
(X,(X,S,CNS),z) is Element of the carrier of X
[z,(X,S,CNS)] is set
{z,(X,S,CNS)} is set
{z} is non empty trivial 1 -element set
{{z,(X,S,CNS)},{z}} is set
the of X . [z,(X,S,CNS)] is set
g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,(z * CNS)) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[(z * CNS),g] is set
{(z * CNS),g} is set
{{(z * CNS),g},{(z * CNS)}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [(z * CNS),g] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[CNS,g] is set
{CNS,g} is set
{{CNS,g},{CNS}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [CNS,g] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS),z) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[z,(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)] is set
{z,(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)} is set
{{z,(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)},{z}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [z,(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),g,CNS)] is set
z is Element of the carrier of X
(X,z,1r) is Element of the carrier of X
[1r,z] is set
{1r,z} is set
{1r} is non empty trivial 1 -element set
{{1r,z},{1r}} is set
the of X . [1r,z] is set
CNS is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),CNS,1r) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[1r,CNS] is set
{1r,CNS} is set
{{1r,CNS},{1r}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [1r,CNS] is set
z is Element of the carrier of X
S is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
CNS is Element of the carrier of X
g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
z + CNS is Element of the carrier of X
the addF of X . (z,CNS) is Element of the carrier of X
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of X . [z,CNS] is set
S + g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (S,g) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[S,g] is set
{S,g} is set
{S} is non empty trivial 1 -element set
{{S,g},{S}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [S,g] is set
h is complex set
(X,z,h) is Element of the carrier of X
[h,z] is set
{h,z} is set
{h} is non empty trivial 1 -element set
{{h,z},{h}} is set
the of X . [h,z] is set
(( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()),S,h) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[h,S] is set
{h,S} is set
{{h,S},{h}} is set
the of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [h,S] is set
z is Element of the carrier of X
CNS is Element of the carrier of X
z + CNS is Element of the carrier of X
the addF of X . (z,CNS) is Element of the carrier of X
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of X . [z,CNS] is set
CNS + z is Element of the carrier of X
the addF of X . (CNS,z) is Element of the carrier of X
[CNS,z] is set
{CNS,z} is set
{CNS} is non empty trivial 1 -element set
{{CNS,z},{CNS}} is set
the addF of X . [CNS,z] is set
g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
S is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
g + S is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (g,S) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[g,S] is set
{g,S} is set
{g} is non empty trivial 1 -element set
{{g,S},{g}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [g,S] is set
z is Element of the carrier of X
CNS is Element of the carrier of X
z + CNS is Element of the carrier of X
the addF of X . (z,CNS) is Element of the carrier of X
[z,CNS] is set
{z,CNS} is set
{z} is non empty trivial 1 -element set
{{z,CNS},{z}} is set
the addF of X . [z,CNS] is set
S is Element of the carrier of X
(z + CNS) + S is Element of the carrier of X
the addF of X . ((z + CNS),S) is Element of the carrier of X
[(z + CNS),S] is set
{(z + CNS),S} is set
{(z + CNS)} is non empty trivial 1 -element set
{{(z + CNS),S},{(z + CNS)}} is set
the addF of X . [(z + CNS),S] is set
CNS + S is Element of the carrier of X
the addF of X . (CNS,S) is Element of the carrier of X
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the addF of X . [CNS,S] is set
z + (CNS + S) is Element of the carrier of X
the addF of X . (z,(CNS + S)) is Element of the carrier of X
[z,(CNS + S)] is set
{z,(CNS + S)} is set
{{z,(CNS + S)},{z}} is set
the addF of X . [z,(CNS + S)] is set
g is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
h is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
g + h is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (g,h) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [g,h] is set
r is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
(g + h) + r is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . ((g + h),r) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[(g + h),r] is set
{(g + h),r} is set
{(g + h)} is non empty trivial 1 -element set
{{(g + h),r},{(g + h)}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [(g + h),r] is set
h + r is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (h,r) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[h,r] is set
{h,r} is set
{h} is non empty trivial 1 -element set
{{h,r},{h}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [h,r] is set
g + (h + r) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (g,(h + r)) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[g,(h + r)] is set
{g,(h + r)} is set
{{g,(h + r)},{g}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [g,(h + r)] is set
z is Element of the carrier of X
z + (0. X) is Element of the carrier of X
the addF of X . (z,(0. X)) is Element of the carrier of X
[z,(0. X)] is set
{z,(0. X)} is set
{z} is non empty trivial 1 -element set
{{z,(0. X)},{z}} is set
the addF of X . [z,(0. X)] is set
CNS is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
CNS + (0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (CNS,(0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()))) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[CNS,(0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()))] is set
{CNS,(0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()))} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()))},{CNS}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [CNS,(0. ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()))] is set
z is Element of the carrier of X
CNS is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
S is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
CNS + S is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . (CNS,S) is right_complementable Element of the carrier of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ())
[CNS,S] is set
{CNS,S} is set
{CNS} is non empty trivial 1 -element set
{{CNS,S},{CNS}} is set
the addF of ( the non empty right_complementable Abelian add-associative right_zeroed () () () () ()) . [CNS,S] is set
g is Element of the carrier of X
z + g is Element of the carrier of X
the addF of X . (z,g) is Element of the carrier of X
[z,g] is set
{z,g} is set
{z} is non empty trivial 1 -element set
{{z,g},{z}} is set
the addF of X . [z,g] is set
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
0. z is zero right_complementable Element of the carrier of z
the carrier of z is non empty set
the ZeroF of z is right_complementable Element of the carrier of z
||.(0. z).|| is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (0. z) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
- CNS is right_complementable Element of the carrier of z
||.(- CNS).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (- CNS) is complex real ext-real Element of REAL
||.CNS.|| is complex real ext-real Element of REAL
the normF of z . CNS is complex real ext-real Element of REAL
|.(- 1r).| is complex real ext-real Element of REAL
(z,CNS,(- 1r)) is right_complementable Element of the carrier of z
the of z is Relation-like [:COMPLEX, the carrier of z:] -defined the carrier of z -valued Function-like V18([:COMPLEX, the carrier of z:], the carrier of z) Element of bool [:[:COMPLEX, the carrier of z:], the carrier of z:]
[:COMPLEX, the carrier of z:] is non empty V50() set
[:[:COMPLEX, the carrier of z:], the carrier of z:] is non empty V50() set
bool [:[:COMPLEX, the carrier of z:], the carrier of z:] is non empty V50() set
[(- 1r),CNS] is set
{(- 1r),CNS} is set
{(- 1r)} is non empty trivial 1 -element set
{{(- 1r),CNS},{(- 1r)}} is set
the of z . [(- 1r),CNS] is set
||.(z,CNS,(- 1r)).|| is complex real ext-real Element of REAL
the normF of z . (z,CNS,(- 1r)) is complex real ext-real Element of REAL
|.(- 1r).| * ||.CNS.|| is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
||.CNS.|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . CNS is complex real ext-real Element of REAL
S is right_complementable Element of the carrier of z
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
||.(CNS - S).|| is complex real ext-real Element of REAL
the normF of z . (CNS - S) is complex real ext-real Element of REAL
||.S.|| is complex real ext-real Element of REAL
the normF of z . S is complex real ext-real Element of REAL
||.CNS.|| + ||.S.|| is complex real ext-real Element of REAL
||.(- S).|| is complex real ext-real Element of REAL
the normF of z . (- S) is complex real ext-real Element of REAL
||.CNS.|| + ||.(- S).|| is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
||.CNS.|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . CNS is complex real ext-real Element of REAL
CNS - CNS is right_complementable Element of the carrier of z
- CNS is right_complementable Element of the carrier of z
CNS + (- CNS) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- CNS)) is right_complementable Element of the carrier of z
[CNS,(- CNS)] is set
{CNS,(- CNS)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- CNS)},{CNS}} is set
the addF of z . [CNS,(- CNS)] is set
||.(CNS - CNS).|| is complex real ext-real Element of REAL
the normF of z . (CNS - CNS) is complex real ext-real Element of REAL
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
||.H1(z).|| is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered Element of REAL
the normF of z . (0. z) is complex real ext-real Element of REAL
||.CNS.|| + ||.CNS.|| is complex real ext-real Element of REAL
(||.CNS.|| + ||.CNS.||) / 2 is complex real ext-real Element of REAL
z is complex set
|.z.| is complex real ext-real Element of REAL
CNS is complex set
|.CNS.| is complex real ext-real Element of REAL
S is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of S is non empty set
g is right_complementable Element of the carrier of S
(S,g,z) is right_complementable Element of the carrier of S
the of S is Relation-like [:COMPLEX, the carrier of S:] -defined the carrier of S -valued Function-like V18([:COMPLEX, the carrier of S:], the carrier of S) Element of bool [:[:COMPLEX, the carrier of S:], the carrier of S:]
[:COMPLEX, the carrier of S:] is non empty V50() set
[:[:COMPLEX, the carrier of S:], the carrier of S:] is non empty V50() set
bool [:[:COMPLEX, the carrier of S:], the carrier of S:] is non empty V50() set
[z,g] is set
{z,g} is set
{z} is non empty trivial 1 -element set
{{z,g},{z}} is set
the of S . [z,g] is set
||.g.|| is complex real ext-real Element of REAL
the normF of S is Relation-like the carrier of S -defined REAL -valued Function-like V18( the carrier of S, REAL ) Element of bool [: the carrier of S,REAL:]
[: the carrier of S,REAL:] is non empty V50() set
bool [: the carrier of S,REAL:] is non empty V50() set
the normF of S . g is complex real ext-real Element of REAL
|.z.| * ||.g.|| is complex real ext-real Element of REAL
h is right_complementable Element of the carrier of S
(S,h,CNS) is right_complementable Element of the carrier of S
[CNS,h] is set
{CNS,h} is set
{CNS} is non empty trivial 1 -element set
{{CNS,h},{CNS}} is set
the of S . [CNS,h] is set
(S,g,z) + (S,h,CNS) is right_complementable Element of the carrier of S
the addF of S is Relation-like [: the carrier of S, the carrier of S:] -defined the carrier of S -valued Function-like V18([: the carrier of S, the carrier of S:], the carrier of S) Element of bool [:[: the carrier of S, the carrier of S:], the carrier of S:]
[: the carrier of S, the carrier of S:] is non empty set
[:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
bool [:[: the carrier of S, the carrier of S:], the carrier of S:] is non empty set
the addF of S . ((S,g,z),(S,h,CNS)) is right_complementable Element of the carrier of S
[(S,g,z),(S,h,CNS)] is set
{(S,g,z),(S,h,CNS)} is set
{(S,g,z)} is non empty trivial 1 -element set
{{(S,g,z),(S,h,CNS)},{(S,g,z)}} is set
the addF of S . [(S,g,z),(S,h,CNS)] is set
||.((S,g,z) + (S,h,CNS)).|| is complex real ext-real Element of REAL
the normF of S . ((S,g,z) + (S,h,CNS)) is complex real ext-real Element of REAL
||.h.|| is complex real ext-real Element of REAL
the normF of S . h is complex real ext-real Element of REAL
|.CNS.| * ||.h.|| is complex real ext-real Element of REAL
(|.z.| * ||.g.||) + (|.CNS.| * ||.h.||) is complex real ext-real Element of REAL
||.(S,g,z).|| is complex real ext-real Element of REAL
the normF of S . (S,g,z) is complex real ext-real Element of REAL
||.(S,h,CNS).|| is complex real ext-real Element of REAL
the normF of S . (S,h,CNS) is complex real ext-real Element of REAL
