:: CSSPACE semantic presentation

REAL is non empty V52() V64() V65() V66() V70() set
NAT is non empty V26() V27() V28() V64() V65() V66() V67() V68() V69() V70() Element of bool REAL
bool REAL is non empty set
COMPLEX is non empty V52() V64() V70() set
NAT is non empty V26() V27() V28() V64() V65() V66() V67() V68() V69() V70() set
bool NAT is non empty set
bool NAT is non empty set
RAT is non empty V52() V64() V65() V66() V67() V70() set
INT is non empty V52() V64() V65() V66() V67() V68() V70() set
[:NAT,REAL:] is non empty V38() V39() V40() set
bool [:NAT,REAL:] is non empty set
[:NAT,COMPLEX:] is non empty V38() set
bool [:NAT,COMPLEX:] is non empty set
{} is Function-like functional empty V26() V27() V28() V30() V31() V32() complex ext-real non positive non negative V64() V65() V66() V67() V68() V69() V70() set
1 is non empty V26() V27() V28() V32() complex V34() ext-real positive non negative V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
0 is Function-like functional empty V26() V27() V28() V30() V31() V32() complex V34() ext-real non positive non negative V50() V63() V64() V65() V66() V67() V68() V69() V70() Element of NAT
sqrt 0 is complex V34() ext-real Element of REAL
1r is complex Element of COMPLEX
- 1r is complex Element of COMPLEX
Re 0 is complex V34() ext-real Element of REAL
Im 0 is complex V34() ext-real Element of REAL
<i> is complex Element of COMPLEX
0 *' is complex Element of COMPLEX
1r *' is complex Element of COMPLEX
|.0.| is complex V34() ext-real V63() Element of REAL
|.1r.| is complex V34() ext-real Element of REAL
Funcs (NAT,COMPLEX) is functional non empty FUNCTION_DOMAIN of NAT , COMPLEX
V0 is set
the Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:] is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
nilfunc is non empty set
X0 is set
X0 is set
seq is set
V0 is non empty set
nilfunc is non empty set
X0 is set
X0 is set
() is non empty set
V0 is set
V0 is set
[:(),():] is non empty set
[:[:(),():],():] is non empty set
bool [:[:(),():],():] is non empty set
V0 is Element of ()
nilfunc is Element of ()
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) + (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is Relation-like [:(),():] -defined () -valued Function-like non empty V14([:(),():]) quasi_total Element of bool [:[:(),():],():]
V0 is Relation-like [:(),():] -defined () -valued Function-like non empty V14([:(),():]) quasi_total Element of bool [:[:(),():],():]
V0 is Relation-like [:(),():] -defined () -valued Function-like non empty V14([:(),():]) quasi_total Element of bool [:[:(),():],():]
nilfunc is Relation-like [:(),():] -defined () -valued Function-like non empty V14([:(),():]) quasi_total Element of bool [:[:(),():],():]
() is Relation-like [:(),():] -defined () -valued Function-like non empty V14([:(),():]) quasi_total Element of bool [:[:(),():],():]
[:COMPLEX,():] is non empty set
[:[:COMPLEX,():],():] is non empty set
bool [:[:COMPLEX,():],():] is non empty set
V0 is set
nilfunc is set
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) is complex set
(V0) (#) (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is Relation-like [:COMPLEX,():] -defined () -valued Function-like non empty V14([:COMPLEX,():]) quasi_total Element of bool [:[:COMPLEX,():],():]
nilfunc is set
X0 is set
V0 . (nilfunc,X0) is set
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
V0 . [nilfunc,X0] is set
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) is complex set
(nilfunc) (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is Relation-like [:COMPLEX,():] -defined () -valued Function-like non empty V14([:COMPLEX,():]) quasi_total Element of bool [:[:COMPLEX,():],():]
nilfunc is Relation-like [:COMPLEX,():] -defined () -valued Function-like non empty V14([:COMPLEX,():]) quasi_total Element of bool [:[:COMPLEX,():],():]
X0 is complex Element of COMPLEX
seq is Element of ()
V0 . (X0,seq) is Element of ()
[X0,seq] is set
{X0,seq} is non empty set
{X0} is non empty V64() set
{{X0,seq},{X0}} is non empty set
V0 . [X0,seq] is set
nilfunc . (X0,seq) is Element of ()
nilfunc . [X0,seq] is set
(seq) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(X0) is complex set
(X0) (#) (seq) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
() is Relation-like [:COMPLEX,():] -defined () -valued Function-like non empty V14([:COMPLEX,():]) quasi_total Element of bool [:[:COMPLEX,():],():]
0c is Function-like functional empty V26() V27() V28() V30() V31() V32() complex ext-real non positive non negative V64() V65() V66() V67() V68() V69() V70() Element of COMPLEX
NAT --> 0c is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() V41() Element of bool [:NAT,COMPLEX:]
V0 is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
nilfunc is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
V0 . nilfunc is complex Element of COMPLEX
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is Element of ()
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
nilfunc is Element of ()
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
X0 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(V0) . X0 is complex Element of COMPLEX
(nilfunc) . X0 is complex Element of COMPLEX
() is Element of ()
V0 is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
CLSStruct(# (),(),(),() #) is non empty strict CLSStruct
the carrier of CLSStruct(# (),(),(),() #) is non empty set
V0 is Element of the carrier of CLSStruct(# (),(),(),() #)
nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
V0 + nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) is Relation-like [: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
the addF of CLSStruct(# (),(),(),() #) . (V0,nilfunc) is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,nilfunc] is set
{V0,nilfunc} is non empty set
{V0} is non empty set
{{V0,nilfunc},{V0}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [V0,nilfunc] is set
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) + (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is complex set
nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
V0 * nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
the Mult of CLSStruct(# (),(),(),() #) is Relation-like [:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[V0,nilfunc] is set
{V0,nilfunc} is non empty set
{V0} is non empty V64() set
{{V0,nilfunc},{V0}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [V0,nilfunc] is set
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
() . (V0,nilfunc) is set
() . [V0,nilfunc] is set
(V0) is complex set
(V0) (#) (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is Element of the carrier of CLSStruct(# (),(),(),() #)
nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
V0 + nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) is Relation-like [: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
the addF of CLSStruct(# (),(),(),() #) . (V0,nilfunc) is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,nilfunc] is set
{V0,nilfunc} is non empty set
{V0} is non empty set
{{V0,nilfunc},{V0}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [V0,nilfunc] is set
nilfunc + V0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) . (nilfunc,V0) is Element of the carrier of CLSStruct(# (),(),(),() #)
[nilfunc,V0] is set
{nilfunc,V0} is non empty set
{nilfunc} is non empty set
{{nilfunc,V0},{nilfunc}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [nilfunc,V0] is set
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) + (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is Element of the carrier of CLSStruct(# (),(),(),() #)
nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
V0 + nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) is Relation-like [: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
the addF of CLSStruct(# (),(),(),() #) . (V0,nilfunc) is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,nilfunc] is set
{V0,nilfunc} is non empty set
{V0} is non empty set
{{V0,nilfunc},{V0}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [V0,nilfunc] is set
X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
(V0 + nilfunc) + X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) . ((V0 + nilfunc),X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
[(V0 + nilfunc),X0] is set
{(V0 + nilfunc),X0} is non empty set
{(V0 + nilfunc)} is non empty set
{{(V0 + nilfunc),X0},{(V0 + nilfunc)}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [(V0 + nilfunc),X0] is set
nilfunc + X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) . (nilfunc,X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [nilfunc,X0] is set
V0 + (nilfunc + X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) . (V0,(nilfunc + X0)) is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,(nilfunc + X0)] is set
{V0,(nilfunc + X0)} is non empty set
{{V0,(nilfunc + X0)},{V0}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [V0,(nilfunc + X0)] is set
((V0 + nilfunc)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 + nilfunc)) + (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) + (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(((V0) + (nilfunc))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(((V0) + (nilfunc))) + (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0) + (nilfunc)) + (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) + (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) + ((nilfunc) + (X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(((nilfunc) + (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) + (((nilfunc) + (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((nilfunc + X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0) + ((nilfunc + X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
0. CLSStruct(# (),(),(),() #) is zero Element of the carrier of CLSStruct(# (),(),(),() #)
the ZeroF of CLSStruct(# (),(),(),() #) is Element of the carrier of CLSStruct(# (),(),(),() #)
nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
nilfunc + (0. CLSStruct(# (),(),(),() #)) is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) is Relation-like [: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
the addF of CLSStruct(# (),(),(),() #) . (nilfunc,(0. CLSStruct(# (),(),(),() #))) is Element of the carrier of CLSStruct(# (),(),(),() #)
[nilfunc,(0. CLSStruct(# (),(),(),() #))] is set
{nilfunc,(0. CLSStruct(# (),(),(),() #))} is non empty set
{nilfunc} is non empty set
{{nilfunc,(0. CLSStruct(# (),(),(),() #))},{nilfunc}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [nilfunc,(0. CLSStruct(# (),(),(),() #))] is set
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(()) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) + (()) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
X0 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
((nilfunc) + (())) . X0 is complex Element of COMPLEX
(nilfunc) . X0 is complex Element of COMPLEX
(()) . X0 is complex Element of COMPLEX
((nilfunc) . X0) + ((()) . X0) is complex Element of COMPLEX
((nilfunc) . X0) + 0c is complex Element of COMPLEX
nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
- (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) + (- (nilfunc)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(()) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
seq is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
((nilfunc) + (- (nilfunc))) . seq is complex Element of COMPLEX
(()) . seq is complex Element of COMPLEX
(nilfunc) . seq is complex Element of COMPLEX
(- (nilfunc)) . seq is complex Element of COMPLEX
((nilfunc) . seq) + ((- (nilfunc)) . seq) is complex Element of COMPLEX
- ((nilfunc) . seq) is complex Element of COMPLEX
((nilfunc) . seq) + (- ((nilfunc) . seq)) is complex Element of COMPLEX
X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
nilfunc + X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) is Relation-like [: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
the addF of CLSStruct(# (),(),(),() #) . (nilfunc,X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [nilfunc,X0] is set
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) + (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is complex set
nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
nilfunc + X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) is Relation-like [: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
the addF of CLSStruct(# (),(),(),() #) . (nilfunc,X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [nilfunc,X0] is set
V0 * (nilfunc + X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
the Mult of CLSStruct(# (),(),(),() #) is Relation-like [:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[V0,(nilfunc + X0)] is set
{V0,(nilfunc + X0)} is non empty set
{V0} is non empty V64() set
{{V0,(nilfunc + X0)},{V0}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [V0,(nilfunc + X0)] is set
V0 * nilfunc is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,nilfunc] is set
{V0,nilfunc} is non empty set
{{V0,nilfunc},{V0}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [V0,nilfunc] is set
V0 * X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,X0] is set
{V0,X0} is non empty set
{{V0,X0},{V0}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [V0,X0] is set
(V0 * nilfunc) + (V0 * X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) . ((V0 * nilfunc),(V0 * X0)) is Element of the carrier of CLSStruct(# (),(),(),() #)
[(V0 * nilfunc),(V0 * X0)] is set
{(V0 * nilfunc),(V0 * X0)} is non empty set
{(V0 * nilfunc)} is non empty set
{{(V0 * nilfunc),(V0 * X0)},{(V0 * nilfunc)}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [(V0 * nilfunc),(V0 * X0)] is set
((nilfunc + X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) ((nilfunc + X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(nilfunc) + (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(((nilfunc) + (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) (((nilfunc) + (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) ((nilfunc) + (X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) (nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0 (#) (nilfunc)) + (V0 (#) (X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 * nilfunc)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 * nilfunc)) + ((V0 * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 (#) (nilfunc))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 (#) (nilfunc))) + ((V0 * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 (#) (nilfunc))) + ((V0 (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0 (#) (nilfunc)) + ((V0 (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is complex set