||.(S,g,z).|| + ||.(S,h,CNS).|| is complex real ext-real Element of REAL
(|.z.| * ||.g.||) + ||.(S,h,CNS).|| is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
S is right_complementable Element of the carrier of z
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
||.(CNS - S).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (CNS - S) is complex real ext-real Element of REAL
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
S is right_complementable Element of the carrier of z
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
||.(CNS - S).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (CNS - S) is complex real ext-real Element of REAL
S - CNS is right_complementable Element of the carrier of z
- CNS is right_complementable Element of the carrier of z
S + (- CNS) is right_complementable Element of the carrier of z
the addF of z . (S,(- CNS)) is right_complementable Element of the carrier of z
[S,(- CNS)] is set
{S,(- CNS)} is set
{S} is non empty trivial 1 -element set
{{S,(- CNS)},{S}} is set
the addF of z . [S,(- CNS)] is set
||.(S - CNS).|| is complex real ext-real Element of REAL
the normF of z . (S - CNS) is complex real ext-real Element of REAL
- (S - CNS) is right_complementable Element of the carrier of z
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
||.CNS.|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . CNS is complex real ext-real Element of REAL
S is right_complementable Element of the carrier of z
||.S.|| is complex real ext-real Element of REAL
the normF of z . S is complex real ext-real Element of REAL
||.CNS.|| - ||.S.|| is complex real ext-real Element of REAL
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
||.(CNS - S).|| is complex real ext-real Element of REAL
the normF of z . (CNS - S) is complex real ext-real Element of REAL
(CNS - S) + S is right_complementable Element of the carrier of z
the addF of z . ((CNS - S),S) is right_complementable Element of the carrier of z
[(CNS - S),S] is set
{(CNS - S),S} is set
{(CNS - S)} is non empty trivial 1 -element set
{{(CNS - S),S},{(CNS - S)}} is set
the addF of z . [(CNS - S),S] is set
S - S is right_complementable Element of the carrier of z
S + (- S) is right_complementable Element of the carrier of z
the addF of z . (S,(- S)) is right_complementable Element of the carrier of z
[S,(- S)] is set
{S,(- S)} is set
{S} is non empty trivial 1 -element set
{{S,(- S)},{S}} is set
the addF of z . [S,(- S)] is set
CNS - (S - S) is right_complementable Element of the carrier of z
- (S - S) is right_complementable Element of the carrier of z
CNS + (- (S - S)) is right_complementable Element of the carrier of z
the addF of z . (CNS,(- (S - S))) is right_complementable Element of the carrier of z
[CNS,(- (S - S))] is set
{CNS,(- (S - S))} is set
{{CNS,(- (S - S))},{CNS}} is set
the addF of z . [CNS,(- (S - S))] is set
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
CNS - H1(z) is right_complementable Element of the carrier of z
- (0. z) is right_complementable Element of the carrier of z
CNS + (- (0. z)) is right_complementable Element of the carrier of z
the addF of z . (CNS,(- (0. z))) is right_complementable Element of the carrier of z
[CNS,(- (0. z))] is set
{CNS,(- (0. z))} is set
{{CNS,(- (0. z))},{CNS}} is set
the addF of z . [CNS,(- (0. z))] is set
||.(CNS - S).|| + ||.S.|| is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
||.CNS.|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . CNS is complex real ext-real Element of REAL
S is right_complementable Element of the carrier of z
||.S.|| is complex real ext-real Element of REAL
the normF of z . S is complex real ext-real Element of REAL
||.CNS.|| - ||.S.|| is complex real ext-real Element of REAL
abs (||.CNS.|| - ||.S.||) is complex real ext-real Element of REAL
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
||.(CNS - S).|| is complex real ext-real Element of REAL
the normF of z . (CNS - S) is complex real ext-real Element of REAL
S - CNS is right_complementable Element of the carrier of z
- CNS is right_complementable Element of the carrier of z
S + (- CNS) is right_complementable Element of the carrier of z
the addF of z . (S,(- CNS)) is right_complementable Element of the carrier of z
[S,(- CNS)] is set
{S,(- CNS)} is set
{S} is non empty trivial 1 -element set
{{S,(- CNS)},{S}} is set
the addF of z . [S,(- CNS)] is set
(S - CNS) + CNS is right_complementable Element of the carrier of z
the addF of z . ((S - CNS),CNS) is right_complementable Element of the carrier of z
[(S - CNS),CNS] is set
{(S - CNS),CNS} is set
{(S - CNS)} is non empty trivial 1 -element set
{{(S - CNS),CNS},{(S - CNS)}} is set
the addF of z . [(S - CNS),CNS] is set
CNS - CNS is right_complementable Element of the carrier of z
CNS + (- CNS) is right_complementable Element of the carrier of z
the addF of z . (CNS,(- CNS)) is right_complementable Element of the carrier of z
[CNS,(- CNS)] is set
{CNS,(- CNS)} is set
{{CNS,(- CNS)},{CNS}} is set
the addF of z . [CNS,(- CNS)] is set
S - (CNS - CNS) is right_complementable Element of the carrier of z
- (CNS - CNS) is right_complementable Element of the carrier of z
S + (- (CNS - CNS)) is right_complementable Element of the carrier of z
the addF of z . (S,(- (CNS - CNS))) is right_complementable Element of the carrier of z
[S,(- (CNS - CNS))] is set
{S,(- (CNS - CNS))} is set
{{S,(- (CNS - CNS))},{S}} is set
the addF of z . [S,(- (CNS - CNS))] is set
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
S - H1(z) is right_complementable Element of the carrier of z
- (0. z) is right_complementable Element of the carrier of z
S + (- (0. z)) is right_complementable Element of the carrier of z
the addF of z . (S,(- (0. z))) is right_complementable Element of the carrier of z
[S,(- (0. z))] is set
{S,(- (0. z))} is set
{{S,(- (0. z))},{S}} is set
the addF of z . [S,(- (0. z))] is set
||.(S - CNS).|| is complex real ext-real Element of REAL
the normF of z . (S - CNS) is complex real ext-real Element of REAL
||.(S - CNS).|| + ||.CNS.|| is complex real ext-real Element of REAL
||.S.|| - ||.CNS.|| is complex real ext-real Element of REAL
- ||.(CNS - S).|| is complex real ext-real Element of REAL
- (||.S.|| - ||.CNS.||) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
S is right_complementable Element of the carrier of z
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
||.(CNS - S).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (CNS - S) is complex real ext-real Element of REAL
g is right_complementable Element of the carrier of z
CNS - g is right_complementable Element of the carrier of z
- g is right_complementable Element of the carrier of z
CNS + (- g) is right_complementable Element of the carrier of z
the addF of z . (CNS,(- g)) is right_complementable Element of the carrier of z
[CNS,(- g)] is set
{CNS,(- g)} is set
{{CNS,(- g)},{CNS}} is set
the addF of z . [CNS,(- g)] is set
||.(CNS - g).|| is complex real ext-real Element of REAL
the normF of z . (CNS - g) is complex real ext-real Element of REAL
g - S is right_complementable Element of the carrier of z
g + (- S) is right_complementable Element of the carrier of z
the addF of z . (g,(- S)) is right_complementable Element of the carrier of z
[g,(- S)] is set
{g,(- S)} is set
{g} is non empty trivial 1 -element set
{{g,(- S)},{g}} is set
the addF of z . [g,(- S)] is set
||.(g - S).|| is complex real ext-real Element of REAL
the normF of z . (g - S) is complex real ext-real Element of REAL
||.(CNS - g).|| + ||.(g - S).|| is complex real ext-real Element of REAL
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
H1(z) + (- S) is right_complementable Element of the carrier of z
the addF of z . ((0. z),(- S)) is right_complementable Element of the carrier of z
[(0. z),(- S)] is set
{(0. z),(- S)} is set
{(0. z)} is non empty trivial 1 -element set
{{(0. z),(- S)},{(0. z)}} is set
the addF of z . [(0. z),(- S)] is set
CNS + (H1(z) + (- S)) is right_complementable Element of the carrier of z
the addF of z . (CNS,(H1(z) + (- S))) is right_complementable Element of the carrier of z
[CNS,(H1(z) + (- S))] is set
{CNS,(H1(z) + (- S))} is set
{{CNS,(H1(z) + (- S))},{CNS}} is set
the addF of z . [CNS,(H1(z) + (- S))] is set
(- g) + g is right_complementable Element of the carrier of z
the addF of z . ((- g),g) is right_complementable Element of the carrier of z
[(- g),g] is set
{(- g),g} is set
{(- g)} is non empty trivial 1 -element set
{{(- g),g},{(- g)}} is set
the addF of z . [(- g),g] is set
((- g) + g) + (- S) is right_complementable Element of the carrier of z
the addF of z . (((- g) + g),(- S)) is right_complementable Element of the carrier of z
[((- g) + g),(- S)] is set
{((- g) + g),(- S)} is set
{((- g) + g)} is non empty trivial 1 -element set
{{((- g) + g),(- S)},{((- g) + g)}} is set
the addF of z . [((- g) + g),(- S)] is set
CNS + (((- g) + g) + (- S)) is right_complementable Element of the carrier of z
the addF of z . (CNS,(((- g) + g) + (- S))) is right_complementable Element of the carrier of z
[CNS,(((- g) + g) + (- S))] is set
{CNS,(((- g) + g) + (- S))} is set
{{CNS,(((- g) + g) + (- S))},{CNS}} is set
the addF of z . [CNS,(((- g) + g) + (- S))] is set
g + (- S) is right_complementable Element of the carrier of z
(- g) + (g + (- S)) is right_complementable Element of the carrier of z
the addF of z . ((- g),(g + (- S))) is right_complementable Element of the carrier of z
[(- g),(g + (- S))] is set
{(- g),(g + (- S))} is set
{{(- g),(g + (- S))},{(- g)}} is set
the addF of z . [(- g),(g + (- S))] is set
CNS + ((- g) + (g + (- S))) is right_complementable Element of the carrier of z
the addF of z . (CNS,((- g) + (g + (- S)))) is right_complementable Element of the carrier of z
[CNS,((- g) + (g + (- S)))] is set
{CNS,((- g) + (g + (- S)))} is set
{{CNS,((- g) + (g + (- S)))},{CNS}} is set
the addF of z . [CNS,((- g) + (g + (- S)))] is set
(CNS - g) + (g - S) is right_complementable Element of the carrier of z
the addF of z . ((CNS - g),(g - S)) is right_complementable Element of the carrier of z
[(CNS - g),(g - S)] is set
{(CNS - g),(g - S)} is set
{(CNS - g)} is non empty trivial 1 -element set
{{(CNS - g),(g - S)},{(CNS - g)}} is set
the addF of z . [(CNS - g),(g - S)] is set
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
CNS is right_complementable Element of the carrier of z
S is right_complementable Element of the carrier of z
CNS - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
CNS + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (CNS,(- S)) is right_complementable Element of the carrier of z
[CNS,(- S)] is set
{CNS,(- S)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- S)},{CNS}} is set
the addF of z . [CNS,(- S)] is set
||.(CNS - S).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (CNS - S) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
S is complex set
g is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
h is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
r is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
g . r is right_complementable Element of the carrier of z
h . r is right_complementable Element of the carrier of z
CNS . r is right_complementable Element of the carrier of z
(z,(CNS . r),S) is right_complementable Element of the carrier of z
the of z is Relation-like [:COMPLEX, the carrier of z:] -defined the carrier of z -valued Function-like V18([:COMPLEX, the carrier of z:], the carrier of z) Element of bool [:[:COMPLEX, the carrier of z:], the carrier of z:]
[:COMPLEX, the carrier of z:] is non empty V50() set
[:[:COMPLEX, the carrier of z:], the carrier of z:] is non empty V50() set
bool [:[:COMPLEX, the carrier of z:], the carrier of z:] is non empty V50() set
[S,(CNS . r)] is set
{S,(CNS . r)} is set
{S} is non empty trivial 1 -element set
{{S,(CNS . r)},{S}} is set
the of z . [S,(CNS . r)] is set
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
CNS + S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
g is right_complementable Element of the carrier of z
h is right_complementable Element of the carrier of z
g + h is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (g,h) is right_complementable Element of the carrier of z
[g,h] is set
{g,h} is set
{g} is non empty trivial 1 -element set
{{g,h},{g}} is set
the addF of z . [g,h] is set
r is right_complementable Element of the carrier of z
m1 is complex real ext-real Element of REAL
m1 / 2 is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k + n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
(CNS + S) . n is right_complementable Element of the carrier of z
((CNS + S) . n) - r is right_complementable Element of the carrier of z
- r is right_complementable Element of the carrier of z
((CNS + S) . n) + (- r) is right_complementable Element of the carrier of z
the addF of z . (((CNS + S) . n),(- r)) is right_complementable Element of the carrier of z
[((CNS + S) . n),(- r)] is set
{((CNS + S) . n),(- r)} is set
{((CNS + S) . n)} is non empty trivial 1 -element set
{{((CNS + S) . n),(- r)},{((CNS + S) . n)}} is set
the addF of z . [((CNS + S) . n),(- r)] is set