nilfunc is complex set
V0 + nilfunc is complex set
X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
(V0 + nilfunc) * X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the Mult of CLSStruct(# (),(),(),() #) is Relation-like [:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[(V0 + nilfunc),X0] is set
{(V0 + nilfunc),X0} is non empty set
{(V0 + nilfunc)} is non empty V64() set
{{(V0 + nilfunc),X0},{(V0 + nilfunc)}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [(V0 + nilfunc),X0] is set
V0 * X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,X0] is set
{V0,X0} is non empty set
{V0} is non empty V64() set
{{V0,X0},{V0}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [V0,X0] is set
nilfunc * X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty V64() set
{{nilfunc,X0},{nilfunc}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [nilfunc,X0] is set
(V0 * X0) + (nilfunc * X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
the addF of CLSStruct(# (),(),(),() #) is Relation-like [: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[: the carrier of CLSStruct(# (),(),(),() #), the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
the addF of CLSStruct(# (),(),(),() #) . ((V0 * X0),(nilfunc * X0)) is Element of the carrier of CLSStruct(# (),(),(),() #)
[(V0 * X0),(nilfunc * X0)] is set
{(V0 * X0),(nilfunc * X0)} is non empty set
{(V0 * X0)} is non empty set
{{(V0 * X0),(nilfunc * X0)},{(V0 * X0)}} is non empty set
the addF of CLSStruct(# (),(),(),() #) . [(V0 * X0),(nilfunc * X0)] is set
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0 + nilfunc) (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
nilfunc (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0 (#) (X0)) + (nilfunc (#) (X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
seq is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
((V0 + nilfunc) (#) (X0)) . seq is complex Element of COMPLEX
((V0 (#) (X0)) + (nilfunc (#) (X0))) . seq is complex Element of COMPLEX
(X0) . seq is complex Element of COMPLEX
(V0 + nilfunc) * ((X0) . seq) is complex set
V0 * ((X0) . seq) is complex set
nilfunc * ((X0) . seq) is complex set
(V0 * ((X0) . seq)) + (nilfunc * ((X0) . seq)) is complex set
(V0 (#) (X0)) . seq is complex Element of COMPLEX
((V0 (#) (X0)) . seq) + (nilfunc * ((X0) . seq)) is complex set
(nilfunc (#) (X0)) . seq is complex Element of COMPLEX
((V0 (#) (X0)) . seq) + ((nilfunc (#) (X0)) . seq) is complex Element of COMPLEX
((V0 * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((nilfunc * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 * X0)) + ((nilfunc * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 (#) (X0))) + ((nilfunc * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((nilfunc (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((V0 (#) (X0))) + ((nilfunc (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0 (#) (X0)) + ((nilfunc (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is complex set
nilfunc is complex set
V0 * nilfunc is complex set
X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
(V0 * nilfunc) * X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the Mult of CLSStruct(# (),(),(),() #) is Relation-like [:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[(V0 * nilfunc),X0] is set
{(V0 * nilfunc),X0} is non empty set
{(V0 * nilfunc)} is non empty V64() set
{{(V0 * nilfunc),X0},{(V0 * nilfunc)}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [(V0 * nilfunc),X0] is set
nilfunc * X0 is Element of the carrier of CLSStruct(# (),(),(),() #)
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty V64() set
{{nilfunc,X0},{nilfunc}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [nilfunc,X0] is set
V0 * (nilfunc * X0) is Element of the carrier of CLSStruct(# (),(),(),() #)
[V0,(nilfunc * X0)] is set
{V0,(nilfunc * X0)} is non empty set
{V0} is non empty V64() set
{{V0,(nilfunc * X0)},{V0}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [V0,(nilfunc * X0)] is set
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(V0 * nilfunc) (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
nilfunc (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) (nilfunc (#) (X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((nilfunc (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) ((nilfunc (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((nilfunc * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 (#) ((nilfunc * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
V0 is Element of the carrier of CLSStruct(# (),(),(),() #)
1r * V0 is Element of the carrier of CLSStruct(# (),(),(),() #)
the Mult of CLSStruct(# (),(),(),() #) is Relation-like [:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] -defined the carrier of CLSStruct(# (),(),(),() #) -valued Function-like non empty V14([:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):]) quasi_total Element of bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):]
[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
bool [:[:COMPLEX, the carrier of CLSStruct(# (),(),(),() #):], the carrier of CLSStruct(# (),(),(),() #):] is non empty set
[1r,V0] is set
{1r,V0} is non empty set
{1r} is non empty V64() set
{{1r,V0},{1r}} is non empty set
the Mult of CLSStruct(# (),(),(),() #) . [1r,V0] is set
(V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
1r (#) (V0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
() is non empty strict CLSStruct
the carrier of () is non empty set
nilfunc is Element of the carrier of ()
X0 is Element of the carrier of ()
nilfunc + X0 is Element of the carrier of ()
the addF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([: the carrier of (), the carrier of ():]) quasi_total Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty set
[:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
bool [:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
the addF of () . (nilfunc,X0) is Element of the carrier of ()
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the addF of () . [nilfunc,X0] is set
seq is Element of the carrier of ()
(nilfunc + X0) + seq is Element of the carrier of ()
the addF of () . ((nilfunc + X0),seq) is Element of the carrier of ()
[(nilfunc + X0),seq] is set
{(nilfunc + X0),seq} is non empty set
{(nilfunc + X0)} is non empty set
{{(nilfunc + X0),seq},{(nilfunc + X0)}} is non empty set
the addF of () . [(nilfunc + X0),seq] is set
X0 + seq is Element of the carrier of ()
the addF of () . (X0,seq) is Element of the carrier of ()
[X0,seq] is set
{X0,seq} is non empty set
{X0} is non empty set
{{X0,seq},{X0}} is non empty set
the addF of () . [X0,seq] is set
nilfunc + (X0 + seq) is Element of the carrier of ()
the addF of () . (nilfunc,(X0 + seq)) is Element of the carrier of ()
[nilfunc,(X0 + seq)] is set
{nilfunc,(X0 + seq)} is non empty set
{{nilfunc,(X0 + seq)},{nilfunc}} is non empty set
the addF of () . [nilfunc,(X0 + seq)] is set
the carrier of () is non empty set
nilfunc is Element of the carrier of ()
0. () is zero Element of the carrier of ()
the ZeroF of () is Element of the carrier of ()
nilfunc + (0. ()) is Element of the carrier of ()
the addF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([: the carrier of (), the carrier of ():]) quasi_total Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty set
[:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
bool [:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
the addF of () . (nilfunc,(0. ())) is Element of the carrier of ()
[nilfunc,(0. ())] is set
{nilfunc,(0. ())} is non empty set
{nilfunc} is non empty set
{{nilfunc,(0. ())},{nilfunc}} is non empty set
the addF of () . [nilfunc,(0. ())] is set
the carrier of () is non empty set
nilfunc is Element of the carrier of ()
0. () is zero Element of the carrier of ()
the ZeroF of () is Element of the carrier of ()
X0 is Element of the carrier of ()
nilfunc + X0 is Element of the carrier of ()
the addF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([: the carrier of (), the carrier of ():]) quasi_total Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty set
[:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
bool [:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
the addF of () . (nilfunc,X0) is Element of the carrier of ()
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the addF of () . [nilfunc,X0] is set
the carrier of () is non empty set
X0 is Element of the carrier of ()
seq is Element of the carrier of ()
X0 + seq is Element of the carrier of ()
the addF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([: the carrier of (), the carrier of ():]) quasi_total Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty set
[:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
bool [:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
the addF of () . (X0,seq) is Element of the carrier of ()
[X0,seq] is set
{X0,seq} is non empty set
{X0} is non empty set
{{X0,seq},{X0}} is non empty set
the addF of () . [X0,seq] is set
nilfunc is complex set
nilfunc * (X0 + seq) is Element of the carrier of ()
the Mult of () is Relation-like [:COMPLEX, the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([:COMPLEX, the carrier of ():]) quasi_total Element of bool [:[:COMPLEX, the carrier of ():], the carrier of ():]
[:COMPLEX, the carrier of ():] is non empty set
[:[:COMPLEX, the carrier of ():], the carrier of ():] is non empty set
bool [:[:COMPLEX, the carrier of ():], the carrier of ():] is non empty set
[nilfunc,(X0 + seq)] is set
{nilfunc,(X0 + seq)} is non empty set
{nilfunc} is non empty V64() set
{{nilfunc,(X0 + seq)},{nilfunc}} is non empty set
the Mult of () . [nilfunc,(X0 + seq)] is set
nilfunc * X0 is Element of the carrier of ()
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the Mult of () . [nilfunc,X0] is set
nilfunc * seq is Element of the carrier of ()
[nilfunc,seq] is set
{nilfunc,seq} is non empty set
{{nilfunc,seq},{nilfunc}} is non empty set
the Mult of () . [nilfunc,seq] is set
(nilfunc * X0) + (nilfunc * seq) is Element of the carrier of ()
the addF of () . ((nilfunc * X0),(nilfunc * seq)) is Element of the carrier of ()
[(nilfunc * X0),(nilfunc * seq)] is set
{(nilfunc * X0),(nilfunc * seq)} is non empty set
{(nilfunc * X0)} is non empty set
{{(nilfunc * X0),(nilfunc * seq)},{(nilfunc * X0)}} is non empty set
the addF of () . [(nilfunc * X0),(nilfunc * seq)] is set
v is Element of the carrier of ()
p is complex set
m is complex set
p + m is complex set
(p + m) * v is Element of the carrier of ()
[(p + m),v] is set
{(p + m),v} is non empty set
{(p + m)} is non empty V64() set
{{(p + m),v},{(p + m)}} is non empty set
the Mult of () . [(p + m),v] is set
p * v is Element of the carrier of ()
[p,v] is set
{p,v} is non empty set
{p} is non empty V64() set
{{p,v},{p}} is non empty set
the Mult of () . [p,v] is set
m * v is Element of the carrier of ()
[m,v] is set
{m,v} is non empty set
{m} is non empty V64() set
{{m,v},{m}} is non empty set
the Mult of () . [m,v] is set
(p * v) + (m * v) is Element of the carrier of ()
the addF of () . ((p * v),(m * v)) is Element of the carrier of ()
[(p * v),(m * v)] is set
{(p * v),(m * v)} is non empty set
{(p * v)} is non empty set
{{(p * v),(m * v)},{(p * v)}} is non empty set
the addF of () . [(p * v),(m * v)] is set
w is Element of the carrier of ()
v1 is complex set
w1 is complex set
v1 * w1 is complex set
(v1 * w1) * w is Element of the carrier of ()
[(v1 * w1),w] is set
{(v1 * w1),w} is non empty set
{(v1 * w1)} is non empty V64() set
{{(v1 * w1),w},{(v1 * w1)}} is non empty set
the Mult of () . [(v1 * w1),w] is set
w1 * w is Element of the carrier of ()
[w1,w] is set
{w1,w} is non empty set
{w1} is non empty V64() set
{{w1,w},{w1}} is non empty set
the Mult of () . [w1,w] is set
v1 * (w1 * w) is Element of the carrier of ()
[v1,(w1 * w)] is set
{v1,(w1 * w)} is non empty set
{v1} is non empty V64() set
{{v1,(w1 * w)},{v1}} is non empty set
the Mult of () . [v1,(w1 * w)] is set
c₁₁ is Element of the carrier of ()
1r * c₁₁ is Element of the carrier of ()
[1r,c₁₁] is set
{1r,c₁₁} is non empty set
{1r} is non empty V64() set
{{1r,c₁₁},{1r}} is non empty set
the Mult of () . [1r,c₁₁] is set
V0 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V0 is non empty set
bool the carrier of V0 is non empty set
nilfunc is Element of bool the carrier of V0
the addF of V0 is Relation-like [: the carrier of V0, the carrier of V0:] -defined the carrier of V0 -valued Function-like non empty V14([: the carrier of V0, the carrier of V0:]) quasi_total Element of bool [:[: the carrier of V0, the carrier of V0:], the carrier of V0:]
[: the carrier of V0, the carrier of V0:] is non empty set
[:[: the carrier of V0, the carrier of V0:], the carrier of V0:] is non empty set
bool [:[: the carrier of V0, the carrier of V0:], the carrier of V0:] is non empty set
the addF of V0 || nilfunc is Relation-like Function-like set
[:nilfunc,nilfunc:] is set
the addF of V0 | [:nilfunc,nilfunc:] is Relation-like Function-like set
[:[:nilfunc,nilfunc:],nilfunc:] is set
bool [:[:nilfunc,nilfunc:],nilfunc:] is non empty set
dom the addF of V0 is Relation-like set
X0 is set
( the addF of V0 || nilfunc) . X0 is set
seq is set
p is set
[seq,p] is set
{seq,p} is non empty set
{seq} is non empty set
{{seq,p},{seq}} is non empty set
dom ( the addF of V0 || nilfunc) is set
v is right_complementable Element of the carrier of V0
m is right_complementable Element of the carrier of V0
v + m is right_complementable Element of the carrier of V0
the addF of V0 . (v,m) is right_complementable Element of the carrier of V0
[v,m] is set
{v,m} is non empty set
{v} is non empty set
{{v,m},{v}} is non empty set
the addF of V0 . [v,m] is set
dom ( the addF of V0 || nilfunc) is set
V0 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V0 is non empty set