||.(((CNS + S) . n) - r).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (((CNS + S) . n) - r) is complex real ext-real Element of REAL
S . n is right_complementable Element of the carrier of z
(S . n) - h is right_complementable Element of the carrier of z
- h is right_complementable Element of the carrier of z
(S . n) + (- h) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- h)) is right_complementable Element of the carrier of z
[(S . n),(- h)] is set
{(S . n),(- h)} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- h)},{(S . n)}} is set
the addF of z . [(S . n),(- h)] is set
||.((S . n) - h).|| is complex real ext-real Element of REAL
the normF of z . ((S . n) - h) is complex real ext-real Element of REAL
- (g + h) is right_complementable Element of the carrier of z
CNS . n is right_complementable Element of the carrier of z
(CNS . n) + (S . n) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(S . n)) is right_complementable Element of the carrier of z
[(CNS . n),(S . n)] is set
{(CNS . n),(S . n)} is set
{(CNS . n)} is non empty trivial 1 -element set
{{(CNS . n),(S . n)},{(CNS . n)}} is set
the addF of z . [(CNS . n),(S . n)] is set
(- (g + h)) + ((CNS . n) + (S . n)) is right_complementable Element of the carrier of z
the addF of z . ((- (g + h)),((CNS . n) + (S . n))) is right_complementable Element of the carrier of z
[(- (g + h)),((CNS . n) + (S . n))] is set
{(- (g + h)),((CNS . n) + (S . n))} is set
{(- (g + h))} is non empty trivial 1 -element set
{{(- (g + h)),((CNS . n) + (S . n))},{(- (g + h))}} is set
the addF of z . [(- (g + h)),((CNS . n) + (S . n))] is set
||.((- (g + h)) + ((CNS . n) + (S . n))).|| is complex real ext-real Element of REAL
the normF of z . ((- (g + h)) + ((CNS . n) + (S . n))) is complex real ext-real Element of REAL
- g is right_complementable Element of the carrier of z
(- g) + (- h) is right_complementable Element of the carrier of z
the addF of z . ((- g),(- h)) is right_complementable Element of the carrier of z
[(- g),(- h)] is set
{(- g),(- h)} is set
{(- g)} is non empty trivial 1 -element set
{{(- g),(- h)},{(- g)}} is set
the addF of z . [(- g),(- h)] is set
((- g) + (- h)) + ((CNS . n) + (S . n)) is right_complementable Element of the carrier of z
the addF of z . (((- g) + (- h)),((CNS . n) + (S . n))) is right_complementable Element of the carrier of z
[((- g) + (- h)),((CNS . n) + (S . n))] is set
{((- g) + (- h)),((CNS . n) + (S . n))} is set
{((- g) + (- h))} is non empty trivial 1 -element set
{{((- g) + (- h)),((CNS . n) + (S . n))},{((- g) + (- h))}} is set
the addF of z . [((- g) + (- h)),((CNS . n) + (S . n))] is set
||.(((- g) + (- h)) + ((CNS . n) + (S . n))).|| is complex real ext-real Element of REAL
the normF of z . (((- g) + (- h)) + ((CNS . n) + (S . n))) is complex real ext-real Element of REAL
(CNS . n) + ((- g) + (- h)) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),((- g) + (- h))) is right_complementable Element of the carrier of z
[(CNS . n),((- g) + (- h))] is set
{(CNS . n),((- g) + (- h))} is set
{{(CNS . n),((- g) + (- h))},{(CNS . n)}} is set
the addF of z . [(CNS . n),((- g) + (- h))] is set
((CNS . n) + ((- g) + (- h))) + (S . n) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) + ((- g) + (- h))),(S . n)) is right_complementable Element of the carrier of z
[((CNS . n) + ((- g) + (- h))),(S . n)] is set
{((CNS . n) + ((- g) + (- h))),(S . n)} is set
{((CNS . n) + ((- g) + (- h)))} is non empty trivial 1 -element set
{{((CNS . n) + ((- g) + (- h))),(S . n)},{((CNS . n) + ((- g) + (- h)))}} is set
the addF of z . [((CNS . n) + ((- g) + (- h))),(S . n)] is set
||.(((CNS . n) + ((- g) + (- h))) + (S . n)).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) + ((- g) + (- h))) + (S . n)) is complex real ext-real Element of REAL
(CNS . n) - g is right_complementable Element of the carrier of z
(CNS . n) + (- g) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- g)) is right_complementable Element of the carrier of z
[(CNS . n),(- g)] is set
{(CNS . n),(- g)} is set
{{(CNS . n),(- g)},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- g)] is set
((CNS . n) - g) + (- h) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - g),(- h)) is right_complementable Element of the carrier of z
[((CNS . n) - g),(- h)] is set
{((CNS . n) - g),(- h)} is set
{((CNS . n) - g)} is non empty trivial 1 -element set
{{((CNS . n) - g),(- h)},{((CNS . n) - g)}} is set
the addF of z . [((CNS . n) - g),(- h)] is set
(((CNS . n) - g) + (- h)) + (S . n) is right_complementable Element of the carrier of z
the addF of z . ((((CNS . n) - g) + (- h)),(S . n)) is right_complementable Element of the carrier of z
[(((CNS . n) - g) + (- h)),(S . n)] is set
{(((CNS . n) - g) + (- h)),(S . n)} is set
{(((CNS . n) - g) + (- h))} is non empty trivial 1 -element set
{{(((CNS . n) - g) + (- h)),(S . n)},{(((CNS . n) - g) + (- h))}} is set
the addF of z . [(((CNS . n) - g) + (- h)),(S . n)] is set
||.((((CNS . n) - g) + (- h)) + (S . n)).|| is complex real ext-real Element of REAL
the normF of z . ((((CNS . n) - g) + (- h)) + (S . n)) is complex real ext-real Element of REAL
((CNS . n) - g) + ((S . n) - h) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - g),((S . n) - h)) is right_complementable Element of the carrier of z
[((CNS . n) - g),((S . n) - h)] is set
{((CNS . n) - g),((S . n) - h)} is set
{{((CNS . n) - g),((S . n) - h)},{((CNS . n) - g)}} is set
the addF of z . [((CNS . n) - g),((S . n) - h)] is set
||.(((CNS . n) - g) + ((S . n) - h)).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - g) + ((S . n) - h)) is complex real ext-real Element of REAL
||.((CNS . n) - g).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . n) - g) is complex real ext-real Element of REAL
||.((CNS . n) - g).|| + ||.((S . n) - h).|| is complex real ext-real Element of REAL
(m1 / 2) + (m1 / 2) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
CNS - S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
g is right_complementable Element of the carrier of z
h is right_complementable Element of the carrier of z
g - h is right_complementable Element of the carrier of z
- h is right_complementable Element of the carrier of z
g + (- h) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (g,(- h)) is right_complementable Element of the carrier of z
[g,(- h)] is set
{g,(- h)} is set
{g} is non empty trivial 1 -element set
{{g,(- h)},{g}} is set
the addF of z . [g,(- h)] is set
r is right_complementable Element of the carrier of z
m1 is complex real ext-real Element of REAL
m1 / 2 is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k + n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
(CNS - S) . n is right_complementable Element of the carrier of z
((CNS - S) . n) - r is right_complementable Element of the carrier of z
- r is right_complementable Element of the carrier of z
((CNS - S) . n) + (- r) is right_complementable Element of the carrier of z
the addF of z . (((CNS - S) . n),(- r)) is right_complementable Element of the carrier of z
[((CNS - S) . n),(- r)] is set
{((CNS - S) . n),(- r)} is set
{((CNS - S) . n)} is non empty trivial 1 -element set
{{((CNS - S) . n),(- r)},{((CNS - S) . n)}} is set
the addF of z . [((CNS - S) . n),(- r)] is set
||.(((CNS - S) . n) - r).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (((CNS - S) . n) - r) is complex real ext-real Element of REAL
S . n is right_complementable Element of the carrier of z
(S . n) - h is right_complementable Element of the carrier of z
(S . n) + (- h) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- h)) is right_complementable Element of the carrier of z
[(S . n),(- h)] is set
{(S . n),(- h)} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- h)},{(S . n)}} is set
the addF of z . [(S . n),(- h)] is set
||.((S . n) - h).|| is complex real ext-real Element of REAL
the normF of z . ((S . n) - h) is complex real ext-real Element of REAL
CNS . n is right_complementable Element of the carrier of z
(CNS . n) - (S . n) is right_complementable Element of the carrier of z
- (S . n) is right_complementable Element of the carrier of z
(CNS . n) + (- (S . n)) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- (S . n))) is right_complementable Element of the carrier of z
[(CNS . n),(- (S . n))] is set
{(CNS . n),(- (S . n))} is set
{(CNS . n)} is non empty trivial 1 -element set
{{(CNS . n),(- (S . n))},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- (S . n))] is set
((CNS . n) - (S . n)) - (g - h) is right_complementable Element of the carrier of z
- (g - h) is right_complementable Element of the carrier of z
((CNS . n) - (S . n)) + (- (g - h)) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (S . n)),(- (g - h))) is right_complementable Element of the carrier of z
[((CNS . n) - (S . n)),(- (g - h))] is set
{((CNS . n) - (S . n)),(- (g - h))} is set
{((CNS . n) - (S . n))} is non empty trivial 1 -element set
{{((CNS . n) - (S . n)),(- (g - h))},{((CNS . n) - (S . n))}} is set
the addF of z . [((CNS . n) - (S . n)),(- (g - h))] is set
||.(((CNS . n) - (S . n)) - (g - h)).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - (S . n)) - (g - h)) is complex real ext-real Element of REAL
((CNS . n) - (S . n)) - g is right_complementable Element of the carrier of z
- g is right_complementable Element of the carrier of z
((CNS . n) - (S . n)) + (- g) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (S . n)),(- g)) is right_complementable Element of the carrier of z
[((CNS . n) - (S . n)),(- g)] is set
{((CNS . n) - (S . n)),(- g)} is set
{{((CNS . n) - (S . n)),(- g)},{((CNS . n) - (S . n))}} is set
the addF of z . [((CNS . n) - (S . n)),(- g)] is set
(((CNS . n) - (S . n)) - g) + h is right_complementable Element of the carrier of z
the addF of z . ((((CNS . n) - (S . n)) - g),h) is right_complementable Element of the carrier of z
[(((CNS . n) - (S . n)) - g),h] is set
{(((CNS . n) - (S . n)) - g),h} is set
{(((CNS . n) - (S . n)) - g)} is non empty trivial 1 -element set
{{(((CNS . n) - (S . n)) - g),h},{(((CNS . n) - (S . n)) - g)}} is set
the addF of z . [(((CNS . n) - (S . n)) - g),h] is set
||.((((CNS . n) - (S . n)) - g) + h).|| is complex real ext-real Element of REAL
the normF of z . ((((CNS . n) - (S . n)) - g) + h) is complex real ext-real Element of REAL
g + (S . n) is right_complementable Element of the carrier of z
the addF of z . (g,(S . n)) is right_complementable Element of the carrier of z
[g,(S . n)] is set
{g,(S . n)} is set
{{g,(S . n)},{g}} is set
the addF of z . [g,(S . n)] is set
(CNS . n) - (g + (S . n)) is right_complementable Element of the carrier of z
- (g + (S . n)) is right_complementable Element of the carrier of z
(CNS . n) + (- (g + (S . n))) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- (g + (S . n)))) is right_complementable Element of the carrier of z
[(CNS . n),(- (g + (S . n)))] is set
{(CNS . n),(- (g + (S . n)))} is set
{{(CNS . n),(- (g + (S . n)))},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- (g + (S . n)))] is set
((CNS . n) - (g + (S . n))) + h is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (g + (S . n))),h) is right_complementable Element of the carrier of z
[((CNS . n) - (g + (S . n))),h] is set
{((CNS . n) - (g + (S . n))),h} is set
{((CNS . n) - (g + (S . n)))} is non empty trivial 1 -element set
{{((CNS . n) - (g + (S . n))),h},{((CNS . n) - (g + (S . n)))}} is set
the addF of z . [((CNS . n) - (g + (S . n))),h] is set
||.(((CNS . n) - (g + (S . n))) + h).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - (g + (S . n))) + h) is complex real ext-real Element of REAL
(CNS . n) - g is right_complementable Element of the carrier of z
(CNS . n) + (- g) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- g)) is right_complementable Element of the carrier of z
[(CNS . n),(- g)] is set
{(CNS . n),(- g)} is set
{{(CNS . n),(- g)},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- g)] is set
((CNS . n) - g) - (S . n) is right_complementable Element of the carrier of z
((CNS . n) - g) + (- (S . n)) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - g),(- (S . n))) is right_complementable Element of the carrier of z
[((CNS . n) - g),(- (S . n))] is set
{((CNS . n) - g),(- (S . n))} is set
{((CNS . n) - g)} is non empty trivial 1 -element set
{{((CNS . n) - g),(- (S . n))},{((CNS . n) - g)}} is set
the addF of z . [((CNS . n) - g),(- (S . n))] is set
(((CNS . n) - g) - (S . n)) + h is right_complementable Element of the carrier of z
the addF of z . ((((CNS . n) - g) - (S . n)),h) is right_complementable Element of the carrier of z
[(((CNS . n) - g) - (S . n)),h] is set
{(((CNS . n) - g) - (S . n)),h} is set
{(((CNS . n) - g) - (S . n))} is non empty trivial 1 -element set
{{(((CNS . n) - g) - (S . n)),h},{(((CNS . n) - g) - (S . n))}} is set
the addF of z . [(((CNS . n) - g) - (S . n)),h] is set
||.((((CNS . n) - g) - (S . n)) + h).|| is complex real ext-real Element of REAL
the normF of z . ((((CNS . n) - g) - (S . n)) + h) is complex real ext-real Element of REAL
((CNS . n) - g) - ((S . n) - h) is right_complementable Element of the carrier of z
- ((S . n) - h) is right_complementable Element of the carrier of z
((CNS . n) - g) + (- ((S . n) - h)) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - g),(- ((S . n) - h))) is right_complementable Element of the carrier of z
[((CNS . n) - g),(- ((S . n) - h))] is set
{((CNS . n) - g),(- ((S . n) - h))} is set
{{((CNS . n) - g),(- ((S . n) - h))},{((CNS . n) - g)}} is set
the addF of z . [((CNS . n) - g),(- ((S . n) - h))] is set
||.(((CNS . n) - g) - ((S . n) - h)).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - g) - ((S . n) - h)) is complex real ext-real Element of REAL
||.((CNS . n) - g).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . n) - g) is complex real ext-real Element of REAL
||.((CNS . n) - g).|| + ||.((S . n) - h).|| is complex real ext-real Element of REAL
(m1 / 2) + (m1 / 2) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is right_complementable Element of the carrier of z
S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
S - CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
g is right_complementable Element of the carrier of z
g - CNS is right_complementable Element of the carrier of z
- CNS is right_complementable Element of the carrier of z
g + (- CNS) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (g,(- CNS)) is right_complementable Element of the carrier of z
[g,(- CNS)] is set
{g,(- CNS)} is set
{g} is non empty trivial 1 -element set
{{g,(- CNS)},{g}} is set
the addF of z . [g,(- CNS)] is set
h is right_complementable Element of the carrier of z
r is complex real ext-real Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
(S - CNS) . n is right_complementable Element of the carrier of z
((S - CNS) . n) - h is right_complementable Element of the carrier of z
- h is right_complementable Element of the carrier of z
((S - CNS) . n) + (- h) is right_complementable Element of the carrier of z
the addF of z . (((S - CNS) . n),(- h)) is right_complementable Element of the carrier of z
[((S - CNS) . n),(- h)] is set
{((S - CNS) . n),(- h)} is set
{((S - CNS) . n)} is non empty trivial 1 -element set
{{((S - CNS) . n),(- h)},{((S - CNS) . n)}} is set
the addF of z . [((S - CNS) . n),(- h)] is set
||.(((S - CNS) . n) - h).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (((S - CNS) . n) - h) is complex real ext-real Element of REAL
S . n is right_complementable Element of the carrier of z
(S . n) - g is right_complementable Element of the carrier of z
- g is right_complementable Element of the carrier of z
(S . n) + (- g) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- g)) is right_complementable Element of the carrier of z
[(S . n),(- g)] is set
{(S . n),(- g)} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- g)},{(S . n)}} is set
the addF of z . [(S . n),(- g)] is set
||.((S . n) - g).|| is complex real ext-real Element of REAL
the normF of z . ((S . n) - g) is complex real ext-real Element of REAL
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
(S . n) - H1(z) is right_complementable Element of the carrier of z
- (0. z) is right_complementable Element of the carrier of z
(S . n) + (- (0. z)) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- (0. z))) is right_complementable Element of the carrier of z
[(S . n),(- (0. z))] is set
{(S . n),(- (0. z))} is set
{{(S . n),(- (0. z))},{(S . n)}} is set
the addF of z . [(S . n),(- (0. z))] is set
((S . n) - H1(z)) - g is right_complementable Element of the carrier of z
((S . n) - H1(z)) + (- g) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - H1(z)),(- g)) is right_complementable Element of the carrier of z
[((S . n) - H1(z)),(- g)] is set
{((S . n) - H1(z)),(- g)} is set
{((S . n) - H1(z))} is non empty trivial 1 -element set
{{((S . n) - H1(z)),(- g)},{((S . n) - H1(z))}} is set
the addF of z . [((S . n) - H1(z)),(- g)] is set
||.(((S . n) - H1(z)) - g).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - H1(z)) - g) is complex real ext-real Element of REAL
CNS - CNS is right_complementable Element of the carrier of z
CNS + (- CNS) is right_complementable Element of the carrier of z
the addF of z . (CNS,(- CNS)) is right_complementable Element of the carrier of z
[CNS,(- CNS)] is set
{CNS,(- CNS)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- CNS)},{CNS}} is set
the addF of z . [CNS,(- CNS)] is set
(S . n) - (CNS - CNS) is right_complementable Element of the carrier of z
- (CNS - CNS) is right_complementable Element of the carrier of z
(S . n) + (- (CNS - CNS)) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- (CNS - CNS))) is right_complementable Element of the carrier of z
[(S . n),(- (CNS - CNS))] is set
{(S . n),(- (CNS - CNS))} is set
{{(S . n),(- (CNS - CNS))},{(S . n)}} is set
the addF of z . [(S . n),(- (CNS - CNS))] is set
((S . n) - (CNS - CNS)) - g is right_complementable Element of the carrier of z
((S . n) - (CNS - CNS)) + (- g) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - (CNS - CNS)),(- g)) is right_complementable Element of the carrier of z
[((S . n) - (CNS - CNS)),(- g)] is set
{((S . n) - (CNS - CNS)),(- g)} is set
{((S . n) - (CNS - CNS))} is non empty trivial 1 -element set
{{((S . n) - (CNS - CNS)),(- g)},{((S . n) - (CNS - CNS))}} is set
the addF of z . [((S . n) - (CNS - CNS)),(- g)] is set
||.(((S . n) - (CNS - CNS)) - g).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - (CNS - CNS)) - g) is complex real ext-real Element of REAL
(S . n) - CNS is right_complementable Element of the carrier of z
(S . n) + (- CNS) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- CNS)) is right_complementable Element of the carrier of z
[(S . n),(- CNS)] is set
{(S . n),(- CNS)} is set
{{(S . n),(- CNS)},{(S . n)}} is set
the addF of z . [(S . n),(- CNS)] is set
((S . n) - CNS) + CNS is right_complementable Element of the carrier of z
the addF of z . (((S . n) - CNS),CNS) is right_complementable Element of the carrier of z
[((S . n) - CNS),CNS] is set
{((S . n) - CNS),CNS} is set
{((S . n) - CNS)} is non empty trivial 1 -element set
{{((S . n) - CNS),CNS},{((S . n) - CNS)}} is set
the addF of z . [((S . n) - CNS),CNS] is set
(((S . n) - CNS) + CNS) - g is right_complementable Element of the carrier of z
(((S . n) - CNS) + CNS) + (- g) is right_complementable Element of the carrier of z
the addF of z . ((((S . n) - CNS) + CNS),(- g)) is right_complementable Element of the carrier of z
[(((S . n) - CNS) + CNS),(- g)] is set
{(((S . n) - CNS) + CNS),(- g)} is set
{(((S . n) - CNS) + CNS)} is non empty trivial 1 -element set
{{(((S . n) - CNS) + CNS),(- g)},{(((S . n) - CNS) + CNS)}} is set
the addF of z . [(((S . n) - CNS) + CNS),(- g)] is set
||.((((S . n) - CNS) + CNS) - g).|| is complex real ext-real Element of REAL
the normF of z . ((((S . n) - CNS) + CNS) - g) is complex real ext-real Element of REAL
(- g) + CNS is right_complementable Element of the carrier of z
the addF of z . ((- g),CNS) is right_complementable Element of the carrier of z
[(- g),CNS] is set
{(- g),CNS} is set
{(- g)} is non empty trivial 1 -element set
{{(- g),CNS},{(- g)}} is set
the addF of z . [(- g),CNS] is set
((S . n) - CNS) + ((- g) + CNS) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - CNS),((- g) + CNS)) is right_complementable Element of the carrier of z
[((S . n) - CNS),((- g) + CNS)] is set
{((S . n) - CNS),((- g) + CNS)} is set
{{((S . n) - CNS),((- g) + CNS)},{((S . n) - CNS)}} is set
the addF of z . [((S . n) - CNS),((- g) + CNS)] is set
||.(((S . n) - CNS) + ((- g) + CNS)).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - CNS) + ((- g) + CNS)) is complex real ext-real Element of REAL
((S . n) - CNS) - h is right_complementable Element of the carrier of z
((S . n) - CNS) + (- h) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - CNS),(- h)) is right_complementable Element of the carrier of z
[((S . n) - CNS),(- h)] is set
{((S . n) - CNS),(- h)} is set
{{((S . n) - CNS),(- h)},{((S . n) - CNS)}} is set
the addF of z . [((S . n) - CNS),(- h)] is set
||.(((S . n) - CNS) - h).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - CNS) - h) is complex real ext-real Element of REAL
z is complex set
CNS is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of CNS is non empty set
[:NAT, the carrier of CNS:] is non empty V50() set
bool [:NAT, the carrier of CNS:] is non empty V50() set
S is Relation-like NAT -defined the carrier of CNS -valued Function-like V18( NAT , the carrier of CNS) Element of bool [:NAT, the carrier of CNS:]
(CNS,S,z) is Relation-like NAT -defined the carrier of CNS -valued Function-like V18( NAT , the carrier of CNS) Element of bool [:NAT, the carrier of CNS:]
g is right_complementable Element of the carrier of CNS
(CNS,g,z) is right_complementable Element of the carrier of CNS
the of CNS is Relation-like [:COMPLEX, the carrier of CNS:] -defined the carrier of CNS -valued Function-like V18([:COMPLEX, the carrier of CNS:], the carrier of CNS) Element of bool [:[:COMPLEX, the carrier of CNS:], the carrier of CNS:]
[:COMPLEX, the carrier of CNS:] is non empty V50() set
[:[:COMPLEX, the carrier of CNS:], the carrier of CNS:] is non empty V50() set
bool [:[:COMPLEX, the carrier of CNS:], the carrier of CNS:] is non empty V50() set
[z,g] is set
{z,g} is set
{z} is non empty trivial 1 -element set
{{z,g},{z}} is set
the of CNS . [z,g] is set
h is right_complementable Element of the carrier of CNS
0c is complex Element of COMPLEX
|.z.| is complex real ext-real Element of REAL
r is complex real ext-real Element of REAL
r / |.z.| is complex real ext-real Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . n is right_complementable Element of the carrier of CNS
(S . n) - g is right_complementable Element of the carrier of CNS
- g is right_complementable Element of the carrier of CNS
(S . n) + (- g) is right_complementable Element of the carrier of CNS
the addF of CNS is Relation-like [: the carrier of CNS, the carrier of CNS:] -defined the carrier of CNS -valued Function-like V18([: the carrier of CNS, the carrier of CNS:], the carrier of CNS) Element of bool [:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:]
[: the carrier of CNS, the carrier of CNS:] is non empty set
[:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:] is non empty set
bool [:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:] is non empty set
the addF of CNS . ((S . n),(- g)) is right_complementable Element of the carrier of CNS
[(S . n),(- g)] is set
{(S . n),(- g)} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- g)},{(S . n)}} is set
the addF of CNS . [(S . n),(- g)] is set
||.((S . n) - g).|| is complex real ext-real Element of REAL
the normF of CNS is Relation-like the carrier of CNS -defined REAL -valued Function-like V18( the carrier of CNS, REAL ) Element of bool [: the carrier of CNS,REAL:]
[: the carrier of CNS,REAL:] is non empty V50() set
bool [: the carrier of CNS,REAL:] is non empty V50() set
the normF of CNS . ((S . n) - g) is complex real ext-real Element of REAL
|.z.| * (r / |.z.|) is complex real ext-real Element of REAL
|.z.| " is complex real ext-real Element of REAL
(|.z.| ") * r is complex real ext-real Element of REAL
|.z.| * ((|.z.| ") * r) is complex real ext-real Element of REAL
|.z.| * (|.z.| ") is complex real ext-real Element of REAL
(|.z.| * (|.z.| ")) * r is complex real ext-real Element of REAL
1 * r is complex real ext-real Element of REAL
(CNS,(S . n),z) is right_complementable Element of the carrier of CNS
[z,(S . n)] is set
{z,(S . n)} is set
{{z,(S . n)},{z}} is set
the of CNS . [z,(S . n)] is set
(CNS,(S . n),z) - (CNS,g,z) is right_complementable Element of the carrier of CNS
- (CNS,g,z) is right_complementable Element of the carrier of CNS
(CNS,(S . n),z) + (- (CNS,g,z)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),z),(- (CNS,g,z))) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),z),(- (CNS,g,z))] is set
{(CNS,(S . n),z),(- (CNS,g,z))} is set
{(CNS,(S . n),z)} is non empty trivial 1 -element set
{{(CNS,(S . n),z),(- (CNS,g,z))},{(CNS,(S . n),z)}} is set
the addF of CNS . [(CNS,(S . n),z),(- (CNS,g,z))] is set
||.((CNS,(S . n),z) - (CNS,g,z)).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),z) - (CNS,g,z)) is complex real ext-real Element of REAL
(CNS,((S . n) - g),z) is right_complementable Element of the carrier of CNS
[z,((S . n) - g)] is set
{z,((S . n) - g)} is set
{{z,((S . n) - g)},{z}} is set
the of CNS . [z,((S . n) - g)] is set
||.(CNS,((S . n) - g),z).|| is complex real ext-real Element of REAL
the normF of CNS . (CNS,((S . n) - g),z) is complex real ext-real Element of REAL
|.z.| * ||.((S . n) - g).|| is complex real ext-real Element of REAL
(CNS,(S . n),z) - h is right_complementable Element of the carrier of CNS
- h is right_complementable Element of the carrier of CNS
(CNS,(S . n),z) + (- h) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),z),(- h)) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),z),(- h)] is set
{(CNS,(S . n),z),(- h)} is set
{{(CNS,(S . n),z),(- h)},{(CNS,(S . n),z)}} is set
the addF of CNS . [(CNS,(S . n),z),(- h)] is set
||.((CNS,(S . n),z) - h).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),z) - h) is complex real ext-real Element of REAL
(CNS,S,z) . n is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) - h is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) + (- h) is right_complementable Element of the carrier of CNS