bool the carrier of V0 is non empty set
nilfunc is Element of bool the carrier of V0
the Mult of V0 is Relation-like [:COMPLEX, the carrier of V0:] -defined the carrier of V0 -valued Function-like non empty V14([:COMPLEX, the carrier of V0:]) quasi_total Element of bool [:[:COMPLEX, the carrier of V0:], the carrier of V0:]
[:COMPLEX, the carrier of V0:] is non empty set
[:[:COMPLEX, the carrier of V0:], the carrier of V0:] is non empty set
bool [:[:COMPLEX, the carrier of V0:], the carrier of V0:] is non empty set
[:COMPLEX,nilfunc:] is set
the Mult of V0 | [:COMPLEX,nilfunc:] is Relation-like Function-like set
[:[:COMPLEX,nilfunc:],nilfunc:] is set
bool [:[:COMPLEX,nilfunc:],nilfunc:] is non empty set
dom the Mult of V0 is Relation-like set
X0 is set
( the Mult of V0 | [:COMPLEX,nilfunc:]) . X0 is set
seq is set
p is set
[seq,p] is set
{seq,p} is non empty set
{seq} is non empty set
{{seq,p},{seq}} is non empty set
m is complex set
[m,p] is set
{m,p} is non empty set
{m} is non empty V64() set
{{m,p},{m}} is non empty set
dom ( the Mult of V0 | [:COMPLEX,nilfunc:]) is set
v is right_complementable Element of the carrier of V0
m * v is right_complementable Element of the carrier of V0
[m,v] is set
{m,v} is non empty set
{{m,v},{m}} is non empty set
the Mult of V0 . [m,v] is set
dom ( the Mult of V0 | [:COMPLEX,nilfunc:]) is set
V0 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V0 is non empty set
bool the carrier of V0 is non empty set
nilfunc is Element of bool the carrier of V0
0. V0 is zero right_complementable Element of the carrier of V0
the ZeroF of V0 is right_complementable Element of the carrier of V0
the Element of nilfunc is Element of nilfunc
seq is right_complementable Element of the carrier of V0
seq - seq is right_complementable Element of the carrier of V0
- seq is right_complementable Element of the carrier of V0
seq + (- seq) is right_complementable Element of the carrier of V0
the addF of V0 is Relation-like [: the carrier of V0, the carrier of V0:] -defined the carrier of V0 -valued Function-like non empty V14([: the carrier of V0, the carrier of V0:]) quasi_total Element of bool [:[: the carrier of V0, the carrier of V0:], the carrier of V0:]
[: the carrier of V0, the carrier of V0:] is non empty set
[:[: the carrier of V0, the carrier of V0:], the carrier of V0:] is non empty set
bool [:[: the carrier of V0, the carrier of V0:], the carrier of V0:] is non empty set
the addF of V0 . (seq,(- seq)) is right_complementable Element of the carrier of V0
[seq,(- seq)] is set
{seq,(- seq)} is non empty set
{seq} is non empty set
{{seq,(- seq)},{seq}} is non empty set
the addF of V0 . [seq,(- seq)] is set
V0 is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of V0 is non empty set
bool the carrier of V0 is non empty set
nilfunc is Element of bool the carrier of V0
(V0,nilfunc) is Element of nilfunc
(V0,nilfunc) is Relation-like [:nilfunc,nilfunc:] -defined nilfunc -valued Function-like quasi_total Element of bool [:[:nilfunc,nilfunc:],nilfunc:]
[:nilfunc,nilfunc:] is set
[:[:nilfunc,nilfunc:],nilfunc:] is set
bool [:[:nilfunc,nilfunc:],nilfunc:] is non empty set
(V0,nilfunc) is Relation-like [:COMPLEX,nilfunc:] -defined nilfunc -valued Function-like quasi_total Element of bool [:[:COMPLEX,nilfunc:],nilfunc:]
[:COMPLEX,nilfunc:] is set
[:[:COMPLEX,nilfunc:],nilfunc:] is set
bool [:[:COMPLEX,nilfunc:],nilfunc:] is non empty set
CLSStruct(# nilfunc,(V0,nilfunc),(V0,nilfunc),(V0,nilfunc) #) is strict CLSStruct
the addF of V0 is Relation-like [: the carrier of V0, the carrier of V0:] -defined the carrier of V0 -valued Function-like non empty V14([: the carrier of V0, the carrier of V0:]) quasi_total Element of bool [:[: the carrier of V0, the carrier of V0:], the carrier of V0:]
[: the carrier of V0, the carrier of V0:] is non empty set
[:[: the carrier of V0, the carrier of V0:], the carrier of V0:] is non empty set
bool [:[: the carrier of V0, the carrier of V0:], the carrier of V0:] is non empty set
the addF of V0 || nilfunc is Relation-like Function-like set
the addF of V0 | [:nilfunc,nilfunc:] is Relation-like Function-like set
the Mult of V0 is Relation-like [:COMPLEX, the carrier of V0:] -defined the carrier of V0 -valued Function-like non empty V14([:COMPLEX, the carrier of V0:]) quasi_total Element of bool [:[:COMPLEX, the carrier of V0:], the carrier of V0:]
[:COMPLEX, the carrier of V0:] is non empty set
[:[:COMPLEX, the carrier of V0:], the carrier of V0:] is non empty set
bool [:[:COMPLEX, the carrier of V0:], the carrier of V0:] is non empty set
the Mult of V0 | [:COMPLEX,nilfunc:] is Relation-like Function-like set
0. V0 is zero right_complementable Element of the carrier of V0
the ZeroF of V0 is right_complementable Element of the carrier of V0
the carrier of () is non empty set
bool the carrier of () is non empty set
V0 is set
nilfunc is set
bool () is non empty set
(()) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.(()).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.(()).| (#) |.(()).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
nilfunc is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
X0 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
nilfunc . X0 is complex V34() ext-real Element of REAL
|.(()).| . X0 is complex V34() ext-real Element of REAL
(|.(()).| . X0) * (|.(()).| . X0) is complex V34() ext-real Element of REAL
(()) . X0 is complex Element of COMPLEX
|.((()) . X0).| is complex V34() ext-real Element of REAL
(|.(()).| . X0) * |.((()) . X0).| is complex V34() ext-real Element of REAL
(|.(()).| . X0) * 0 is complex V34() ext-real Element of REAL
V0 is Element of bool the carrier of ()
nilfunc is Element of bool the carrier of ()
X0 is set
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.(X0).| (#) |.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
X0 is set
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.(X0).| (#) |.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
() is Element of bool the carrier of ()
nilfunc is right_complementable Element of the carrier of ()
X0 is right_complementable Element of the carrier of ()
nilfunc + X0 is right_complementable Element of the carrier of ()
the addF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([: the carrier of (), the carrier of ():]) quasi_total Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty set
[:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
bool [:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
the addF of () . (nilfunc,X0) is right_complementable Element of the carrier of ()
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the addF of () . [nilfunc,X0] is set
((nilfunc + X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.((nilfunc + X0)).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.((nilfunc + X0)).| (#) |.((nilfunc + X0)).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.(X0).| (#) |.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
(nilfunc) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.(nilfunc).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.(nilfunc).| (#) |.(nilfunc).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
v is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(|.((nilfunc + X0)).| (#) |.((nilfunc + X0)).|) . v is complex V34() ext-real Element of REAL
|.((nilfunc + X0)).| . v is complex V34() ext-real Element of REAL
(|.((nilfunc + X0)).| . v) * (|.((nilfunc + X0)).| . v) is complex V34() ext-real Element of REAL
2 is non empty V26() V27() V28() V32() complex V34() ext-real positive non negative V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
2 (#) (|.(nilfunc).| (#) |.(nilfunc).|) is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
2 (#) (|.(X0).| (#) |.(X0).|) is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
(2 (#) (|.(nilfunc).| (#) |.(nilfunc).|)) + (2 (#) (|.(X0).| (#) |.(X0).|)) is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
w1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(|.((nilfunc + X0)).| (#) |.((nilfunc + X0)).|) . w1 is complex V34() ext-real Element of REAL
((2 (#) (|.(nilfunc).| (#) |.(nilfunc).|)) + (2 (#) (|.(X0).| (#) |.(X0).|))) . w1 is complex V34() ext-real Element of REAL
|.(nilfunc).| . w1 is complex V34() ext-real Element of REAL
|.(X0).| . w1 is complex V34() ext-real Element of REAL
|.((nilfunc + X0)).| . w1 is complex V34() ext-real Element of REAL
(|.((nilfunc + X0)).| . w1) ^2 is complex V34() ext-real Element of REAL
(|.((nilfunc + X0)).| . w1) * (|.((nilfunc + X0)).| . w1) is complex set
(2 (#) (|.(nilfunc).| (#) |.(nilfunc).|)) . w1 is complex V34() ext-real Element of REAL
(2 (#) (|.(X0).| (#) |.(X0).|)) . w1 is complex V34() ext-real Element of REAL
((2 (#) (|.(nilfunc).| (#) |.(nilfunc).|)) . w1) + ((2 (#) (|.(X0).| (#) |.(X0).|)) . w1) is complex V34() ext-real Element of REAL
(|.(nilfunc).| (#) |.(nilfunc).|) . w1 is complex V34() ext-real Element of REAL
2 * ((|.(nilfunc).| (#) |.(nilfunc).|) . w1) is complex V34() ext-real Element of REAL
(2 * ((|.(nilfunc).| (#) |.(nilfunc).|) . w1)) + ((2 (#) (|.(X0).| (#) |.(X0).|)) . w1) is complex V34() ext-real Element of REAL
(|.(X0).| (#) |.(X0).|) . w1 is complex V34() ext-real Element of REAL
2 * ((|.(X0).| (#) |.(X0).|) . w1) is complex V34() ext-real Element of REAL
(2 * ((|.(nilfunc).| (#) |.(nilfunc).|) . w1)) + (2 * ((|.(X0).| (#) |.(X0).|) . w1)) is complex V34() ext-real Element of REAL
(|.(nilfunc).| . w1) * (|.(nilfunc).| . w1) is complex V34() ext-real Element of REAL
2 * ((|.(nilfunc).| . w1) * (|.(nilfunc).| . w1)) is complex V34() ext-real Element of REAL
(2 * ((|.(nilfunc).| . w1) * (|.(nilfunc).| . w1))) + (2 * ((|.(X0).| (#) |.(X0).|) . w1)) is complex V34() ext-real Element of REAL
w is complex V34() ext-real Element of REAL
w ^2 is complex V34() ext-real Element of REAL
w * w is complex set
2 * (w ^2) is complex V34() ext-real Element of REAL
c₁₁ is complex V34() ext-real Element of REAL
c₁₁ ^2 is complex V34() ext-real Element of REAL
c₁₁ * c₁₁ is complex set
2 * (c₁₁ ^2) is complex V34() ext-real Element of REAL
(2 * (w ^2)) + (2 * (c₁₁ ^2)) is complex V34() ext-real Element of REAL
2 * w is complex V34() ext-real Element of REAL
(2 * w) * c₁₁ is complex V34() ext-real Element of REAL
(w ^2) + ((2 * w) * c₁₁) is complex V34() ext-real Element of REAL
((w ^2) + ((2 * w) * c₁₁)) + (c₁₁ ^2) is complex V34() ext-real Element of REAL
(((2 (#) (|.(nilfunc).| (#) |.(nilfunc).|)) + (2 (#) (|.(X0).| (#) |.(X0).|))) . w1) - (((w ^2) + ((2 * w) * c₁₁)) + (c₁₁ ^2)) is complex V34() ext-real Element of REAL
w - c₁₁ is complex V34() ext-real Element of REAL
(w - c₁₁) ^2 is complex V34() ext-real Element of REAL
(w - c₁₁) * (w - c₁₁) is complex set
(nilfunc) + (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(((nilfunc) + (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((nilfunc + X0)) . w1 is complex Element of COMPLEX
|.(((nilfunc + X0)) . w1).| is complex V34() ext-real Element of REAL
(nilfunc) . w1 is complex Element of COMPLEX
(X0) . w1 is complex Element of COMPLEX
((nilfunc) . w1) + ((X0) . w1) is complex Element of COMPLEX
|.(((nilfunc) . w1) + ((X0) . w1)).| is complex V34() ext-real Element of REAL
|.((nilfunc) . w1).| is complex V34() ext-real Element of REAL
|.((X0) . w1).| is complex V34() ext-real Element of REAL
|.((nilfunc) . w1).| + |.((X0) . w1).| is complex V34() ext-real Element of REAL
(|.(nilfunc).| . w1) + |.((X0) . w1).| is complex V34() ext-real Element of REAL
(|.(nilfunc).| . w1) + (|.(X0).| . w1) is complex V34() ext-real Element of REAL
0 + (((w ^2) + ((2 * w) * c₁₁)) + (c₁₁ ^2)) is complex V34() ext-real Element of REAL
((|.(nilfunc).| . w1) + (|.(X0).| . w1)) ^2 is complex V34() ext-real Element of REAL
((|.(nilfunc).| . w1) + (|.(X0).| . w1)) * ((|.(nilfunc).| . w1) + (|.(X0).| . w1)) is complex set
nilfunc is complex set
X0 is right_complementable Element of the carrier of ()
nilfunc * X0 is right_complementable Element of the carrier of ()
the Mult of () is Relation-like [:COMPLEX, the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([:COMPLEX, the carrier of ():]) quasi_total Element of bool [:[:COMPLEX, the carrier of ():], the carrier of ():]
[:COMPLEX, the carrier of ():] is non empty set
[:[:COMPLEX, the carrier of ():], the carrier of ():] is non empty set
bool [:[:COMPLEX, the carrier of ():], the carrier of ():] is non empty set
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty V64() set
{{nilfunc,X0},{nilfunc}} is non empty set
the Mult of () . [nilfunc,X0] is set
(X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.(X0).| (#) |.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
((nilfunc * X0)) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
nilfunc (#) (X0) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
((nilfunc (#) (X0))) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
|.((nilfunc * X0)).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.nilfunc.| is complex V34() ext-real Element of REAL
|.nilfunc.| (#) |.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.((nilfunc * X0)).| (#) |.((nilfunc * X0)).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
(|.nilfunc.| (#) |.(X0).|) (#) |.(X0).| is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.nilfunc.| (#) ((|.nilfunc.| (#) |.(X0).|) (#) |.(X0).|) is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.nilfunc.| (#) (|.(X0).| (#) |.(X0).|) is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.nilfunc.| (#) (|.nilfunc.| (#) (|.(X0).| (#) |.(X0).|)) is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
|.nilfunc.| * |.nilfunc.| is complex V34() ext-real Element of REAL
(|.nilfunc.| * |.nilfunc.|) (#) (|.(X0).| (#) |.(X0).|) is Relation-like NAT -defined REAL -valued Function-like non empty V14( NAT ) quasi_total V38() V39() V40() Element of bool [:NAT,REAL:]
((),()) is Element of ()
((),()) is Relation-like [:(),():] -defined () -valued Function-like quasi_total Element of bool [:[:(),():],():]
[:(),():] is set
[:[:(),():],():] is set
bool [:[:(),():],():] is non empty set
((),()) is Relation-like [:COMPLEX,():] -defined () -valued Function-like quasi_total Element of bool [:[:COMPLEX,():],():]
[:COMPLEX,():] is set
[:[:COMPLEX,():],():] is set