the addF of CNS . (((CNS,S,z) . n),(- h)) is right_complementable Element of the carrier of CNS
[((CNS,S,z) . n),(- h)] is set
{((CNS,S,z) . n),(- h)} is set
{((CNS,S,z) . n)} is non empty trivial 1 -element set
{{((CNS,S,z) . n),(- h)},{((CNS,S,z) . n)}} is set
the addF of CNS . [((CNS,S,z) . n),(- h)] is set
||.(((CNS,S,z) . n) - h).|| is complex real ext-real Element of REAL
the normF of CNS . (((CNS,S,z) . n) - h) is complex real ext-real Element of REAL
r is complex real ext-real Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . n is right_complementable Element of the carrier of CNS
(S . n) - g is right_complementable Element of the carrier of CNS
(S . n) + (- g) is right_complementable Element of the carrier of CNS
the addF of CNS . ((S . n),(- g)) is right_complementable Element of the carrier of CNS
[(S . n),(- g)] is set
{(S . n),(- g)} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- g)},{(S . n)}} is set
the addF of CNS . [(S . n),(- g)] is set
||.((S . n) - g).|| is complex real ext-real Element of REAL
the normF of CNS . ((S . n) - g) is complex real ext-real Element of REAL
(CNS,(S . n),z) is right_complementable Element of the carrier of CNS
[z,(S . n)] is set
{z,(S . n)} is set
{{z,(S . n)},{z}} is set
the of CNS . [z,(S . n)] is set
(CNS,(S . n),z) - (CNS,g,z) is right_complementable Element of the carrier of CNS
(CNS,(S . n),z) + (- (CNS,g,z)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),z),(- (CNS,g,z))) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),z),(- (CNS,g,z))] is set
{(CNS,(S . n),z),(- (CNS,g,z))} is set
{(CNS,(S . n),z)} is non empty trivial 1 -element set
{{(CNS,(S . n),z),(- (CNS,g,z))},{(CNS,(S . n),z)}} is set
the addF of CNS . [(CNS,(S . n),z),(- (CNS,g,z))] is set
||.((CNS,(S . n),z) - (CNS,g,z)).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),z) - (CNS,g,z)) is complex real ext-real Element of REAL
(CNS,(S . n),0c) is right_complementable Element of the carrier of CNS
[0c,(S . n)] is set
{0c,(S . n)} is set
{0c} is non empty trivial 1 -element set
{{0c,(S . n)},{0c}} is set
the of CNS . [0c,(S . n)] is set
0. CNS is zero right_complementable Element of the carrier of CNS
the ZeroF of CNS is right_complementable Element of the carrier of CNS
(CNS,(S . n),0c) - H1(CNS) is right_complementable Element of the carrier of CNS
- (0. CNS) is right_complementable Element of the carrier of CNS
(CNS,(S . n),0c) + (- (0. CNS)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),0c),(- (0. CNS))) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),0c),(- (0. CNS))] is set
{(CNS,(S . n),0c),(- (0. CNS))} is set
{(CNS,(S . n),0c)} is non empty trivial 1 -element set
{{(CNS,(S . n),0c),(- (0. CNS))},{(CNS,(S . n),0c)}} is set
the addF of CNS . [(CNS,(S . n),0c),(- (0. CNS))] is set
||.((CNS,(S . n),0c) - H1(CNS)).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),0c) - H1(CNS)) is complex real ext-real Element of REAL
H1(CNS) - H1(CNS) is right_complementable Element of the carrier of CNS
(0. CNS) + (- (0. CNS)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((0. CNS),(- (0. CNS))) is right_complementable Element of the carrier of CNS
[(0. CNS),(- (0. CNS))] is set
{(0. CNS),(- (0. CNS))} is set
{(0. CNS)} is non empty trivial 1 -element set
{{(0. CNS),(- (0. CNS))},{(0. CNS)}} is set
the addF of CNS . [(0. CNS),(- (0. CNS))] is set
||.(H1(CNS) - H1(CNS)).|| is complex real ext-real Element of REAL
the normF of CNS . (H1(CNS) - H1(CNS)) is complex real ext-real Element of REAL
||.H1(CNS).|| is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered Element of REAL
the normF of CNS . (0. CNS) is complex real ext-real Element of REAL
(CNS,(S . n),z) - h is right_complementable Element of the carrier of CNS
(CNS,(S . n),z) + (- h) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),z),(- h)) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),z),(- h)] is set
{(CNS,(S . n),z),(- h)} is set
{{(CNS,(S . n),z),(- h)},{(CNS,(S . n),z)}} is set
the addF of CNS . [(CNS,(S . n),z),(- h)] is set
||.((CNS,(S . n),z) - h).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),z) - h) is complex real ext-real Element of REAL
(CNS,S,z) . n is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) - h is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) + (- h) is right_complementable Element of the carrier of CNS
the addF of CNS . (((CNS,S,z) . n),(- h)) is right_complementable Element of the carrier of CNS
[((CNS,S,z) . n),(- h)] is set
{((CNS,S,z) . n),(- h)} is set
{((CNS,S,z) . n)} is non empty trivial 1 -element set
{{((CNS,S,z) . n),(- h)},{((CNS,S,z) . n)}} is set
the addF of CNS . [((CNS,S,z) . n),(- h)] is set
||.(((CNS,S,z) . n) - h).|| is complex real ext-real Element of REAL
the normF of CNS . (((CNS,S,z) . n) - h) is complex real ext-real Element of REAL
r is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
||.CNS.|| is Relation-like NAT -defined REAL -valued Function-like V18( NAT , REAL ) Element of bool [:NAT,REAL:]
S is right_complementable Element of the carrier of z
g is complex real ext-real set
h is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
CNS . m1 is right_complementable Element of the carrier of z
(CNS . m1) - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
(CNS . m1) + (- S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . ((CNS . m1),(- S)) is right_complementable Element of the carrier of z
[(CNS . m1),(- S)] is set
{(CNS . m1),(- S)} is set
{(CNS . m1)} is non empty trivial 1 -element set
{{(CNS . m1),(- S)},{(CNS . m1)}} is set
the addF of z . [(CNS . m1),(- S)] is set
||.((CNS . m1) - S).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . ((CNS . m1) - S) is complex real ext-real Element of REAL
||.(CNS . m1).|| is complex real ext-real Element of REAL
the normF of z . (CNS . m1) is complex real ext-real Element of REAL
||.S.|| is complex real ext-real Element of REAL
the normF of z . S is complex real ext-real Element of REAL
||.(CNS . m1).|| - ||.S.|| is complex real ext-real Element of REAL
abs (||.(CNS . m1).|| - ||.S.||) is complex real ext-real Element of REAL
||.CNS.|| . m1 is complex real ext-real Element of REAL
(||.CNS.|| . m1) - ||.S.|| is complex real ext-real Element of REAL
abs ((||.CNS.|| . m1) - ||.S.||) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
S is right_complementable Element of the carrier of z
g is right_complementable Element of the carrier of z
S - g is right_complementable Element of the carrier of z
- g is right_complementable Element of the carrier of z
S + (- g) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . (S,(- g)) is right_complementable Element of the carrier of z
[S,(- g)] is set
{S,(- g)} is set
{S} is non empty trivial 1 -element set
{{S,(- g)},{S}} is set
the addF of z . [S,(- g)] is set
||.(S - g).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . (S - g) is complex real ext-real Element of REAL
4 is non empty epsilon-transitive epsilon-connected ordinal natural complex real ext-real positive non negative V50() cardinal Element of NAT
||.(S - g).|| / 4 is complex real ext-real Element of REAL
h is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
CNS . h is right_complementable Element of the carrier of z
S - (CNS . h) is right_complementable Element of the carrier of z
- (CNS . h) is right_complementable Element of the carrier of z
S + (- (CNS . h)) is right_complementable Element of the carrier of z
the addF of z . (S,(- (CNS . h))) is right_complementable Element of the carrier of z
[S,(- (CNS . h))] is set
{S,(- (CNS . h))} is set
{{S,(- (CNS . h))},{S}} is set
the addF of z . [S,(- (CNS . h))] is set
||.(S - (CNS . h)).|| is complex real ext-real Element of REAL
the normF of z . (S - (CNS . h)) is complex real ext-real Element of REAL
(CNS . h) - g is right_complementable Element of the carrier of z
(CNS . h) + (- g) is right_complementable Element of the carrier of z
the addF of z . ((CNS . h),(- g)) is right_complementable Element of the carrier of z
[(CNS . h),(- g)] is set
{(CNS . h),(- g)} is set
{(CNS . h)} is non empty trivial 1 -element set
{{(CNS . h),(- g)},{(CNS . h)}} is set
the addF of z . [(CNS . h),(- g)] is set
||.((CNS . h) - g).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . h) - g) is complex real ext-real Element of REAL
||.(S - (CNS . h)).|| + ||.((CNS . h) - g).|| is complex real ext-real Element of REAL
(CNS . h) - S is right_complementable Element of the carrier of z
- S is right_complementable Element of the carrier of z
(CNS . h) + (- S) is right_complementable Element of the carrier of z
the addF of z . ((CNS . h),(- S)) is right_complementable Element of the carrier of z
[(CNS . h),(- S)] is set
{(CNS . h),(- S)} is set
{{(CNS . h),(- S)},{(CNS . h)}} is set
the addF of z . [(CNS . h),(- S)] is set
||.((CNS . h) - S).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . h) - S) is complex real ext-real Element of REAL
||.((CNS . h) - S).|| + ||.((CNS . h) - g).|| is complex real ext-real Element of REAL
(||.(S - g).|| / 4) + (||.(S - g).|| / 4) is complex real ext-real Element of REAL
||.(S - g).|| / 2 is complex real ext-real Element of REAL
CNS . r is right_complementable Element of the carrier of z
S - (CNS . r) is right_complementable Element of the carrier of z
- (CNS . r) is right_complementable Element of the carrier of z
S + (- (CNS . r)) is right_complementable Element of the carrier of z
the addF of z . (S,(- (CNS . r))) is right_complementable Element of the carrier of z
[S,(- (CNS . r))] is set
{S,(- (CNS . r))} is set
{{S,(- (CNS . r))},{S}} is set
the addF of z . [S,(- (CNS . r))] is set
||.(S - (CNS . r)).|| is complex real ext-real Element of REAL
the normF of z . (S - (CNS . r)) is complex real ext-real Element of REAL
(CNS . r) - g is right_complementable Element of the carrier of z
(CNS . r) + (- g) is right_complementable Element of the carrier of z
the addF of z . ((CNS . r),(- g)) is right_complementable Element of the carrier of z
[(CNS . r),(- g)] is set
{(CNS . r),(- g)} is set
{(CNS . r)} is non empty trivial 1 -element set
{{(CNS . r),(- g)},{(CNS . r)}} is set
the addF of z . [(CNS . r),(- g)] is set
||.((CNS . r) - g).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . r) - g) is complex real ext-real Element of REAL
||.(S - (CNS . r)).|| + ||.((CNS . r) - g).|| is complex real ext-real Element of REAL
(CNS . r) - S is right_complementable Element of the carrier of z
(CNS . r) + (- S) is right_complementable Element of the carrier of z
the addF of z . ((CNS . r),(- S)) is right_complementable Element of the carrier of z
[(CNS . r),(- S)] is set
{(CNS . r),(- S)} is set
{{(CNS . r),(- S)},{(CNS . r)}} is set
the addF of z . [(CNS . r),(- S)] is set
||.((CNS . r) - S).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . r) - S) is complex real ext-real Element of REAL
||.((CNS . r) - S).|| + ||.((CNS . r) - g).|| is complex real ext-real Element of REAL
S is right_complementable Element of the carrier of z
g is right_complementable Element of the carrier of z
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is right_complementable Element of the carrier of z
S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
(z,S) is right_complementable Element of the carrier of z
S - CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
||.(S - CNS).|| is Relation-like NAT -defined REAL -valued Function-like V18( NAT , REAL ) Element of bool [:NAT,REAL:]
lim ||.(S - CNS).|| is complex real ext-real Element of REAL
g is complex real ext-real set
h is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
r is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . m1 is right_complementable Element of the carrier of z
(S . m1) - CNS is right_complementable Element of the carrier of z
- CNS is right_complementable Element of the carrier of z
(S . m1) + (- CNS) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . ((S . m1),(- CNS)) is right_complementable Element of the carrier of z
[(S . m1),(- CNS)] is set
{(S . m1),(- CNS)} is set
{(S . m1)} is non empty trivial 1 -element set
{{(S . m1),(- CNS)},{(S . m1)}} is set
the addF of z . [(S . m1),(- CNS)] is set
||.((S . m1) - CNS).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . ((S . m1) - CNS) is complex real ext-real Element of REAL
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
((S . m1) - CNS) - H1(z) is right_complementable Element of the carrier of z
- (0. z) is right_complementable Element of the carrier of z
((S . m1) - CNS) + (- (0. z)) is right_complementable Element of the carrier of z
the addF of z . (((S . m1) - CNS),(- (0. z))) is right_complementable Element of the carrier of z
[((S . m1) - CNS),(- (0. z))] is set
{((S . m1) - CNS),(- (0. z))} is set
{((S . m1) - CNS)} is non empty trivial 1 -element set
{{((S . m1) - CNS),(- (0. z))},{((S . m1) - CNS)}} is set
the addF of z . [((S . m1) - CNS),(- (0. z))] is set
||.(((S . m1) - CNS) - H1(z)).|| is complex real ext-real Element of REAL
the normF of z . (((S . m1) - CNS) - H1(z)) is complex real ext-real Element of REAL
||.H1(z).|| is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered Element of REAL