bool [:[:COMPLEX,():],():] is non empty set
CLSStruct(# (),((),()),((),()),((),()) #) is strict CLSStruct
V0 is set
nilfunc is set
X0 is set
seq is set
p is right_complementable Element of the carrier of ()
(p) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
m is right_complementable Element of the carrier of ()
v is right_complementable Element of the carrier of ()
m + v is right_complementable Element of the carrier of ()
the addF of () is Relation-like [: the carrier of (), the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([: the carrier of (), the carrier of ():]) quasi_total Element of bool [:[: the carrier of (), the carrier of ():], the carrier of ():]
[: the carrier of (), the carrier of ():] is non empty set
[:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
bool [:[: the carrier of (), the carrier of ():], the carrier of ():] is non empty set
the addF of () . (m,v) is right_complementable Element of the carrier of ()
[m,v] is set
{m,v} is non empty set
{m} is non empty set
{{m,v},{m}} is non empty set
the addF of () . [m,v] is set
(m) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(v) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(m) + (v) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
w1 is right_complementable Element of the carrier of ()
v1 is complex set
v1 * w1 is right_complementable Element of the carrier of ()
the Mult of () is Relation-like [:COMPLEX, the carrier of ():] -defined the carrier of () -valued Function-like non empty V14([:COMPLEX, the carrier of ():]) quasi_total Element of bool [:[:COMPLEX, the carrier of ():], the carrier of ():]
[:COMPLEX, the carrier of ():] is non empty set
[:[:COMPLEX, the carrier of ():], the carrier of ():] is non empty set
bool [:[:COMPLEX, the carrier of ():], the carrier of ():] is non empty set
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty V64() set
{{v1,w1},{v1}} is non empty set
the Mult of () . [v1,w1] is set
(w1) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
v1 (#) (w1) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
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 non empty V14([: the non empty set , the non empty set :]) quasi_total 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 non empty V14([: the non empty set , the non empty set :]) quasi_total Element of bool [:[: the non empty set , the non empty set :], the non empty set :]
[:COMPLEX, the non empty set :] is non empty set
[:[:COMPLEX, the non empty set :], the non empty set :] is non empty set
bool [:[:COMPLEX, the non empty set :], the non empty set :] is non empty set
the Relation-like [:COMPLEX, the non empty set :] -defined the non empty set -valued Function-like non empty V14([:COMPLEX, the non empty set :]) quasi_total 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 non empty V14([:COMPLEX, the non empty set :]) quasi_total Element of bool [:[:COMPLEX, the non empty set :], the non empty set :]
[:[: the non empty set , the non empty set :],COMPLEX:] is non empty V38() set
bool [:[: the non empty set , the non empty set :],COMPLEX:] is non empty set
the Relation-like [: the non empty set , the non empty set :] -defined COMPLEX -valued Function-like non empty V14([: the non empty set , the non empty set :]) quasi_total V38() Element of bool [:[: the non empty set , the non empty set :],COMPLEX:] is Relation-like [: the non empty set , the non empty set :] -defined COMPLEX -valued Function-like non empty V14([: the non empty set , the non empty set :]) quasi_total V38() Element of bool [:[: the non empty set , the non empty set :],COMPLEX:]
( 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 non empty V14([: the non empty set , the non empty set :]) quasi_total 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 non empty V14([:COMPLEX, the non empty set :]) quasi_total Element of bool [:[:COMPLEX, the non empty set :], the non empty set :], the Relation-like [: the non empty set , the non empty set :] -defined COMPLEX -valued Function-like non empty V14([: the non empty set , the non empty set :]) quasi_total V38() Element of bool [:[: the non empty set , the non empty set :],COMPLEX:]) 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 non empty V14([: the non empty set , the non empty set :]) quasi_total 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 non empty V14([:COMPLEX, the non empty set :]) quasi_total Element of bool [:[:COMPLEX, the non empty set :], the non empty set :], the Relation-like [: the non empty set , the non empty set :] -defined COMPLEX -valued Function-like non empty V14([: the non empty set , the non empty set :]) quasi_total V38() Element of bool [:[: the non empty set , the non empty set :],COMPLEX:]) is set
V0 is non empty set
[:V0,V0:] is non empty set
[:[:V0,V0:],V0:] is non empty set
bool [:[:V0,V0:],V0:] is non empty set
[:COMPLEX,V0:] is non empty set
[:[:COMPLEX,V0:],V0:] is non empty set
bool [:[:COMPLEX,V0:],V0:] is non empty set
[:[:V0,V0:],COMPLEX:] is non empty V38() set
bool [:[:V0,V0:],COMPLEX:] is non empty set
nilfunc is Element of V0
X0 is Relation-like [:V0,V0:] -defined V0 -valued Function-like non empty V14([:V0,V0:]) quasi_total Element of bool [:[:V0,V0:],V0:]
seq is Relation-like [:COMPLEX,V0:] -defined V0 -valued Function-like non empty V14([:COMPLEX,V0:]) quasi_total Element of bool [:[:COMPLEX,V0:],V0:]
p is Relation-like [:V0,V0:] -defined COMPLEX -valued Function-like non empty V14([:V0,V0:]) quasi_total V38() Element of bool [:[:V0,V0:],COMPLEX:]
(V0,nilfunc,X0,seq,p) is () ()
V0 is non empty ()
the carrier of V0 is non empty set
the of V0 is Relation-like [: the carrier of V0, the carrier of V0:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of V0, the carrier of V0:]) quasi_total V38() Element of bool [:[: the carrier of V0, the carrier of V0:],COMPLEX:]
[: the carrier of V0, the carrier of V0:] is non empty set
[:[: the carrier of V0, the carrier of V0:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of V0, the carrier of V0:],COMPLEX:] is non empty set
nilfunc is Element of the carrier of V0
X0 is Element of the carrier of V0
the of V0 . (nilfunc,X0) is complex Element of COMPLEX
[nilfunc,X0] is set
{nilfunc,X0} is non empty set
{nilfunc} is non empty set
{{nilfunc,X0},{nilfunc}} is non empty set
the of V0 . [nilfunc,X0] is complex set
the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
(0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct is non empty right_complementable Abelian add-associative right_zeroed strict vector-distributive scalar-distributive scalar-associative scalar-unital Subspace of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) is non empty set
the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct is non empty set
0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct is zero right_complementable Element of the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the ZeroF of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct is right_complementable Element of the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
{(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )} is non empty Element of bool the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
bool the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct is non empty set
[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
[:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):],COMPLEX:] is non empty V38() set
bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):],COMPLEX:] is non empty set
[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] --> 0c is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] -defined COMPLEX -valued Function-like non empty V14([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]) quasi_total V38() V39() V40() V41() Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):],COMPLEX:]
nilfunc is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] -defined COMPLEX -valued Function-like non empty V14([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]) quasi_total V38() Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):],COMPLEX:]
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
seq is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[X0,seq] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{X0,seq} is non empty set
{X0} is non empty set
{{X0,seq},{X0}} is non empty set
nilfunc . [X0,seq] is complex Element of COMPLEX
[(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )] is Element of [: the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct , the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct :]
[: the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct , the carrier of the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct :] is non empty set
{(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )} is non empty set
{(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )} is non empty set
{{(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )},{(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )}} is non empty set
nilfunc . [(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )] is complex set
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[X0,X0] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{X0,X0} is non empty set
{X0} is non empty set
{{X0,X0},{X0}} is non empty set
nilfunc . [X0,X0] is complex Element of COMPLEX
Re (nilfunc . [X0,X0]) is complex V34() ext-real Element of REAL
seq is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[seq,seq] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{seq,seq} is non empty set
{seq} is non empty set
{{seq,seq},{seq}} is non empty set
nilfunc . [seq,seq] is complex Element of COMPLEX
Im (nilfunc . [seq,seq]) is complex V34() ext-real Element of REAL
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
seq is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[X0,seq] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{X0,seq} is non empty set
{X0} is non empty set
{{X0,seq},{X0}} is non empty set
nilfunc . [X0,seq] is complex Element of COMPLEX
[seq,X0] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{seq,X0} is non empty set
{seq} is non empty set
{{seq,X0},{seq}} is non empty set
nilfunc . [seq,X0] is complex Element of COMPLEX
(nilfunc . [seq,X0]) *' is complex Element of COMPLEX
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
seq is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
X0 + seq is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) -valued Function-like non empty V14([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]) quasi_total Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
[:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (X0,seq) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[X0,seq] is set
{X0,seq} is non empty set
{X0} is non empty set
{{X0,seq},{X0}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [X0,seq] is set
p is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(X0 + seq),p] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{(X0 + seq),p} is non empty set
{(X0 + seq)} is non empty set
{{(X0 + seq),p},{(X0 + seq)}} is non empty set
nilfunc . [(X0 + seq),p] is complex Element of COMPLEX
[X0,p] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{X0,p} is non empty set
{{X0,p},{X0}} is non empty set
nilfunc . [X0,p] is complex Element of COMPLEX
[seq,p] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{seq,p} is non empty set
{seq} is non empty set
{{seq,p},{seq}} is non empty set
nilfunc . [seq,p] is complex Element of COMPLEX
(nilfunc . [X0,p]) + (nilfunc . [seq,p]) is complex Element of COMPLEX
X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
seq is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[X0,seq] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{X0,seq} is non empty set
{X0} is non empty set
{{X0,seq},{X0}} is non empty set
nilfunc . [X0,seq] is complex Element of COMPLEX
p is complex set
p * X0 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) is Relation-like [:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) -valued Function-like non empty V14([:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]) quasi_total Element of bool [:[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
[:[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
bool [:[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
[p,X0] is set
{p,X0} is non empty set
{p} is non empty V64() set
{{p,X0},{p}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [p,X0] is set
[(p * X0),seq] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{(p * X0),seq} is non empty set
{(p * X0)} is non empty set
{{(p * X0),seq},{(p * X0)}} is non empty set
nilfunc . [(p * X0),seq] is complex Element of COMPLEX
p * (nilfunc . [X0,seq]) is complex set
0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) is zero right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the ZeroF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) is Relation-like [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) -valued Function-like non empty V14([: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]) quasi_total Element of bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
[:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
bool [:[: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) is Relation-like [:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] -defined the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) -valued Function-like non empty V14([:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]) quasi_total Element of bool [:[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
[:[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
bool [:[:COMPLEX, the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):], the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):] is non empty set
( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) is non empty () ()
the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) is non empty set
0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) is zero Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the ZeroF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),seq,seq) is complex set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) is Relation-like [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] -defined COMPLEX -valued Function-like non empty V14([: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):]) quasi_total V38() Element of bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):],COMPLEX:]
[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] is non empty set
[:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):],COMPLEX:] is non empty V38() set
bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):],COMPLEX:] is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,seq) is complex Element of COMPLEX
[seq,seq] is set
{seq,seq} is non empty set
{seq} is non empty set
{{seq,seq},{seq}} is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,seq] is complex set
Re (( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),seq,seq) is complex V34() ext-real Element of REAL
Im (( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),seq,seq) is complex V34() ext-real Element of REAL
p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),seq,p) is complex set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,p) is complex Element of COMPLEX
[seq,p] is set
{seq,p} is non empty set
{{seq,p},{seq}} is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,p] is complex set
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),p,seq) is complex set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (p,seq) is complex Element of COMPLEX
[p,seq] is set
{p,seq} is non empty set
{p} is non empty set
{{p,seq},{p}} is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [p,seq] is complex set
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),p,seq) *' is complex Element of COMPLEX
seq + p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) is Relation-like [: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] -defined the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) -valued Function-like non empty V14([: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):]) quasi_total Element of bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):]
[:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] is non empty set
bool [:[: the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc), the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,p) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,p] is set
m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),(seq + p),m) is complex set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . ((seq + p),m) is complex Element of COMPLEX
[(seq + p),m] is set
{(seq + p),m} is non empty set
{(seq + p)} is non empty set
{{(seq + p),m},{(seq + p)}} is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [(seq + p),m] is complex set
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),seq,m) is complex set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,m) is complex Element of COMPLEX
[seq,m] is set
{seq,m} is non empty set
{{seq,m},{seq}} is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,m] is complex set
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),p,m) is complex set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [p,m] is complex set
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),seq,m) + (( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),p,m) is complex set
v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
w1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
v1 + w1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (v1,w1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty set
{{v1,w1},{v1}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v1,w1] is set
w is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(v1 + w1),w] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{(v1 + w1),w} is non empty set
{(v1 + w1)} is non empty set
{{(v1 + w1),w},{(v1 + w1)}} is non empty set
nilfunc . [(v1 + w1),w] is complex Element of COMPLEX
v is complex set
v * seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) is Relation-like [:COMPLEX, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] -defined the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) -valued Function-like non empty V14([:COMPLEX, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):]) quasi_total Element of bool [:[:COMPLEX, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):]
[:COMPLEX, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] is non empty set
[:[:COMPLEX, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] is non empty set
bool [:[:COMPLEX, the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):], the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc):] is non empty set
[v,seq] is set
{v,seq} is non empty set
{v} is non empty V64() set
{{v,seq},{v}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [v,seq] is set
(( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),(v * seq),p) is complex set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . ((v * seq),p) is complex Element of COMPLEX
[(v * seq),p] is set
{(v * seq),p} is non empty set
{(v * seq)} is non empty set
{{(v * seq),p},{(v * seq)}} is non empty set
the of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [(v * seq),p] is complex set
v * (( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc),seq,p) is complex set
v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
v * v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v,v1] is set
{v,v1} is non empty set
{{v,v1},{v}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v,v1] is set
w1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(v * v1),w1] is Element of [: the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ):]
{(v * v1),w1} is non empty set
{(v * v1)} is non empty set
{{(v * v1),w1},{(v * v1)}} is non empty set
nilfunc . [(v * v1),w1] is complex Element of COMPLEX
seq is complex set
p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
p + m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (p,m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [p,m] is set
seq * (p + m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,(p + m)] is set
{seq,(p + m)} is non empty set
{seq} is non empty V64() set
{{seq,(p + m)},{seq}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,(p + m)] is set
seq * p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,p] is set
{seq,p} is non empty set
{{seq,p},{seq}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,p] is set
seq * m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,m] is set
{seq,m} is non empty set
{{seq,m},{seq}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,m] is set
(seq * p) + (seq * m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . ((seq * p),(seq * m)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[(seq * p),(seq * m)] is set
{(seq * p),(seq * m)} is non empty set
{(seq * p)} is non empty set
{{(seq * p),(seq * m)},{(seq * p)}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [(seq * p),(seq * m)] is set
v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
v + v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (v,v1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v,v1] is set
seq * (v + v1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[seq,(v + v1)] is set
{seq,(v + v1)} is non empty set
{{seq,(v + v1)},{seq}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [seq,(v + v1)] is set
seq * v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[seq,v] is set
{seq,v} is non empty set
{{seq,v},{seq}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [seq,v] is set
seq * v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[seq,v1] is set
{seq,v1} is non empty set
{{seq,v1},{seq}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [seq,v1] is set
(seq * v) + (seq * v1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . ((seq * v),(seq * v1)) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(seq * v),(seq * v1)] is set
{(seq * v),(seq * v1)} is non empty set
{(seq * v)} is non empty set
{{(seq * v),(seq * v1)},{(seq * v)}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [(seq * v),(seq * v1)] is set
seq is complex set
p is complex set
seq + p is complex set
m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
(seq + p) * m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[(seq + p),m] is set
{(seq + p),m} is non empty set
{(seq + p)} is non empty V64() set
{{(seq + p),m},{(seq + p)}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [(seq + p),m] is set
seq * m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,m] is set
{seq,m} is non empty set
{seq} is non empty V64() set
{{seq,m},{seq}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,m] is set
p * m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[p,m] is set
{p,m} is non empty set
{p} is non empty V64() set
{{p,m},{p}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [p,m] is set
(seq * m) + (p * m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . ((seq * m),(p * m)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[(seq * m),(p * m)] is set
{(seq * m),(p * m)} is non empty set
{(seq * m)} is non empty set
{{(seq * m),(p * m)},{(seq * m)}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [(seq * m),(p * m)] is set
v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
(seq + p) * v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(seq + p),v] is set
{(seq + p),v} is non empty set
{{(seq + p),v},{(seq + p)}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [(seq + p),v] is set
seq * v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[seq,v] is set
{seq,v} is non empty set
{{seq,v},{seq}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [seq,v] is set
p * v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[p,v] is set
{p,v} is non empty set
{{p,v},{p}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [p,v] is set
(seq * v) + (p * v) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . ((seq * v),(p * v)) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(seq * v),(p * v)] is set
{(seq * v),(p * v)} is non empty set
{(seq * v)} is non empty set
{{(seq * v),(p * v)},{(seq * v)}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [(seq * v),(p * v)] is set
seq is complex set
p is complex set
seq * p is complex set
m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
(seq * p) * m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[(seq * p),m] is set
{(seq * p),m} is non empty set
{(seq * p)} is non empty V64() set
{{(seq * p),m},{(seq * p)}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [(seq * p),m] is set
p * m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[p,m] is set
{p,m} is non empty set
{p} is non empty V64() set
{{p,m},{p}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [p,m] is set
seq * (p * m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,(p * m)] is set
{seq,(p * m)} is non empty set
{seq} is non empty V64() set
{{seq,(p * m)},{seq}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,(p * m)] is set
v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
(seq * p) * v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(seq * p),v] is set
{(seq * p),v} is non empty set
{{(seq * p),v},{(seq * p)}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [(seq * p),v] is set
p * v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[p,v] is set
{p,v} is non empty set
{{p,v},{p}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [p,v] is set
seq * (p * v) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[seq,(p * v)] is set
{seq,(p * v)} is non empty set
{{seq,(p * v)},{seq}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [seq,(p * v)] is set
seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
1r * seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[1r,seq] is set
{1r,seq} is non empty set
{1r} is non empty V64() set
{{1r,seq},{1r}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [1r,seq] is set
p is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
1r * p is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[1r,p] is set
{1r,p} is non empty set
{{1r,p},{1r}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [1r,p] is set
seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
m is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
seq + p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,p) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,p] is set
{seq,p} is non empty set
{seq} is non empty set
{{seq,p},{seq}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,p] is set
m + v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (m,v) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[m,v] is set
{m,v} is non empty set
{m} is non empty set
{{m,v},{m}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [m,v] is set
v1 is complex set
v1 * seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[v1,seq] is set
{v1,seq} is non empty set
{v1} is non empty V64() set
{{v1,seq},{v1}} is non empty set
the Mult of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [v1,seq] is set
v1 * m is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v1,m] is set
{v1,m} is non empty set
{{v1,m},{v1}} is non empty set
the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v1,m] is set
seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
seq + p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,p) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,p] is set
{seq,p} is non empty set
{seq} is non empty set
{{seq,p},{seq}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,p] is set
p + seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (p,seq) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[p,seq] is set
{p,seq} is non empty set
{p} is non empty set
{{p,seq},{p}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [p,seq] is set
v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
m is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
v + m is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (v,m) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v,m] is set
{v,m} is non empty set
{v} is non empty set
{{v,m},{v}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v,m] is set
seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