the normF of z . (0. z) is complex real ext-real Element of REAL
||.((S . m1) - CNS).|| - ||.H1(z).|| is complex real ext-real Element of REAL
abs (||.((S . m1) - CNS).|| - ||.H1(z).||) is complex real ext-real Element of REAL
||.((S . m1) - CNS).|| - 0 is complex real ext-real Element of REAL
abs (||.((S . m1) - CNS).|| - 0) is complex real ext-real Element of REAL
(S - CNS) . m1 is right_complementable Element of the carrier of z
||.((S - CNS) . m1).|| is complex real ext-real Element of REAL
the normF of z . ((S - CNS) . m1) is complex real ext-real Element of REAL
||.((S - CNS) . m1).|| - 0 is complex real ext-real Element of REAL
abs (||.((S - CNS) . m1).|| - 0) is complex real ext-real Element of REAL
||.(S - CNS).|| . m1 is complex real ext-real Element of REAL
(||.(S - CNS).|| . m1) - 0 is complex real ext-real Element of REAL
abs ((||.(S - CNS).|| . m1) - 0) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
(z,CNS) is right_complementable Element of the carrier of z
S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
CNS + S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
(z,(CNS + S)) is right_complementable Element of the carrier of z
(z,S) is right_complementable Element of the carrier of z
(z,CNS) + (z,S) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . ((z,CNS),(z,S)) is right_complementable Element of the carrier of z
[(z,CNS),(z,S)] is set
{(z,CNS),(z,S)} is set
{(z,CNS)} is non empty trivial 1 -element set
{{(z,CNS),(z,S)},{(z,CNS)}} is set
the addF of z . [(z,CNS),(z,S)] is set
m1 is complex real ext-real Element of REAL
m1 / 2 is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k + n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . n is right_complementable Element of the carrier of z
(S . n) - (z,S) is right_complementable Element of the carrier of z
- (z,S) is right_complementable Element of the carrier of z
(S . n) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- (z,S))) is right_complementable Element of the carrier of z
[(S . n),(- (z,S))] is set
{(S . n),(- (z,S))} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- (z,S))},{(S . n)}} is set
the addF of z . [(S . n),(- (z,S))] is set
||.((S . n) - (z,S)).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . ((S . n) - (z,S)) is complex real ext-real Element of REAL
(CNS + S) . n is right_complementable Element of the carrier of z
((CNS + S) . n) - ((z,CNS) + (z,S)) is right_complementable Element of the carrier of z
- ((z,CNS) + (z,S)) is right_complementable Element of the carrier of z
((CNS + S) . n) + (- ((z,CNS) + (z,S))) is right_complementable Element of the carrier of z
the addF of z . (((CNS + S) . n),(- ((z,CNS) + (z,S)))) is right_complementable Element of the carrier of z
[((CNS + S) . n),(- ((z,CNS) + (z,S)))] is set
{((CNS + S) . n),(- ((z,CNS) + (z,S)))} is set
{((CNS + S) . n)} is non empty trivial 1 -element set
{{((CNS + S) . n),(- ((z,CNS) + (z,S)))},{((CNS + S) . n)}} is set
the addF of z . [((CNS + S) . n),(- ((z,CNS) + (z,S)))] is set
||.(((CNS + S) . n) - ((z,CNS) + (z,S))).|| is complex real ext-real Element of REAL
the normF of z . (((CNS + S) . n) - ((z,CNS) + (z,S))) is complex real ext-real Element of REAL
CNS . n is right_complementable Element of the carrier of z
(CNS . n) + (S . n) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(S . n)) is right_complementable Element of the carrier of z
[(CNS . n),(S . n)] is set
{(CNS . n),(S . n)} is set
{(CNS . n)} is non empty trivial 1 -element set
{{(CNS . n),(S . n)},{(CNS . n)}} is set
the addF of z . [(CNS . n),(S . n)] is set
(- ((z,CNS) + (z,S))) + ((CNS . n) + (S . n)) is right_complementable Element of the carrier of z
the addF of z . ((- ((z,CNS) + (z,S))),((CNS . n) + (S . n))) is right_complementable Element of the carrier of z
[(- ((z,CNS) + (z,S))),((CNS . n) + (S . n))] is set
{(- ((z,CNS) + (z,S))),((CNS . n) + (S . n))} is set
{(- ((z,CNS) + (z,S)))} is non empty trivial 1 -element set
{{(- ((z,CNS) + (z,S))),((CNS . n) + (S . n))},{(- ((z,CNS) + (z,S)))}} is set
the addF of z . [(- ((z,CNS) + (z,S))),((CNS . n) + (S . n))] is set
||.((- ((z,CNS) + (z,S))) + ((CNS . n) + (S . n))).|| is complex real ext-real Element of REAL
the normF of z . ((- ((z,CNS) + (z,S))) + ((CNS . n) + (S . n))) is complex real ext-real Element of REAL
- (z,CNS) is right_complementable Element of the carrier of z
(- (z,CNS)) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . ((- (z,CNS)),(- (z,S))) is right_complementable Element of the carrier of z
[(- (z,CNS)),(- (z,S))] is set
{(- (z,CNS)),(- (z,S))} is set
{(- (z,CNS))} is non empty trivial 1 -element set
{{(- (z,CNS)),(- (z,S))},{(- (z,CNS))}} is set
the addF of z . [(- (z,CNS)),(- (z,S))] is set
((- (z,CNS)) + (- (z,S))) + ((CNS . n) + (S . n)) is right_complementable Element of the carrier of z
the addF of z . (((- (z,CNS)) + (- (z,S))),((CNS . n) + (S . n))) is right_complementable Element of the carrier of z
[((- (z,CNS)) + (- (z,S))),((CNS . n) + (S . n))] is set
{((- (z,CNS)) + (- (z,S))),((CNS . n) + (S . n))} is set
{((- (z,CNS)) + (- (z,S)))} is non empty trivial 1 -element set
{{((- (z,CNS)) + (- (z,S))),((CNS . n) + (S . n))},{((- (z,CNS)) + (- (z,S)))}} is set
the addF of z . [((- (z,CNS)) + (- (z,S))),((CNS . n) + (S . n))] is set
||.(((- (z,CNS)) + (- (z,S))) + ((CNS . n) + (S . n))).|| is complex real ext-real Element of REAL
the normF of z . (((- (z,CNS)) + (- (z,S))) + ((CNS . n) + (S . n))) is complex real ext-real Element of REAL
(CNS . n) + ((- (z,CNS)) + (- (z,S))) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),((- (z,CNS)) + (- (z,S)))) is right_complementable Element of the carrier of z
[(CNS . n),((- (z,CNS)) + (- (z,S)))] is set
{(CNS . n),((- (z,CNS)) + (- (z,S)))} is set
{{(CNS . n),((- (z,CNS)) + (- (z,S)))},{(CNS . n)}} is set
the addF of z . [(CNS . n),((- (z,CNS)) + (- (z,S)))] is set
((CNS . n) + ((- (z,CNS)) + (- (z,S)))) + (S . n) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) + ((- (z,CNS)) + (- (z,S)))),(S . n)) is right_complementable Element of the carrier of z
[((CNS . n) + ((- (z,CNS)) + (- (z,S)))),(S . n)] is set
{((CNS . n) + ((- (z,CNS)) + (- (z,S)))),(S . n)} is set
{((CNS . n) + ((- (z,CNS)) + (- (z,S))))} is non empty trivial 1 -element set
{{((CNS . n) + ((- (z,CNS)) + (- (z,S)))),(S . n)},{((CNS . n) + ((- (z,CNS)) + (- (z,S))))}} is set
the addF of z . [((CNS . n) + ((- (z,CNS)) + (- (z,S)))),(S . n)] is set
||.(((CNS . n) + ((- (z,CNS)) + (- (z,S)))) + (S . n)).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) + ((- (z,CNS)) + (- (z,S)))) + (S . n)) is complex real ext-real Element of REAL
(CNS . n) - (z,CNS) is right_complementable Element of the carrier of z
(CNS . n) + (- (z,CNS)) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- (z,CNS))) is right_complementable Element of the carrier of z
[(CNS . n),(- (z,CNS))] is set
{(CNS . n),(- (z,CNS))} is set
{{(CNS . n),(- (z,CNS))},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- (z,CNS))] is set
((CNS . n) - (z,CNS)) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (z,CNS)),(- (z,S))) is right_complementable Element of the carrier of z
[((CNS . n) - (z,CNS)),(- (z,S))] is set
{((CNS . n) - (z,CNS)),(- (z,S))} is set
{((CNS . n) - (z,CNS))} is non empty trivial 1 -element set
{{((CNS . n) - (z,CNS)),(- (z,S))},{((CNS . n) - (z,CNS))}} is set
the addF of z . [((CNS . n) - (z,CNS)),(- (z,S))] is set
(((CNS . n) - (z,CNS)) + (- (z,S))) + (S . n) is right_complementable Element of the carrier of z
the addF of z . ((((CNS . n) - (z,CNS)) + (- (z,S))),(S . n)) is right_complementable Element of the carrier of z
[(((CNS . n) - (z,CNS)) + (- (z,S))),(S . n)] is set
{(((CNS . n) - (z,CNS)) + (- (z,S))),(S . n)} is set
{(((CNS . n) - (z,CNS)) + (- (z,S)))} is non empty trivial 1 -element set
{{(((CNS . n) - (z,CNS)) + (- (z,S))),(S . n)},{(((CNS . n) - (z,CNS)) + (- (z,S)))}} is set
the addF of z . [(((CNS . n) - (z,CNS)) + (- (z,S))),(S . n)] is set
||.((((CNS . n) - (z,CNS)) + (- (z,S))) + (S . n)).|| is complex real ext-real Element of REAL
the normF of z . ((((CNS . n) - (z,CNS)) + (- (z,S))) + (S . n)) is complex real ext-real Element of REAL
((CNS . n) - (z,CNS)) + ((S . n) - (z,S)) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (z,CNS)),((S . n) - (z,S))) is right_complementable Element of the carrier of z
[((CNS . n) - (z,CNS)),((S . n) - (z,S))] is set
{((CNS . n) - (z,CNS)),((S . n) - (z,S))} is set
{{((CNS . n) - (z,CNS)),((S . n) - (z,S))},{((CNS . n) - (z,CNS))}} is set
the addF of z . [((CNS . n) - (z,CNS)),((S . n) - (z,S))] is set
||.(((CNS . n) - (z,CNS)) + ((S . n) - (z,S))).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - (z,CNS)) + ((S . n) - (z,S))) is complex real ext-real Element of REAL
||.((CNS . n) - (z,CNS)).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . n) - (z,CNS)) is complex real ext-real Element of REAL
||.((CNS . n) - (z,CNS)).|| + ||.((S . n) - (z,S)).|| is complex real ext-real Element of REAL
(m1 / 2) + (m1 / 2) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
(z,CNS) is right_complementable Element of the carrier of z
S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
CNS - S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
(z,(CNS - S)) is right_complementable Element of the carrier of z
(z,S) is right_complementable Element of the carrier of z
(z,CNS) - (z,S) is right_complementable Element of the carrier of z
- (z,S) is right_complementable Element of the carrier of z
(z,CNS) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . ((z,CNS),(- (z,S))) is right_complementable Element of the carrier of z
[(z,CNS),(- (z,S))] is set
{(z,CNS),(- (z,S))} is set
{(z,CNS)} is non empty trivial 1 -element set
{{(z,CNS),(- (z,S))},{(z,CNS)}} is set
the addF of z . [(z,CNS),(- (z,S))] is set
m1 is complex real ext-real Element of REAL
m1 / 2 is complex real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k + n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . n is right_complementable Element of the carrier of z
(S . n) - (z,S) is right_complementable Element of the carrier of z
(S . n) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- (z,S))) is right_complementable Element of the carrier of z
[(S . n),(- (z,S))] is set
{(S . n),(- (z,S))} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- (z,S))},{(S . n)}} is set
the addF of z . [(S . n),(- (z,S))] is set
||.((S . n) - (z,S)).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . ((S . n) - (z,S)) is complex real ext-real Element of REAL
(CNS - S) . n is right_complementable Element of the carrier of z
((CNS - S) . n) - ((z,CNS) - (z,S)) is right_complementable Element of the carrier of z
- ((z,CNS) - (z,S)) is right_complementable Element of the carrier of z
((CNS - S) . n) + (- ((z,CNS) - (z,S))) is right_complementable Element of the carrier of z
the addF of z . (((CNS - S) . n),(- ((z,CNS) - (z,S)))) is right_complementable Element of the carrier of z
[((CNS - S) . n),(- ((z,CNS) - (z,S)))] is set
{((CNS - S) . n),(- ((z,CNS) - (z,S)))} is set
{((CNS - S) . n)} is non empty trivial 1 -element set
{{((CNS - S) . n),(- ((z,CNS) - (z,S)))},{((CNS - S) . n)}} is set
the addF of z . [((CNS - S) . n),(- ((z,CNS) - (z,S)))] is set
||.(((CNS - S) . n) - ((z,CNS) - (z,S))).|| is complex real ext-real Element of REAL
the normF of z . (((CNS - S) . n) - ((z,CNS) - (z,S))) is complex real ext-real Element of REAL
CNS . n is right_complementable Element of the carrier of z
(CNS . n) - (S . n) is right_complementable Element of the carrier of z
- (S . n) is right_complementable Element of the carrier of z
(CNS . n) + (- (S . n)) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- (S . n))) is right_complementable Element of the carrier of z
[(CNS . n),(- (S . n))] is set
{(CNS . n),(- (S . n))} is set
{(CNS . n)} is non empty trivial 1 -element set
{{(CNS . n),(- (S . n))},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- (S . n))] is set
((CNS . n) - (S . n)) - ((z,CNS) - (z,S)) is right_complementable Element of the carrier of z
((CNS . n) - (S . n)) + (- ((z,CNS) - (z,S))) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (S . n)),(- ((z,CNS) - (z,S)))) is right_complementable Element of the carrier of z
[((CNS . n) - (S . n)),(- ((z,CNS) - (z,S)))] is set
{((CNS . n) - (S . n)),(- ((z,CNS) - (z,S)))} is set
{((CNS . n) - (S . n))} is non empty trivial 1 -element set
{{((CNS . n) - (S . n)),(- ((z,CNS) - (z,S)))},{((CNS . n) - (S . n))}} is set
the addF of z . [((CNS . n) - (S . n)),(- ((z,CNS) - (z,S)))] is set
||.(((CNS . n) - (S . n)) - ((z,CNS) - (z,S))).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - (S . n)) - ((z,CNS) - (z,S))) is complex real ext-real Element of REAL
((CNS . n) - (S . n)) - (z,CNS) is right_complementable Element of the carrier of z
- (z,CNS) is right_complementable Element of the carrier of z
((CNS . n) - (S . n)) + (- (z,CNS)) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (S . n)),(- (z,CNS))) is right_complementable Element of the carrier of z
[((CNS . n) - (S . n)),(- (z,CNS))] is set
{((CNS . n) - (S . n)),(- (z,CNS))} is set
{{((CNS . n) - (S . n)),(- (z,CNS))},{((CNS . n) - (S . n))}} is set