seq + p is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,p) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,p] is set
{seq,p} is non empty set
{seq} is non empty set
{{seq,p},{seq}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,p] is set
m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
(seq + p) + m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . ((seq + p),m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[(seq + p),m] is set
{(seq + p),m} is non empty set
{(seq + p)} is non empty set
{{(seq + p),m},{(seq + p)}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [(seq + p),m] is set
p + m is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (p,m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [p,m] is set
seq + (p + m) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,(p + m)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,(p + m)] is set
{seq,(p + m)} is non empty set
{{seq,(p + m)},{seq}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,(p + m)] is set
v is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
v + v1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (v,v1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v,v1] is set
w1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
(v + v1) + w1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . ((v + v1),w1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[(v + v1),w1] is set
{(v + v1),w1} is non empty set
{(v + v1)} is non empty set
{{(v + v1),w1},{(v + v1)}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [(v + v1),w1] is set
v1 + w1 is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (v1,w1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty set
{{v1,w1},{v1}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v1,w1] is set
v + (v1 + w1) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (v,(v1 + w1)) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[v,(v1 + w1)] is set
{v,(v1 + w1)} is non empty set
{{v,(v1 + w1)},{v}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [v,(v1 + w1)] is set
seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
seq + (0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,(0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc))) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,(0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc))] is set
{seq,(0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc))} is non empty set
{seq} is non empty set
{{seq,(0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc))},{seq}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,(0. ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc))] is set
p is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
p + (0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (p,(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ))) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[p,(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ))] is set
{p,(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ))} is non empty set
{p} is non empty set
{{p,(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ))},{p}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [p,(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ))] is set
seq is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
p is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
m is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
p + m is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . (p,m) is right_complementable Element of the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ) . [p,m] is set
v is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
seq + v is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . (seq,v) is Element of the carrier of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc)
[seq,v] is set
{seq,v} is non empty set
{seq} is non empty set
{{seq,v},{seq}} is non empty set
the addF of ( the carrier of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),(0. ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct )), the addF of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ), the Mult of ((0). the non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct ),nilfunc) . [seq,v] is set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
0. seq is zero right_complementable Element of the carrier of seq
the carrier of seq is non empty set
the ZeroF of seq is right_complementable Element of the carrier of seq
(seq,(0. seq),(0. seq)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((0. seq),(0. seq)) is complex Element of COMPLEX
[(0. seq),(0. seq)] is set
{(0. seq),(0. seq)} is non empty set
{(0. seq)} is non empty set
{{(0. seq),(0. seq)},{(0. seq)}} is non empty set
the of seq . [(0. seq),(0. seq)] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
v is right_complementable Element of the carrier of seq
m + v is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (m,v) is right_complementable Element of the carrier of seq
[m,v] is set
{m,v} is non empty set
{m} is non empty set
{{m,v},{m}} is non empty set
the addF of seq . [m,v] is set
(seq,p,(m + v)) is complex set
the of seq . (p,(m + v)) is complex Element of COMPLEX
[p,(m + v)] is set
{p,(m + v)} is non empty set
{{p,(m + v)},{p}} is non empty set
the of seq . [p,(m + v)] is complex set
(seq,p,v) is complex set
the of seq . (p,v) is complex Element of COMPLEX
[p,v] is set
{p,v} is non empty set
{{p,v},{p}} is non empty set
the of seq . [p,v] is complex set
(seq,p,m) + (seq,p,v) is complex set
(seq,(m + v),p) is complex set
the of seq . ((m + v),p) is complex Element of COMPLEX
[(m + v),p] is set
{(m + v),p} is non empty set
{(m + v)} is non empty set
{{(m + v),p},{(m + v)}} is non empty set
the of seq . [(m + v),p] is complex set
(seq,(m + v),p) *' is complex Element of COMPLEX
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
(seq,v,p) is complex set
the of seq . (v,p) is complex Element of COMPLEX
[v,p] is set
{v,p} is non empty set
{v} is non empty set
{{v,p},{v}} is non empty set
the of seq . [v,p] is complex set
(seq,m,p) + (seq,v,p) is complex set
((seq,m,p) + (seq,v,p)) *' is complex Element of COMPLEX
(seq,m,p) *' is complex Element of COMPLEX
(seq,v,p) *' is complex Element of COMPLEX
((seq,m,p) *') + ((seq,v,p) *') is complex Element of COMPLEX
(seq,p,m) + ((seq,v,p) *') is complex set
seq is complex set
seq *' is complex Element of COMPLEX
p is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of p is non empty set
m is right_complementable Element of the carrier of p
v is right_complementable Element of the carrier of p
seq * v is right_complementable Element of the carrier of p
the Mult of p is Relation-like [:COMPLEX, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([:COMPLEX, the carrier of p:]) quasi_total Element of bool [:[:COMPLEX, the carrier of p:], the carrier of p:]
[:COMPLEX, the carrier of p:] is non empty set
[:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
bool [:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
[seq,v] is set
{seq,v} is non empty set
{seq} is non empty V64() set
{{seq,v},{seq}} is non empty set
the Mult of p . [seq,v] is set
(p,m,(seq * v)) is complex set
the of p is Relation-like [: the carrier of p, the carrier of p:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of p, the carrier of p:]) quasi_total V38() Element of bool [:[: the carrier of p, the carrier of p:],COMPLEX:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of p, the carrier of p:],COMPLEX:] is non empty set
the of p . (m,(seq * v)) is complex Element of COMPLEX
[m,(seq * v)] is set
{m,(seq * v)} is non empty set
{m} is non empty set
{{m,(seq * v)},{m}} is non empty set
the of p . [m,(seq * v)] is complex set
(p,m,v) is complex set
the of p . (m,v) is complex Element of COMPLEX
[m,v] is set
{m,v} is non empty set
{{m,v},{m}} is non empty set
the of p . [m,v] is complex set
(seq *') * (p,m,v) is complex set
(p,(seq * v),m) is complex set
the of p . ((seq * v),m) is complex Element of COMPLEX
[(seq * v),m] is set
{(seq * v),m} is non empty set
{(seq * v)} is non empty set
{{(seq * v),m},{(seq * v)}} is non empty set
the of p . [(seq * v),m] is complex set
(p,(seq * v),m) *' is complex Element of COMPLEX
(p,v,m) is complex set
the of p . (v,m) is complex Element of COMPLEX
[v,m] is set
{v,m} is non empty set
{v} is non empty set
{{v,m},{v}} is non empty set
the of p . [v,m] is complex set
seq * (p,v,m) is complex set
(seq * (p,v,m)) *' is complex Element of COMPLEX
(p,v,m) *' is complex Element of COMPLEX
(seq *') * ((p,v,m) *') is complex Element of COMPLEX
seq is complex set
seq *' is complex Element of COMPLEX
p is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of p is non empty set
m is right_complementable Element of the carrier of p
seq * m is right_complementable Element of the carrier of p
the Mult of p is Relation-like [:COMPLEX, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([:COMPLEX, the carrier of p:]) quasi_total Element of bool [:[:COMPLEX, the carrier of p:], the carrier of p:]
[:COMPLEX, the carrier of p:] is non empty set
[:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
bool [:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
[seq,m] is set
{seq,m} is non empty set
{seq} is non empty V64() set
{{seq,m},{seq}} is non empty set
the Mult of p . [seq,m] is set
v is right_complementable Element of the carrier of p
(p,(seq * m),v) is complex set
the of p is Relation-like [: the carrier of p, the carrier of p:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of p, the carrier of p:]) quasi_total V38() Element of bool [:[: the carrier of p, the carrier of p:],COMPLEX:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of p, the carrier of p:],COMPLEX:] is non empty set
the of p . ((seq * m),v) is complex Element of COMPLEX
[(seq * m),v] is set
{(seq * m),v} is non empty set
{(seq * m)} is non empty set
{{(seq * m),v},{(seq * m)}} is non empty set
the of p . [(seq * m),v] is complex set
(seq *') * v is right_complementable Element of the carrier of p
[(seq *'),v] is set
{(seq *'),v} is non empty set
{(seq *')} is non empty V64() set
{{(seq *'),v},{(seq *')}} is non empty set
the Mult of p . [(seq *'),v] is set
(p,m,((seq *') * v)) is complex set
the of p . (m,((seq *') * v)) is complex Element of COMPLEX
[m,((seq *') * v)] is set
{m,((seq *') * v)} is non empty set
{m} is non empty set
{{m,((seq *') * v)},{m}} is non empty set
the of p . [m,((seq *') * v)] is complex set
(p,m,v) is complex set
the of p . (m,v) is complex Element of COMPLEX
[m,v] is set
{m,v} is non empty set
{{m,v},{m}} is non empty set
the of p . [m,v] is complex set
seq * (p,m,v) is complex set
(seq *') *' is complex Element of COMPLEX
(p,v,m) is complex set
the of p . (v,m) is complex Element of COMPLEX
[v,m] is set
{v,m} is non empty set
{v} is non empty set
{{v,m},{v}} is non empty set
the of p . [v,m] is complex set
(p,v,m) *' is complex Element of COMPLEX
((seq *') *') * ((p,v,m) *') is complex Element of COMPLEX
(seq *') * (p,v,m) is complex set
((seq *') * (p,v,m)) *' is complex Element of COMPLEX
(p,((seq *') * v),m) is complex set
the of p . (((seq *') * v),m) is complex Element of COMPLEX
[((seq *') * v),m] is set
{((seq *') * v),m} is non empty set
{((seq *') * v)} is non empty set
{{((seq *') * v),m},{((seq *') * v)}} is non empty set
the of p . [((seq *') * v),m] is complex set
(p,((seq *') * v),m) *' is complex Element of COMPLEX
seq is complex set
p is complex set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of m is non empty set
v is right_complementable Element of the carrier of m
seq * v is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[seq,v] is set
{seq,v} is non empty set
{seq} is non empty V64() set
{{seq,v},{seq}} is non empty set
the Mult of m . [seq,v] is set
v1 is right_complementable Element of the carrier of m
p * v1 is right_complementable Element of the carrier of m
[p,v1] is set
{p,v1} is non empty set
{p} is non empty V64() set
{{p,v1},{p}} is non empty set
the Mult of m . [p,v1] is set
(seq * v) + (p * v1) is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . ((seq * v),(p * v1)) is right_complementable Element of the carrier of m
[(seq * v),(p * v1)] is set
{(seq * v),(p * v1)} is non empty set
{(seq * v)} is non empty set
{{(seq * v),(p * v1)},{(seq * v)}} is non empty set
the addF of m . [(seq * v),(p * v1)] is set
w1 is right_complementable Element of the carrier of m
(m,((seq * v) + (p * v1)),w1) is complex set
the of m is Relation-like [: the carrier of m, the carrier of m:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total V38() Element of bool [:[: the carrier of m, the carrier of m:],COMPLEX:]
[:[: the carrier of m, the carrier of m:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of m, the carrier of m:],COMPLEX:] is non empty set
the of m . (((seq * v) + (p * v1)),w1) is complex Element of COMPLEX
[((seq * v) + (p * v1)),w1] is set
{((seq * v) + (p * v1)),w1} is non empty set
{((seq * v) + (p * v1))} is non empty set
{{((seq * v) + (p * v1)),w1},{((seq * v) + (p * v1))}} is non empty set
the of m . [((seq * v) + (p * v1)),w1] is complex set
(m,v,w1) is complex set
the of m . (v,w1) is complex Element of COMPLEX
[v,w1] is set
{v,w1} is non empty set
{v} is non empty set
{{v,w1},{v}} is non empty set
the of m . [v,w1] is complex set
seq * (m,v,w1) is complex set
(m,v1,w1) is complex set
the of m . (v1,w1) is complex Element of COMPLEX
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty set
{{v1,w1},{v1}} is non empty set
the of m . [v1,w1] is complex set
p * (m,v1,w1) is complex set
(seq * (m,v,w1)) + (p * (m,v1,w1)) is complex set
(m,(seq * v),w1) is complex set
the of m . ((seq * v),w1) is complex Element of COMPLEX
[(seq * v),w1] is set
{(seq * v),w1} is non empty set
{{(seq * v),w1},{(seq * v)}} is non empty set
the of m . [(seq * v),w1] is complex set
(m,(p * v1),w1) is complex set
the of m . ((p * v1),w1) is complex Element of COMPLEX
[(p * v1),w1] is set
{(p * v1),w1} is non empty set
{(p * v1)} is non empty set
{{(p * v1),w1},{(p * v1)}} is non empty set
the of m . [(p * v1),w1] is complex set
(m,(seq * v),w1) + (m,(p * v1),w1) is complex set
(seq * (m,v,w1)) + (m,(p * v1),w1) is complex set
seq is complex set
seq *' is complex Element of COMPLEX
p is complex set
p *' is complex Element of COMPLEX
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of m is non empty set
v is right_complementable Element of the carrier of m
v1 is right_complementable Element of the carrier of m
seq * v1 is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[seq,v1] is set
{seq,v1} is non empty set
{seq} is non empty V64() set
{{seq,v1},{seq}} is non empty set
the Mult of m . [seq,v1] is set
(m,v,v1) is complex set
the of m is Relation-like [: the carrier of m, the carrier of m:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total V38() Element of bool [:[: the carrier of m, the carrier of m:],COMPLEX:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of m, the carrier of m:],COMPLEX:] is non empty set
the of m . (v,v1) is complex Element of COMPLEX
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
the of m . [v,v1] is complex set
(seq *') * (m,v,v1) is complex set
w1 is right_complementable Element of the carrier of m
p * w1 is right_complementable Element of the carrier of m
[p,w1] is set
{p,w1} is non empty set
{p} is non empty V64() set
{{p,w1},{p}} is non empty set
the Mult of m . [p,w1] is set
(seq * v1) + (p * w1) is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . ((seq * v1),(p * w1)) is right_complementable Element of the carrier of m
[(seq * v1),(p * w1)] is set
{(seq * v1),(p * w1)} is non empty set
{(seq * v1)} is non empty set
{{(seq * v1),(p * w1)},{(seq * v1)}} is non empty set
the addF of m . [(seq * v1),(p * w1)] is set
(m,v,((seq * v1) + (p * w1))) is complex set
the of m . (v,((seq * v1) + (p * w1))) is complex Element of COMPLEX
[v,((seq * v1) + (p * w1))] is set
{v,((seq * v1) + (p * w1))} is non empty set
{{v,((seq * v1) + (p * w1))},{v}} is non empty set
the of m . [v,((seq * v1) + (p * w1))] is complex set
(m,v,w1) is complex set
the of m . (v,w1) is complex Element of COMPLEX
[v,w1] is set
{v,w1} is non empty set
{{v,w1},{v}} is non empty set
the of m . [v,w1] is complex set
(p *') * (m,v,w1) is complex set
((seq *') * (m,v,v1)) + ((p *') * (m,v,w1)) is complex set
(m,((seq * v1) + (p * w1)),v) is complex set
the of m . (((seq * v1) + (p * w1)),v) is complex Element of COMPLEX
[((seq * v1) + (p * w1)),v] is set
{((seq * v1) + (p * w1)),v} is non empty set
{((seq * v1) + (p * w1))} is non empty set
{{((seq * v1) + (p * w1)),v},{((seq * v1) + (p * w1))}} is non empty set
the of m . [((seq * v1) + (p * w1)),v] is complex set
(m,((seq * v1) + (p * w1)),v) *' is complex Element of COMPLEX
(m,v1,v) is complex set
the of m . (v1,v) is complex Element of COMPLEX
[v1,v] is set
{v1,v} is non empty set
{v1} is non empty set
{{v1,v},{v1}} is non empty set
the of m . [v1,v] is complex set
seq * (m,v1,v) is complex set
(m,w1,v) is complex set
the of m . (w1,v) is complex Element of COMPLEX
[w1,v] is set
{w1,v} is non empty set
{w1} is non empty set
{{w1,v},{w1}} is non empty set
the of m . [w1,v] is complex set
p * (m,w1,v) is complex set
(seq * (m,v1,v)) + (p * (m,w1,v)) is complex set
((seq * (m,v1,v)) + (p * (m,w1,v))) *' is complex Element of COMPLEX
(seq * (m,v1,v)) *' is complex Element of COMPLEX
(p * (m,w1,v)) *' is complex Element of COMPLEX
((seq * (m,v1,v)) *') + ((p * (m,w1,v)) *') is complex Element of COMPLEX
(m,v1,v) *' is complex Element of COMPLEX
(seq *') * ((m,v1,v) *') is complex Element of COMPLEX
((seq *') * ((m,v1,v) *')) + ((p * (m,w1,v)) *') is complex Element of COMPLEX
(m,w1,v) *' is complex Element of COMPLEX
(p *') * ((m,w1,v) *') is complex Element of COMPLEX
((seq *') * ((m,v1,v) *')) + ((p *') * ((m,w1,v) *')) is complex Element of COMPLEX
((seq *') * (m,v,v1)) + ((p *') * ((m,w1,v) *')) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,(- p),m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((- p),m) is complex Element of COMPLEX
[(- p),m] is set
{(- p),m} is non empty set
{(- p)} is non empty set
{{(- p),m},{(- p)}} is non empty set
the of seq . [(- p),m] is complex set
- m is right_complementable Element of the carrier of seq
(seq,p,(- m)) is complex set
the of seq . (p,(- m)) is complex Element of COMPLEX
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the of seq . [p,(- m)] is complex set
(- 1r) * p is right_complementable Element of the carrier of seq
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([:COMPLEX, the carrier of seq:]) quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is non empty set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
[(- 1r),p] is set
{(- 1r),p} is non empty set
{(- 1r)} is non empty V64() set
{{(- 1r),p},{(- 1r)}} is non empty set
the Mult of seq . [(- 1r),p] is set
(seq,((- 1r) * p),m) is complex set
the of seq . (((- 1r) * p),m) is complex Element of COMPLEX
[((- 1r) * p),m] is set
{((- 1r) * p),m} is non empty set
{((- 1r) * p)} is non empty set
{{((- 1r) * p),m},{((- 1r) * p)}} is non empty set
the of seq . [((- 1r) * p),m] is complex set
(- 1r) *' is complex Element of COMPLEX
((- 1r) *') * m is right_complementable Element of the carrier of seq
[((- 1r) *'),m] is set
{((- 1r) *'),m} is non empty set
{((- 1r) *')} is non empty V64() set
{{((- 1r) *'),m},{((- 1r) *')}} is non empty set
the Mult of seq . [((- 1r) *'),m] is set
(seq,p,(((- 1r) *') * m)) is complex set
the of seq . (p,(((- 1r) *') * m)) is complex Element of COMPLEX
[p,(((- 1r) *') * m)] is set
{p,(((- 1r) *') * m)} is non empty set
{{p,(((- 1r) *') * m)},{p}} is non empty set
the of seq . [p,(((- 1r) *') * m)] is complex set
(- 1r) * m is right_complementable Element of the carrier of seq
[(- 1r),m] is set
{(- 1r),m} is non empty set
{{(- 1r),m},{(- 1r)}} is non empty set
the Mult of seq . [(- 1r),m] is set
(seq,p,((- 1r) * m)) is complex set
the of seq . (p,((- 1r) * m)) is complex Element of COMPLEX
[p,((- 1r) * m)] is set
{p,((- 1r) * m)} is non empty set
{{p,((- 1r) * m)},{p}} is non empty set
the of seq . [p,((- 1r) * m)] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,(- p),m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((- p),m) is complex Element of COMPLEX
[(- p),m] is set
{(- p),m} is non empty set
{(- p)} is non empty set
{{(- p),m},{(- p)}} is non empty set
the of seq . [(- p),m] is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
- (seq,p,m) is complex set
(- 1r) * p is right_complementable Element of the carrier of seq
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([:COMPLEX, the carrier of seq:]) quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is non empty set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
[(- 1r),p] is set
{(- 1r),p} is non empty set
{(- 1r)} is non empty V64() set
{{(- 1r),p},{(- 1r)}} is non empty set
the Mult of seq . [(- 1r),p] is set
(seq,((- 1r) * p),m) is complex set
the of seq . (((- 1r) * p),m) is complex Element of COMPLEX
[((- 1r) * p),m] is set
{((- 1r) * p),m} is non empty set
{((- 1r) * p)} is non empty set
{{((- 1r) * p),m},{((- 1r) * p)}} is non empty set
the of seq . [((- 1r) * p),m] is complex set
- 1 is non empty complex V34() ext-real Element of REAL
(- 1) * (seq,p,m) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
(seq,p,(- m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,(- m)) is complex Element of COMPLEX
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the of seq . [p,(- m)] is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
- (seq,p,m) is complex set
- p is right_complementable Element of the carrier of seq
(seq,(- p),m) is complex set
the of seq . ((- p),m) is complex Element of COMPLEX
[(- p),m] is set
{(- p),m} is non empty set
{(- p)} is non empty set
{{(- p),m},{(- p)}} is non empty set
the of seq . [(- p),m] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
(seq,(- p),(- m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((- p),(- m)) is complex Element of COMPLEX
[(- p),(- m)] is set
{(- p),(- m)} is non empty set
{(- p)} is non empty set
{{(- p),(- m)},{(- p)}} is non empty set
the of seq . [(- p),(- m)] is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
(seq,p,(- m)) is complex set
the of seq . (p,(- m)) is complex Element of COMPLEX
[p,(- m)] is set
{p,(- m)} is non empty set
{{p,(- m)},{p}} is non empty set
the of seq . [p,(- m)] is complex set
- (seq,p,(- m)) is complex set
- (seq,p,m) is complex set
- (- (seq,p,m)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
v is right_complementable Element of the carrier of seq
(seq,(p - m),v) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - m),v) is complex Element of COMPLEX
[(p - m),v] is set
{(p - m),v} is non empty set
{(p - m)} is non empty set
{{(p - m),v},{(p - m)}} is non empty set
the of seq . [(p - m),v] is complex set
(seq,p,v) is complex set
the of seq . (p,v) is complex Element of COMPLEX
[p,v] is set
{p,v} is non empty set
{{p,v},{p}} is non empty set
the of seq . [p,v] is complex set
(seq,m,v) is complex set
the of seq . (m,v) is complex Element of COMPLEX
[m,v] is set
{m,v} is non empty set
{m} is non empty set
{{m,v},{m}} is non empty set
the of seq . [m,v] is complex set
(seq,p,v) - (seq,m,v) is complex set
(seq,(- m),v) is complex set
the of seq . ((- m),v) is complex Element of COMPLEX
[(- m),v] is set
{(- m),v} is non empty set
{(- m)} is non empty set
{{(- m),v},{(- m)}} is non empty set
the of seq . [(- m),v] is complex set
(seq,p,v) + (seq,(- m),v) is complex set
- (seq,m,v) is complex set
(seq,p,v) + (- (seq,m,v)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
v is right_complementable Element of the carrier of seq
m - v is right_complementable Element of the carrier of seq
- v is right_complementable Element of the carrier of seq
m + (- v) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (m,(- v)) is right_complementable Element of the carrier of seq
[m,(- v)] is set
{m,(- v)} is non empty set
{m} is non empty set
{{m,(- v)},{m}} is non empty set
the addF of seq . [m,(- v)] is set
(seq,p,(m - v)) is complex set
the of seq . (p,(m - v)) is complex Element of COMPLEX
[p,(m - v)] is set
{p,(m - v)} is non empty set
{{p,(m - v)},{p}} is non empty set
the of seq . [p,(m - v)] is complex set
(seq,p,v) is complex set
the of seq . (p,v) is complex Element of COMPLEX
[p,v] is set
{p,v} is non empty set
{{p,v},{p}} is non empty set
the of seq . [p,v] is complex set
(seq,p,m) - (seq,p,v) is complex set
(seq,p,(- v)) is complex set
the of seq . (p,(- v)) is complex Element of COMPLEX
[p,(- v)] is set
{p,(- v)} is non empty set
{{p,(- v)},{p}} is non empty set
the of seq . [p,(- v)] is complex set
(seq,p,m) + (seq,p,(- v)) is complex set
- (seq,p,v) is complex set
(seq,p,m) + (- (seq,p,v)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
v is right_complementable Element of the carrier of seq
(seq,p,v) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,v) is complex Element of COMPLEX
[p,v] is set
{p,v} is non empty set
{{p,v},{p}} is non empty set
the of seq . [p,v] is complex set
(seq,m,v) is complex set
the of seq . (m,v) is complex Element of COMPLEX
[m,v] is set
{m,v} is non empty set
{m} is non empty set
{{m,v},{m}} is non empty set
the of seq . [m,v] is complex set
v1 is right_complementable Element of the carrier of seq
v - v1 is right_complementable Element of the carrier of seq
- v1 is right_complementable Element of the carrier of seq
v + (- v1) is right_complementable Element of the carrier of seq
the addF of seq . (v,(- v1)) is right_complementable Element of the carrier of seq
[v,(- v1)] is set
{v,(- v1)} is non empty set
{v} is non empty set
{{v,(- v1)},{v}} is non empty set
the addF of seq . [v,(- v1)] is set
(seq,(p - m),(v - v1)) is complex set
the of seq . ((p - m),(v - v1)) is complex Element of COMPLEX
[(p - m),(v - v1)] is set
{(p - m),(v - v1)} is non empty set
{(p - m)} is non empty set
{{(p - m),(v - v1)},{(p - m)}} is non empty set
the of seq . [(p - m),(v - v1)] is complex set
(seq,p,v1) is complex set
the of seq . (p,v1) is complex Element of COMPLEX
[p,v1] is set
{p,v1} is non empty set
{{p,v1},{p}} is non empty set
the of seq . [p,v1] is complex set
(seq,p,v) - (seq,p,v1) is complex set
((seq,p,v) - (seq,p,v1)) - (seq,m,v) is complex set
(seq,m,v1) is complex set
the of seq . (m,v1) is complex Element of COMPLEX
[m,v1] is set
{m,v1} is non empty set
{{m,v1},{m}} is non empty set
the of seq . [m,v1] is complex set
(((seq,p,v) - (seq,p,v1)) - (seq,m,v)) + (seq,m,v1) is complex set
(seq,p,(v - v1)) is complex set
the of seq . (p,(v - v1)) is complex Element of COMPLEX
[p,(v - v1)] is set
{p,(v - v1)} is non empty set
{{p,(v - v1)},{p}} is non empty set
the of seq . [p,(v - v1)] is complex set
(seq,m,(v - v1)) is complex set
the of seq . (m,(v - v1)) is complex Element of COMPLEX
[m,(v - v1)] is set
{m,(v - v1)} is non empty set
{{m,(v - v1)},{m}} is non empty set
the of seq . [m,(v - v1)] is complex set
(seq,p,(v - v1)) - (seq,m,(v - v1)) is complex set
((seq,p,v) - (seq,p,v1)) - (seq,m,(v - v1)) is complex set
(seq,m,v) - (seq,m,v1) is complex set
((seq,p,v) - (seq,p,v1)) - ((seq,m,v) - (seq,m,v1)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
p is right_complementable Element of the carrier of seq
(seq,(0. seq),p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((0. seq),p) is complex Element of COMPLEX
[(0. seq),p] is set
{(0. seq),p} is non empty set
{(0. seq)} is non empty set
{{(0. seq),p},{(0. seq)}} is non empty set
the of seq . [(0. seq),p] is complex set
(seq,H₁(seq),p) is complex set
- p is right_complementable Element of the carrier of seq
p + (- p) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- p)) is right_complementable Element of the carrier of seq
[p,(- p)] is set
{p,(- p)} is non empty set
{p} is non empty set
{{p,(- p)},{p}} is non empty set
the addF of seq . [p,(- p)] is set
(seq,(p + (- p)),p) is complex set
the of seq . ((p + (- p)),p) is complex Element of COMPLEX
[(p + (- p)),p] is set
{(p + (- p)),p} is non empty set
{(p + (- p))} is non empty set
{{(p + (- p)),p},{(p + (- p))}} is non empty set
the of seq . [(p + (- p)),p] is complex set
(seq,p,p) is complex set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
(seq,(- p),p) is complex set
the of seq . ((- p),p) is complex Element of COMPLEX
[(- p),p] is set
{(- p),p} is non empty set
{(- p)} is non empty set
{{(- p),p},{(- p)}} is non empty set
the of seq . [(- p),p] is complex set
(seq,p,p) + (seq,(- p),p) is complex set
- (seq,p,p) is complex set
(seq,p,p) + (- (seq,p,p)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