the addF of z . [((CNS . n) - (S . n)),(- (z,CNS))] is set
(((CNS . n) - (S . n)) - (z,CNS)) + (z,S) is right_complementable Element of the carrier of z
the addF of z . ((((CNS . n) - (S . n)) - (z,CNS)),(z,S)) is right_complementable Element of the carrier of z
[(((CNS . n) - (S . n)) - (z,CNS)),(z,S)] is set
{(((CNS . n) - (S . n)) - (z,CNS)),(z,S)} is set
{(((CNS . n) - (S . n)) - (z,CNS))} is non empty trivial 1 -element set
{{(((CNS . n) - (S . n)) - (z,CNS)),(z,S)},{(((CNS . n) - (S . n)) - (z,CNS))}} is set
the addF of z . [(((CNS . n) - (S . n)) - (z,CNS)),(z,S)] is set
||.((((CNS . n) - (S . n)) - (z,CNS)) + (z,S)).|| is complex real ext-real Element of REAL
the normF of z . ((((CNS . n) - (S . n)) - (z,CNS)) + (z,S)) is complex real ext-real Element of REAL
(z,CNS) + (S . n) is right_complementable Element of the carrier of z
the addF of z . ((z,CNS),(S . n)) is right_complementable Element of the carrier of z
[(z,CNS),(S . n)] is set
{(z,CNS),(S . n)} is set
{{(z,CNS),(S . n)},{(z,CNS)}} is set
the addF of z . [(z,CNS),(S . n)] is set
(CNS . n) - ((z,CNS) + (S . n)) is right_complementable Element of the carrier of z
- ((z,CNS) + (S . n)) is right_complementable Element of the carrier of z
(CNS . n) + (- ((z,CNS) + (S . n))) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- ((z,CNS) + (S . n)))) is right_complementable Element of the carrier of z
[(CNS . n),(- ((z,CNS) + (S . n)))] is set
{(CNS . n),(- ((z,CNS) + (S . n)))} is set
{{(CNS . n),(- ((z,CNS) + (S . n)))},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- ((z,CNS) + (S . n)))] is set
((CNS . n) - ((z,CNS) + (S . n))) + (z,S) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - ((z,CNS) + (S . n))),(z,S)) is right_complementable Element of the carrier of z
[((CNS . n) - ((z,CNS) + (S . n))),(z,S)] is set
{((CNS . n) - ((z,CNS) + (S . n))),(z,S)} is set
{((CNS . n) - ((z,CNS) + (S . n)))} is non empty trivial 1 -element set
{{((CNS . n) - ((z,CNS) + (S . n))),(z,S)},{((CNS . n) - ((z,CNS) + (S . n)))}} is set
the addF of z . [((CNS . n) - ((z,CNS) + (S . n))),(z,S)] is set
||.(((CNS . n) - ((z,CNS) + (S . n))) + (z,S)).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - ((z,CNS) + (S . n))) + (z,S)) is complex real ext-real Element of REAL
(CNS . n) - (z,CNS) is right_complementable Element of the carrier of z
(CNS . n) + (- (z,CNS)) is right_complementable Element of the carrier of z
the addF of z . ((CNS . n),(- (z,CNS))) is right_complementable Element of the carrier of z
[(CNS . n),(- (z,CNS))] is set
{(CNS . n),(- (z,CNS))} is set
{{(CNS . n),(- (z,CNS))},{(CNS . n)}} is set
the addF of z . [(CNS . n),(- (z,CNS))] is set
((CNS . n) - (z,CNS)) - (S . n) is right_complementable Element of the carrier of z
((CNS . n) - (z,CNS)) + (- (S . n)) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (z,CNS)),(- (S . n))) is right_complementable Element of the carrier of z
[((CNS . n) - (z,CNS)),(- (S . n))] is set
{((CNS . n) - (z,CNS)),(- (S . n))} is set
{((CNS . n) - (z,CNS))} is non empty trivial 1 -element set
{{((CNS . n) - (z,CNS)),(- (S . n))},{((CNS . n) - (z,CNS))}} is set
the addF of z . [((CNS . n) - (z,CNS)),(- (S . n))] is set
(((CNS . n) - (z,CNS)) - (S . n)) + (z,S) is right_complementable Element of the carrier of z
the addF of z . ((((CNS . n) - (z,CNS)) - (S . n)),(z,S)) is right_complementable Element of the carrier of z
[(((CNS . n) - (z,CNS)) - (S . n)),(z,S)] is set
{(((CNS . n) - (z,CNS)) - (S . n)),(z,S)} is set
{(((CNS . n) - (z,CNS)) - (S . n))} is non empty trivial 1 -element set
{{(((CNS . n) - (z,CNS)) - (S . n)),(z,S)},{(((CNS . n) - (z,CNS)) - (S . n))}} is set
the addF of z . [(((CNS . n) - (z,CNS)) - (S . n)),(z,S)] is set
||.((((CNS . n) - (z,CNS)) - (S . n)) + (z,S)).|| is complex real ext-real Element of REAL
the normF of z . ((((CNS . n) - (z,CNS)) - (S . n)) + (z,S)) is complex real ext-real Element of REAL
((CNS . n) - (z,CNS)) - ((S . n) - (z,S)) is right_complementable Element of the carrier of z
- ((S . n) - (z,S)) is right_complementable Element of the carrier of z
((CNS . n) - (z,CNS)) + (- ((S . n) - (z,S))) is right_complementable Element of the carrier of z
the addF of z . (((CNS . n) - (z,CNS)),(- ((S . n) - (z,S)))) is right_complementable Element of the carrier of z
[((CNS . n) - (z,CNS)),(- ((S . n) - (z,S)))] is set
{((CNS . n) - (z,CNS)),(- ((S . n) - (z,S)))} is set
{{((CNS . n) - (z,CNS)),(- ((S . n) - (z,S)))},{((CNS . n) - (z,CNS))}} is set
the addF of z . [((CNS . n) - (z,CNS)),(- ((S . n) - (z,S)))] is set
||.(((CNS . n) - (z,CNS)) - ((S . n) - (z,S))).|| is complex real ext-real Element of REAL
the normF of z . (((CNS . n) - (z,CNS)) - ((S . n) - (z,S))) is complex real ext-real Element of REAL
||.((CNS . n) - (z,CNS)).|| is complex real ext-real Element of REAL
the normF of z . ((CNS . n) - (z,CNS)) is complex real ext-real Element of REAL
||.((CNS . n) - (z,CNS)).|| + ||.((S . n) - (z,S)).|| is complex real ext-real Element of REAL
(m1 / 2) + (m1 / 2) is complex real ext-real Element of REAL
z is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of z is non empty set
[:NAT, the carrier of z:] is non empty V50() set
bool [:NAT, the carrier of z:] is non empty V50() set
CNS is right_complementable Element of the carrier of z
S is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
S - CNS is Relation-like NAT -defined the carrier of z -valued Function-like V18( NAT , the carrier of z) Element of bool [:NAT, the carrier of z:]
(z,(S - CNS)) is right_complementable Element of the carrier of z
(z,S) is right_complementable Element of the carrier of z
(z,S) - CNS is right_complementable Element of the carrier of z
- CNS is right_complementable Element of the carrier of z
(z,S) + (- CNS) is right_complementable Element of the carrier of z
the addF of z is Relation-like [: the carrier of z, the carrier of z:] -defined the carrier of z -valued Function-like V18([: the carrier of z, the carrier of z:], the carrier of z) Element of bool [:[: the carrier of z, the carrier of z:], the carrier of z:]
[: the carrier of z, the carrier of z:] is non empty set
[:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
bool [:[: the carrier of z, the carrier of z:], the carrier of z:] is non empty set
the addF of z . ((z,S),(- CNS)) is right_complementable Element of the carrier of z
[(z,S),(- CNS)] is set
{(z,S),(- CNS)} is set
{(z,S)} is non empty trivial 1 -element set
{{(z,S),(- CNS)},{(z,S)}} is set
the addF of z . [(z,S),(- CNS)] is set
r is complex real ext-real Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . n is right_complementable Element of the carrier of z
(S . n) - (z,S) is right_complementable Element of the carrier of z
- (z,S) is right_complementable Element of the carrier of z
(S . n) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- (z,S))) is right_complementable Element of the carrier of z
[(S . n),(- (z,S))] is set
{(S . n),(- (z,S))} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- (z,S))},{(S . n)}} is set
the addF of z . [(S . n),(- (z,S))] is set
||.((S . n) - (z,S)).|| is complex real ext-real Element of REAL
the normF of z is Relation-like the carrier of z -defined REAL -valued Function-like V18( the carrier of z, REAL ) Element of bool [: the carrier of z,REAL:]
[: the carrier of z,REAL:] is non empty V50() set
bool [: the carrier of z,REAL:] is non empty V50() set
the normF of z . ((S . n) - (z,S)) is complex real ext-real Element of REAL
0. z is zero right_complementable Element of the carrier of z
the ZeroF of z is right_complementable Element of the carrier of z
(S . n) - H1(z) is right_complementable Element of the carrier of z
- (0. z) is right_complementable Element of the carrier of z
(S . n) + (- (0. z)) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- (0. z))) is right_complementable Element of the carrier of z
[(S . n),(- (0. z))] is set
{(S . n),(- (0. z))} is set
{{(S . n),(- (0. z))},{(S . n)}} is set
the addF of z . [(S . n),(- (0. z))] is set
((S . n) - H1(z)) - (z,S) is right_complementable Element of the carrier of z
((S . n) - H1(z)) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - H1(z)),(- (z,S))) is right_complementable Element of the carrier of z
[((S . n) - H1(z)),(- (z,S))] is set
{((S . n) - H1(z)),(- (z,S))} is set
{((S . n) - H1(z))} is non empty trivial 1 -element set
{{((S . n) - H1(z)),(- (z,S))},{((S . n) - H1(z))}} is set
the addF of z . [((S . n) - H1(z)),(- (z,S))] is set
||.(((S . n) - H1(z)) - (z,S)).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - H1(z)) - (z,S)) is complex real ext-real Element of REAL
CNS - CNS is right_complementable Element of the carrier of z
CNS + (- CNS) is right_complementable Element of the carrier of z
the addF of z . (CNS,(- CNS)) is right_complementable Element of the carrier of z
[CNS,(- CNS)] is set
{CNS,(- CNS)} is set
{CNS} is non empty trivial 1 -element set
{{CNS,(- CNS)},{CNS}} is set
the addF of z . [CNS,(- CNS)] is set
(S . n) - (CNS - CNS) is right_complementable Element of the carrier of z
- (CNS - CNS) is right_complementable Element of the carrier of z
(S . n) + (- (CNS - CNS)) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- (CNS - CNS))) is right_complementable Element of the carrier of z
[(S . n),(- (CNS - CNS))] is set
{(S . n),(- (CNS - CNS))} is set
{{(S . n),(- (CNS - CNS))},{(S . n)}} is set
the addF of z . [(S . n),(- (CNS - CNS))] is set
((S . n) - (CNS - CNS)) - (z,S) is right_complementable Element of the carrier of z
((S . n) - (CNS - CNS)) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - (CNS - CNS)),(- (z,S))) is right_complementable Element of the carrier of z
[((S . n) - (CNS - CNS)),(- (z,S))] is set
{((S . n) - (CNS - CNS)),(- (z,S))} is set
{((S . n) - (CNS - CNS))} is non empty trivial 1 -element set
{{((S . n) - (CNS - CNS)),(- (z,S))},{((S . n) - (CNS - CNS))}} is set
the addF of z . [((S . n) - (CNS - CNS)),(- (z,S))] is set
||.(((S . n) - (CNS - CNS)) - (z,S)).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - (CNS - CNS)) - (z,S)) is complex real ext-real Element of REAL
(S . n) - CNS is right_complementable Element of the carrier of z
(S . n) + (- CNS) is right_complementable Element of the carrier of z
the addF of z . ((S . n),(- CNS)) is right_complementable Element of the carrier of z
[(S . n),(- CNS)] is set
{(S . n),(- CNS)} is set
{{(S . n),(- CNS)},{(S . n)}} is set
the addF of z . [(S . n),(- CNS)] is set
((S . n) - CNS) + CNS is right_complementable Element of the carrier of z
the addF of z . (((S . n) - CNS),CNS) is right_complementable Element of the carrier of z
[((S . n) - CNS),CNS] is set
{((S . n) - CNS),CNS} is set
{((S . n) - CNS)} is non empty trivial 1 -element set
{{((S . n) - CNS),CNS},{((S . n) - CNS)}} is set
the addF of z . [((S . n) - CNS),CNS] is set
(((S . n) - CNS) + CNS) - (z,S) is right_complementable Element of the carrier of z
(((S . n) - CNS) + CNS) + (- (z,S)) is right_complementable Element of the carrier of z
the addF of z . ((((S . n) - CNS) + CNS),(- (z,S))) is right_complementable Element of the carrier of z
[(((S . n) - CNS) + CNS),(- (z,S))] is set
{(((S . n) - CNS) + CNS),(- (z,S))} is set
{(((S . n) - CNS) + CNS)} is non empty trivial 1 -element set
{{(((S . n) - CNS) + CNS),(- (z,S))},{(((S . n) - CNS) + CNS)}} is set
the addF of z . [(((S . n) - CNS) + CNS),(- (z,S))] is set
||.((((S . n) - CNS) + CNS) - (z,S)).|| is complex real ext-real Element of REAL
the normF of z . ((((S . n) - CNS) + CNS) - (z,S)) is complex real ext-real Element of REAL
(- (z,S)) + CNS is right_complementable Element of the carrier of z
the addF of z . ((- (z,S)),CNS) is right_complementable Element of the carrier of z
[(- (z,S)),CNS] is set
{(- (z,S)),CNS} is set
{(- (z,S))} is non empty trivial 1 -element set
{{(- (z,S)),CNS},{(- (z,S))}} is set
the addF of z . [(- (z,S)),CNS] is set
((S . n) - CNS) + ((- (z,S)) + CNS) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - CNS),((- (z,S)) + CNS)) is right_complementable Element of the carrier of z
[((S . n) - CNS),((- (z,S)) + CNS)] is set
{((S . n) - CNS),((- (z,S)) + CNS)} is set
{{((S . n) - CNS),((- (z,S)) + CNS)},{((S . n) - CNS)}} is set
the addF of z . [((S . n) - CNS),((- (z,S)) + CNS)] is set
||.(((S . n) - CNS) + ((- (z,S)) + CNS)).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - CNS) + ((- (z,S)) + CNS)) is complex real ext-real Element of REAL
((S . n) - CNS) - ((z,S) - CNS) is right_complementable Element of the carrier of z
- ((z,S) - CNS) is right_complementable Element of the carrier of z
((S . n) - CNS) + (- ((z,S) - CNS)) is right_complementable Element of the carrier of z
the addF of z . (((S . n) - CNS),(- ((z,S) - CNS))) is right_complementable Element of the carrier of z
[((S . n) - CNS),(- ((z,S) - CNS))] is set
{((S . n) - CNS),(- ((z,S) - CNS))} is set
{{((S . n) - CNS),(- ((z,S) - CNS))},{((S . n) - CNS)}} is set
the addF of z . [((S . n) - CNS),(- ((z,S) - CNS))] is set
||.(((S . n) - CNS) - ((z,S) - CNS)).|| is complex real ext-real Element of REAL
the normF of z . (((S . n) - CNS) - ((z,S) - CNS)) is complex real ext-real Element of REAL
(S - CNS) . n is right_complementable Element of the carrier of z
((S - CNS) . n) - ((z,S) - CNS) is right_complementable Element of the carrier of z
((S - CNS) . n) + (- ((z,S) - CNS)) is right_complementable Element of the carrier of z
the addF of z . (((S - CNS) . n),(- ((z,S) - CNS))) is right_complementable Element of the carrier of z
[((S - CNS) . n),(- ((z,S) - CNS))] is set
{((S - CNS) . n),(- ((z,S) - CNS))} is set
{((S - CNS) . n)} is non empty trivial 1 -element set
{{((S - CNS) . n),(- ((z,S) - CNS))},{((S - CNS) . n)}} is set
the addF of z . [((S - CNS) . n),(- ((z,S) - CNS))] is set
||.(((S - CNS) . n) - ((z,S) - CNS)).|| is complex real ext-real Element of REAL
the normF of z . (((S - CNS) . n) - ((z,S) - CNS)) is complex real ext-real Element of REAL
z is complex set
CNS is non empty right_complementable Abelian add-associative right_zeroed discerning reflexive () () () () () ()
the carrier of CNS is non empty set
[:NAT, the carrier of CNS:] is non empty V50() set
bool [:NAT, the carrier of CNS:] is non empty V50() set
S is Relation-like NAT -defined the carrier of CNS -valued Function-like V18( NAT , the carrier of CNS) Element of bool [:NAT, the carrier of CNS:]
(CNS,S,z) is Relation-like NAT -defined the carrier of CNS -valued Function-like V18( NAT , the carrier of CNS) Element of bool [:NAT, the carrier of CNS:]
(CNS,(CNS,S,z)) is right_complementable Element of the carrier of CNS
(CNS,S) is right_complementable Element of the carrier of CNS
(CNS,(CNS,S),z) is right_complementable Element of the carrier of CNS
the of CNS is Relation-like [:COMPLEX, the carrier of CNS:] -defined the carrier of CNS -valued Function-like V18([:COMPLEX, the carrier of CNS:], the carrier of CNS) Element of bool [:[:COMPLEX, the carrier of CNS:], the carrier of CNS:]
[:COMPLEX, the carrier of CNS:] is non empty V50() set
[:[:COMPLEX, the carrier of CNS:], the carrier of CNS:] is non empty V50() set
bool [:[:COMPLEX, the carrier of CNS:], the carrier of CNS:] is non empty V50() set
[z,(CNS,S)] is set
{z,(CNS,S)} is set
{z} is non empty trivial 1 -element set
{{z,(CNS,S)},{z}} is set
the of CNS . [z,(CNS,S)] is set
r is complex real ext-real Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . n is right_complementable Element of the carrier of CNS
(S . n) - (CNS,S) is right_complementable Element of the carrier of CNS
- (CNS,S) is right_complementable Element of the carrier of CNS
(S . n) + (- (CNS,S)) is right_complementable Element of the carrier of CNS
the addF of CNS is Relation-like [: the carrier of CNS, the carrier of CNS:] -defined the carrier of CNS -valued Function-like V18([: the carrier of CNS, the carrier of CNS:], the carrier of CNS) Element of bool [:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:]
[: the carrier of CNS, the carrier of CNS:] is non empty set
[:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:] is non empty set
bool [:[: the carrier of CNS, the carrier of CNS:], the carrier of CNS:] is non empty set
the addF of CNS . ((S . n),(- (CNS,S))) is right_complementable Element of the carrier of CNS
[(S . n),(- (CNS,S))] is set
{(S . n),(- (CNS,S))} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- (CNS,S))},{(S . n)}} is set
the addF of CNS . [(S . n),(- (CNS,S))] is set
||.((S . n) - (CNS,S)).|| is complex real ext-real Element of REAL
the normF of CNS is Relation-like the carrier of CNS -defined REAL -valued Function-like V18( the carrier of CNS, REAL ) Element of bool [: the carrier of CNS,REAL:]
[: the carrier of CNS,REAL:] is non empty V50() set
bool [: the carrier of CNS,REAL:] is non empty V50() set
the normF of CNS . ((S . n) - (CNS,S)) is complex real ext-real Element of REAL
(CNS,(S . n),z) is right_complementable Element of the carrier of CNS
[z,(S . n)] is set
{z,(S . n)} is set
{{z,(S . n)},{z}} is set
the of CNS . [z,(S . n)] is set
(CNS,(S . n),z) - (CNS,(CNS,S),z) is right_complementable Element of the carrier of CNS
- (CNS,(CNS,S),z) is right_complementable Element of the carrier of CNS
(CNS,(S . n),z) + (- (CNS,(CNS,S),z)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),z),(- (CNS,(CNS,S),z))) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),z),(- (CNS,(CNS,S),z))] is set
{(CNS,(S . n),z),(- (CNS,(CNS,S),z))} is set
{(CNS,(S . n),z)} is non empty trivial 1 -element set
{{(CNS,(S . n),z),(- (CNS,(CNS,S),z))},{(CNS,(S . n),z)}} is set
the addF of CNS . [(CNS,(S . n),z),(- (CNS,(CNS,S),z))] is set
||.((CNS,(S . n),z) - (CNS,(CNS,S),z)).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),z) - (CNS,(CNS,S),z)) is complex real ext-real Element of REAL
0c is complex Element of COMPLEX
(CNS,(S . n),0c) is right_complementable Element of the carrier of CNS
[0c,(S . n)] is set
{0c,(S . n)} is set
{0c} is non empty trivial 1 -element set
{{0c,(S . n)},{0c}} is set
the of CNS . [0c,(S . n)] is set
0. CNS is zero right_complementable Element of the carrier of CNS
the ZeroF of CNS is right_complementable Element of the carrier of CNS
(CNS,(S . n),0c) - H1(CNS) is right_complementable Element of the carrier of CNS
- (0. CNS) is right_complementable Element of the carrier of CNS
(CNS,(S . n),0c) + (- (0. CNS)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),0c),(- (0. CNS))) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),0c),(- (0. CNS))] is set
{(CNS,(S . n),0c),(- (0. CNS))} is set
{(CNS,(S . n),0c)} is non empty trivial 1 -element set
{{(CNS,(S . n),0c),(- (0. CNS))},{(CNS,(S . n),0c)}} is set
the addF of CNS . [(CNS,(S . n),0c),(- (0. CNS))] is set
||.((CNS,(S . n),0c) - H1(CNS)).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),0c) - H1(CNS)) is complex real ext-real Element of REAL
H1(CNS) - H1(CNS) is right_complementable Element of the carrier of CNS
(0. CNS) + (- (0. CNS)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((0. CNS),(- (0. CNS))) is right_complementable Element of the carrier of CNS
[(0. CNS),(- (0. CNS))] is set
{(0. CNS),(- (0. CNS))} is set
{(0. CNS)} is non empty trivial 1 -element set
{{(0. CNS),(- (0. CNS))},{(0. CNS)}} is set
the addF of CNS . [(0. CNS),(- (0. CNS))] is set
||.(H1(CNS) - H1(CNS)).|| is complex real ext-real Element of REAL
the normF of CNS . (H1(CNS) - H1(CNS)) is complex real ext-real Element of REAL
||.H1(CNS).|| is functional empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural complex real ext-real non positive non negative V50() cardinal {} -element FinSequence-membered Element of REAL
the normF of CNS . (0. CNS) is complex real ext-real Element of REAL
(CNS,S,z) . n is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) - (CNS,(CNS,S),z) is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) + (- (CNS,(CNS,S),z)) is right_complementable Element of the carrier of CNS
the addF of CNS . (((CNS,S,z) . n),(- (CNS,(CNS,S),z))) is right_complementable Element of the carrier of CNS
[((CNS,S,z) . n),(- (CNS,(CNS,S),z))] is set
{((CNS,S,z) . n),(- (CNS,(CNS,S),z))} is set
{((CNS,S,z) . n)} is non empty trivial 1 -element set
{{((CNS,S,z) . n),(- (CNS,(CNS,S),z))},{((CNS,S,z) . n)}} is set
the addF of CNS . [((CNS,S,z) . n),(- (CNS,(CNS,S),z))] is set
||.(((CNS,S,z) . n) - (CNS,(CNS,S),z)).|| is complex real ext-real Element of REAL
the normF of CNS . (((CNS,S,z) . n) - (CNS,(CNS,S),z)) is complex real ext-real Element of REAL
|.z.| is complex real ext-real Element of REAL
r is complex real ext-real Element of REAL
r / |.z.| is complex real ext-real Element of REAL
m1 is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
k is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
n is epsilon-transitive epsilon-connected ordinal natural complex real ext-real V50() cardinal Element of NAT
S . n is right_complementable Element of the carrier of CNS
(S . n) - (CNS,S) is right_complementable Element of the carrier of CNS
(S . n) + (- (CNS,S)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((S . n),(- (CNS,S))) is right_complementable Element of the carrier of CNS
[(S . n),(- (CNS,S))] is set
{(S . n),(- (CNS,S))} is set
{(S . n)} is non empty trivial 1 -element set
{{(S . n),(- (CNS,S))},{(S . n)}} is set
the addF of CNS . [(S . n),(- (CNS,S))] is set
||.((S . n) - (CNS,S)).|| is complex real ext-real Element of REAL
the normF of CNS . ((S . n) - (CNS,S)) is complex real ext-real Element of REAL
|.z.| * (r / |.z.|) is complex real ext-real Element of REAL
|.z.| " is complex real ext-real Element of REAL
(|.z.| ") * r is complex real ext-real Element of REAL
|.z.| * ((|.z.| ") * r) is complex real ext-real Element of REAL
|.z.| * (|.z.| ") is complex real ext-real Element of REAL
(|.z.| * (|.z.| ")) * r is complex real ext-real Element of REAL
1 * r is complex real ext-real Element of REAL
(CNS,(S . n),z) is right_complementable Element of the carrier of CNS
[z,(S . n)] is set
{z,(S . n)} is set
{{z,(S . n)},{z}} is set
the of CNS . [z,(S . n)] is set
(CNS,(S . n),z) - (CNS,(CNS,S),z) is right_complementable Element of the carrier of CNS
(CNS,(S . n),z) + (- (CNS,(CNS,S),z)) is right_complementable Element of the carrier of CNS
the addF of CNS . ((CNS,(S . n),z),(- (CNS,(CNS,S),z))) is right_complementable Element of the carrier of CNS
[(CNS,(S . n),z),(- (CNS,(CNS,S),z))] is set
{(CNS,(S . n),z),(- (CNS,(CNS,S),z))} is set
{(CNS,(S . n),z)} is non empty trivial 1 -element set
{{(CNS,(S . n),z),(- (CNS,(CNS,S),z))},{(CNS,(S . n),z)}} is set
the addF of CNS . [(CNS,(S . n),z),(- (CNS,(CNS,S),z))] is set
||.((CNS,(S . n),z) - (CNS,(CNS,S),z)).|| is complex real ext-real Element of REAL
the normF of CNS . ((CNS,(S . n),z) - (CNS,(CNS,S),z)) is complex real ext-real Element of REAL
(CNS,((S . n) - (CNS,S)),z) is right_complementable Element of the carrier of CNS
[z,((S . n) - (CNS,S))] is set
{z,((S . n) - (CNS,S))} is set
{{z,((S . n) - (CNS,S))},{z}} is set
the of CNS . [z,((S . n) - (CNS,S))] is set
||.(CNS,((S . n) - (CNS,S)),z).|| is complex real ext-real Element of REAL
the normF of CNS . (CNS,((S . n) - (CNS,S)),z) is complex real ext-real Element of REAL
|.z.| * ||.((S . n) - (CNS,S)).|| is complex real ext-real Element of REAL
(CNS,S,z) . n is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) - (CNS,(CNS,S),z) is right_complementable Element of the carrier of CNS
((CNS,S,z) . n) + (- (CNS,(CNS,S),z)) is right_complementable Element of the carrier of CNS
the addF of CNS . (((CNS,S,z) . n),(- (CNS,(CNS,S),z))) is right_complementable Element of the carrier of CNS
[((CNS,S,z) . n),(- (CNS,(CNS,S),z))] is set
{((CNS,S,z) . n),(- (CNS,(CNS,S),z))} is set
{((CNS,S,z) . n)} is non empty trivial 1 -element set
{{((CNS,S,z) . n),(- (CNS,(CNS,S),z))},{((CNS,S,z) . n)}} is set
the addF of CNS . [((CNS,S,z) . n),(- (CNS,(CNS,S),z))] is set
||.(((CNS,S,z) . n) - (CNS,(CNS,S),z)).|| is complex real ext-real Element of REAL
the normF of CNS . (((CNS,S,z) . n) - (CNS,(CNS,S),z)) is complex real ext-real Element of REAL
CNS is non empty set
[:CNS,CNS:] is non empty set
[:[:CNS,CNS:],CNS:] is non empty set
bool [:[:CNS,CNS:],CNS:] is non empty set
[:COMPLEX,CNS:] is non empty V50() set
[:[:COMPLEX,CNS:],CNS:] is non empty V50() set
bool [:[:COMPLEX,CNS:],CNS:] is non empty V50() set
r is non empty right_complementable Abelian add-associative right_zeroed () () () () ()
the carrier of r is non empty set
bool the carrier of r is non empty set
S is Element of CNS
g is Relation-like [:CNS,CNS:] -defined CNS -valued Function-like V18([:CNS,CNS:],CNS) Element of bool [:[:CNS,CNS:],CNS:]
h is Relation-like [:COMPLEX,CNS:] -defined CNS -valued Function-like V18([:COMPLEX,CNS:],CNS) Element of bool [:[:COMPLEX,CNS:],CNS:]
(CNS,S,g,h) is non empty () ()
the carrier of (CNS,S,g,h) is non empty set
m1 is Element of bool the carrier of r
[:COMPLEX, the carrier of r:] is non empty V50() set
the of r is Relation-like [:COMPLEX, the carrier of r:] -defined the carrier of r -valued Function-like V18([:COMPLEX, the carrier of r:], the carrier of r) Element of bool [:[:COMPLEX, the carrier of r:], the carrier of r:]
[:[:COMPLEX, the carrier of r:], the carrier of r:] is non empty V50() set
bool [:[:COMPLEX, the carrier of r:], the carrier of r:] is non empty V50() set
[:COMPLEX,m1:] is set
the of r | [:COMPLEX,m1:] is Relation-like [:COMPLEX, the carrier of r:] -defined the carrier of r -valued Function-like Element of bool [:[:COMPLEX, the carrier of r:], the carrier of r:]
n is Element of the carrier of (CNS,S,g,h)
k is right_complementable Element of the carrier of r
z is complex set
((CNS,S,g,h),n,z) is Element of the carrier of (CNS,S,g,h)
the of (CNS,S,g,h) is Relation-like [:COMPLEX, the carrier of (CNS,S,g,h):] -defined the carrier of (CNS,S,g,h) -valued Function-like V18([:COMPLEX, the carrier of (CNS,S,g,h):], the carrier of (CNS,S,g,h)) Element of bool [:[:COMPLEX, the carrier of (CNS,S,g,h):], the carrier of (CNS,S,g,h):]
[:COMPLEX, the carrier of (CNS,S,g,h):] is non empty V50() set
[:[:COMPLEX, the carrier of (CNS,S,g,h):], the carrier of (CNS,S,g,h):] is non empty V50() set
bool [:[:COMPLEX, the carrier of (CNS,S,g,h):], the carrier of (CNS,S,g,h):] is non empty V50() set
[z,n] is set
{z,n} is set
{z} is non empty trivial 1 -element set
{{z,n},{z}} is set
the of (CNS,S,g,h) . [z,n] is set
(r,k,z) is right_complementable Element of the carrier of r
[z,k] is set
{z,k} is set
{{z,k},{z}} is set
the of r . [z,k] is set