p is right_complementable Element of the carrier of seq
(seq,p,(0. seq)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,(0. seq)) is complex Element of COMPLEX
[p,(0. seq)] is set
{p,(0. seq)} is non empty set
{p} is non empty set
{{p,(0. seq)},{p}} is non empty set
the of seq . [p,(0. seq)] is complex set
(seq,(0. seq),p) is complex set
the of seq . ((0. seq),p) is complex Element of COMPLEX
[(0. seq),p] is set
{(0. seq),p} is non empty set
{(0. seq)} is non empty set
{{(0. seq),p},{(0. seq)}} is non empty set
the of seq . [(0. seq),p] is complex set
(seq,(0. seq),p) *' is complex Element of COMPLEX
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
m is right_complementable Element of the carrier of seq
p + m is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,m) is right_complementable Element of the carrier of seq
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the addF of seq . [p,m] is set
(seq,(p + m),(p + m)) is complex set
the of seq . ((p + m),(p + m)) is complex Element of COMPLEX
[(p + m),(p + m)] is set
{(p + m),(p + m)} is non empty set
{(p + m)} is non empty set
{{(p + m),(p + m)},{(p + m)}} is non empty set
the of seq . [(p + m),(p + m)] is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
the of seq . [p,m] is complex set
(seq,p,p) + (seq,p,m) is complex set
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{m} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
((seq,p,p) + (seq,p,m)) + (seq,m,p) is complex set
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
(((seq,p,p) + (seq,p,m)) + (seq,m,p)) + (seq,m,m) is complex set
(seq,p,(p + m)) is complex set
the of seq . (p,(p + m)) is complex Element of COMPLEX
[p,(p + m)] is set
{p,(p + m)} is non empty set
{{p,(p + m)},{p}} is non empty set
the of seq . [p,(p + m)] is complex set
(seq,m,(p + m)) is complex set
the of seq . (m,(p + m)) is complex Element of COMPLEX
[m,(p + m)] is set
{m,(p + m)} is non empty set
{{m,(p + m)},{m}} is non empty set
the of seq . [m,(p + m)] is complex set
(seq,p,(p + m)) + (seq,m,(p + m)) is complex set
((seq,p,p) + (seq,p,m)) + (seq,m,(p + m)) is complex set
(seq,m,p) + (seq,m,m) is complex set
((seq,p,p) + (seq,p,m)) + ((seq,m,p) + (seq,m,m)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
m is right_complementable Element of the carrier of seq
p + m is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,m) is right_complementable Element of the carrier of seq
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the addF of seq . [p,m] is set
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p + m),(p - m)) is complex set
the of seq . ((p + m),(p - m)) is complex Element of COMPLEX
[(p + m),(p - m)] is set
{(p + m),(p - m)} is non empty set
{(p + m)} is non empty set
{{(p + m),(p - m)},{(p + m)}} is non empty set
the of seq . [(p + m),(p - m)] is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
the of seq . [p,m] is complex set
(seq,p,p) - (seq,p,m) is complex set
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{m} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
((seq,p,p) - (seq,p,m)) + (seq,m,p) is complex set
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
(((seq,p,p) - (seq,p,m)) + (seq,m,p)) - (seq,m,m) is complex set
(seq,p,(p - m)) is complex set
the of seq . (p,(p - m)) is complex Element of COMPLEX
[p,(p - m)] is set
{p,(p - m)} is non empty set
{{p,(p - m)},{p}} is non empty set
the of seq . [p,(p - m)] is complex set
(seq,m,(p - m)) is complex set
the of seq . (m,(p - m)) is complex Element of COMPLEX
[m,(p - m)] is set
{m,(p - m)} is non empty set
{{m,(p - m)},{m}} is non empty set
the of seq . [m,(p - m)] is complex set
(seq,p,(p - m)) + (seq,m,(p - m)) is complex set
((seq,p,p) - (seq,p,m)) + (seq,m,(p - m)) is complex set
(seq,m,p) - (seq,m,m) is complex set
((seq,p,p) - (seq,p,m)) + ((seq,m,p) - (seq,m,m)) is complex set
- (seq,m,m) is complex set
(((seq,p,p) - (seq,p,m)) + (seq,m,p)) + (- (seq,m,m)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m),(p - m)) is complex set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
(seq,p,p) - (seq,p,m) is complex set
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{m} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
((seq,p,p) - (seq,p,m)) - (seq,m,p) is complex set
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
(((seq,p,p) - (seq,p,m)) - (seq,m,p)) + (seq,m,m) is complex set
(seq,p,(p - m)) is complex set
the of seq . (p,(p - m)) is complex Element of COMPLEX
[p,(p - m)] is set
{p,(p - m)} is non empty set
{{p,(p - m)},{p}} is non empty set
the of seq . [p,(p - m)] is complex set
(seq,m,(p - m)) is complex set
the of seq . (m,(p - m)) is complex Element of COMPLEX
[m,(p - m)] is set
{m,(p - m)} is non empty set
{{m,(p - m)},{m}} is non empty set
the of seq . [m,(p - m)] is complex set
(seq,p,(p - m)) - (seq,m,(p - m)) is complex set
((seq,p,p) - (seq,p,m)) - (seq,m,(p - m)) is complex set
(seq,m,p) - (seq,m,m) is complex set
((seq,p,p) - (seq,p,m)) - ((seq,m,p) - (seq,m,m)) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is complex set
m is complex set
p *' is complex Element of COMPLEX
p * (p *') is complex set
m *' is complex Element of COMPLEX
p * (m *') is complex set
(p *') * m is complex set
m * (m *') is complex set
v is right_complementable Element of the carrier of seq
p * v is right_complementable Element of the carrier of seq
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([:COMPLEX, the carrier of seq:]) quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is non empty set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
[p,v] is set
{p,v} is non empty set
{p} is non empty V64() set
{{p,v},{p}} is non empty set
the Mult of seq . [p,v] is set
v1 is right_complementable Element of the carrier of seq
m * v1 is right_complementable Element of the carrier of seq
[m,v1] is set
{m,v1} is non empty set
{m} is non empty V64() set
{{m,v1},{m}} is non empty set
the Mult of seq . [m,v1] is set
(p * v) + (m * v1) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p * v),(m * v1)) is right_complementable Element of the carrier of seq
[(p * v),(m * v1)] is set
{(p * v),(m * v1)} is non empty set
{(p * v)} is non empty set
{{(p * v),(m * v1)},{(p * v)}} is non empty set
the addF of seq . [(p * v),(m * v1)] is set
(seq,((p * v) + (m * v1)),((p * v) + (m * v1))) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (((p * v) + (m * v1)),((p * v) + (m * v1))) is complex Element of COMPLEX
[((p * v) + (m * v1)),((p * v) + (m * v1))] is set
{((p * v) + (m * v1)),((p * v) + (m * v1))} is non empty set
{((p * v) + (m * v1))} is non empty set
{{((p * v) + (m * v1)),((p * v) + (m * v1))},{((p * v) + (m * v1))}} is non empty set
the of seq . [((p * v) + (m * v1)),((p * v) + (m * v1))] is complex set
(seq,v,v) is complex set
the of seq . (v,v) is complex Element of COMPLEX
[v,v] is set
{v,v} is non empty set
{v} is non empty set
{{v,v},{v}} is non empty set
the of seq . [v,v] is complex set
(p * (p *')) * (seq,v,v) is complex set
(seq,v,v1) is complex set
the of seq . (v,v1) is complex Element of COMPLEX
[v,v1] is set
{v,v1} is non empty set
{{v,v1},{v}} is non empty set
the of seq . [v,v1] is complex set
(p * (m *')) * (seq,v,v1) is complex set
((p * (p *')) * (seq,v,v)) + ((p * (m *')) * (seq,v,v1)) is complex set
(seq,v1,v) is complex set
the of seq . (v1,v) is complex Element of COMPLEX
[v1,v] is set
{v1,v} is non empty set
{v1} is non empty set
{{v1,v},{v1}} is non empty set
the of seq . [v1,v] is complex set
((p *') * m) * (seq,v1,v) is complex set
(((p * (p *')) * (seq,v,v)) + ((p * (m *')) * (seq,v,v1))) + (((p *') * m) * (seq,v1,v)) is complex set
(seq,v1,v1) is complex set
the of seq . (v1,v1) is complex Element of COMPLEX
[v1,v1] is set
{v1,v1} is non empty set
{{v1,v1},{v1}} is non empty set
the of seq . [v1,v1] is complex set
(m * (m *')) * (seq,v1,v1) is complex set
((((p * (p *')) * (seq,v,v)) + ((p * (m *')) * (seq,v,v1))) + (((p *') * m) * (seq,v1,v))) + ((m * (m *')) * (seq,v1,v1)) is complex set
(seq,v,((p * v) + (m * v1))) is complex set
the of seq . (v,((p * v) + (m * v1))) is complex Element of COMPLEX
[v,((p * v) + (m * v1))] is set
{v,((p * v) + (m * v1))} is non empty set
{{v,((p * v) + (m * v1))},{v}} is non empty set
the of seq . [v,((p * v) + (m * v1))] is complex set
p * (seq,v,((p * v) + (m * v1))) is complex set
(seq,v1,((p * v) + (m * v1))) is complex set
the of seq . (v1,((p * v) + (m * v1))) is complex Element of COMPLEX
[v1,((p * v) + (m * v1))] is set
{v1,((p * v) + (m * v1))} is non empty set
{{v1,((p * v) + (m * v1))},{v1}} is non empty set
the of seq . [v1,((p * v) + (m * v1))] is complex set
m * (seq,v1,((p * v) + (m * v1))) is complex set
(p * (seq,v,((p * v) + (m * v1)))) + (m * (seq,v1,((p * v) + (m * v1)))) is complex set
(p *') * (seq,v,v) is complex set
(m *') * (seq,v,v1) is complex set
((p *') * (seq,v,v)) + ((m *') * (seq,v,v1)) is complex set
p * (((p *') * (seq,v,v)) + ((m *') * (seq,v,v1))) is complex set
(p * (((p *') * (seq,v,v)) + ((m *') * (seq,v,v1)))) + (m * (seq,v1,((p * v) + (m * v1)))) is complex set
(p *') * (seq,v1,v) is complex set
(m *') * (seq,v1,v1) is complex set
((p *') * (seq,v1,v)) + ((m *') * (seq,v1,v1)) is complex set
m * (((p *') * (seq,v1,v)) + ((m *') * (seq,v1,v1))) is complex set
(((p * (p *')) * (seq,v,v)) + ((p * (m *')) * (seq,v,v1))) + (m * (((p *') * (seq,v1,v)) + ((m *') * (seq,v1,v1)))) is complex set
m * (p *') is complex set
(m * (p *')) * (seq,v1,v) is complex set
((m * (p *')) * (seq,v1,v)) + ((m * (m *')) * (seq,v1,v1)) is complex set
(((p * (p *')) * (seq,v,v)) + ((p * (m *')) * (seq,v,v1))) + (((m * (p *')) * (seq,v1,v)) + ((m * (m *')) * (seq,v1,v1))) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
Re (seq,p,p) is complex V34() ext-real Element of REAL
Im (seq,p,p) is complex V34() ext-real Element of REAL
(Im (seq,p,p)) * <i> is complex set
(Re (seq,p,p)) + ((Im (seq,p,p)) * <i>) is complex set
|.((Re (seq,p,p)) + ((Im (seq,p,p)) * <i>)).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
|.(seq,p,m).| is complex V34() ext-real Element of REAL
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
|.(seq,m,m).| is complex V34() ext-real Element of REAL
sqrt |.(seq,m,m).| is complex V34() ext-real Element of REAL
(sqrt |.(seq,p,p).|) * (sqrt |.(seq,m,m).|) is complex V34() ext-real Element of REAL
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
Re (seq,p,m) is complex V34() ext-real Element of REAL
(Re (seq,p,m)) ^2 is complex V34() ext-real Element of REAL
(Re (seq,p,m)) * (Re (seq,p,m)) is complex set
- (seq,p,m) is complex set
0 * <i> is complex set
|.(seq,m,m).| + (0 * <i>) is complex set
v1 is complex Element of COMPLEX
v1 * (seq,p,p) is complex set
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
(- (seq,p,m)) * (seq,m,p) is complex set
(v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p)) is complex set
v1 * ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p))) is complex set
Re (v1 * ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p)))) is complex V34() ext-real Element of REAL
Re v1 is complex V34() ext-real Element of REAL
Re ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p))) is complex V34() ext-real Element of REAL
(Re v1) * (Re ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p)))) is complex V34() ext-real Element of REAL
Im v1 is complex V34() ext-real Element of REAL
Im ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p))) is complex V34() ext-real Element of REAL
(Im v1) * (Im ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p)))) is complex V34() ext-real Element of REAL
((Re v1) * (Re ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p))))) - ((Im v1) * (Im ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p))))) is complex V34() ext-real Element of REAL
0 * (Im ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p)))) is complex V34() ext-real Element of REAL
((Re v1) * (Re ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p))))) - (0 * (Im ((v1 * (seq,p,p)) + ((- (seq,p,m)) * (seq,m,p))))) is complex V34() ext-real Element of REAL
Re ((- (seq,p,m)) * (seq,m,p)) is complex V34() ext-real Element of REAL
(seq,p,m) * (seq,m,p) is complex set
- ((seq,p,m) * (seq,m,p)) is complex set
Re (- ((seq,p,m) * (seq,m,p))) is complex V34() ext-real Element of REAL
Re ((seq,p,m) * (seq,m,p)) is complex V34() ext-real Element of REAL
- (Re ((seq,p,m) * (seq,m,p))) is complex V34() ext-real Element of REAL
(seq,p,m) *' is complex Element of COMPLEX
(seq,p,m) * ((seq,p,m) *') is complex set
Re ((seq,p,m) * ((seq,p,m) *')) is complex V34() ext-real Element of REAL
- (Re ((seq,p,m) * ((seq,p,m) *'))) is complex V34() ext-real Element of REAL
Im ((seq,p,m) * ((seq,p,m) *')) is complex V34() ext-real Element of REAL
Im (seq,m,m) is complex V34() ext-real Element of REAL
Re (seq,m,m) is complex V34() ext-real Element of REAL
(Im (seq,m,m)) * <i> is complex set
(Re (seq,m,m)) + ((Im (seq,m,m)) * <i>) is complex set
|.((Re (seq,m,m)) + ((Im (seq,m,m)) * <i>)).| is complex V34() ext-real Element of REAL
v1 * p is right_complementable Element of the carrier of seq
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([:COMPLEX, the carrier of seq:]) quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is non empty set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
[v1,p] is set
{v1,p} is non empty set
{v1} is non empty V64() set
{{v1,p},{v1}} is non empty set
the Mult of seq . [v1,p] is set
(- (seq,p,m)) * m is right_complementable Element of the carrier of seq
[(- (seq,p,m)),m] is set
{(- (seq,p,m)),m} is non empty set
{(- (seq,p,m))} is non empty V64() set
{{(- (seq,p,m)),m},{(- (seq,p,m))}} is non empty set
the Mult of seq . [(- (seq,p,m)),m] is set
(v1 * p) + ((- (seq,p,m)) * m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((v1 * p),((- (seq,p,m)) * m)) is right_complementable Element of the carrier of seq
[(v1 * p),((- (seq,p,m)) * m)] is set
{(v1 * p),((- (seq,p,m)) * m)} is non empty set
{(v1 * p)} is non empty set
{{(v1 * p),((- (seq,p,m)) * m)},{(v1 * p)}} is non empty set
the addF of seq . [(v1 * p),((- (seq,p,m)) * m)] is set
(seq,((v1 * p) + ((- (seq,p,m)) * m)),((v1 * p) + ((- (seq,p,m)) * m))) is complex set
the of seq . (((v1 * p) + ((- (seq,p,m)) * m)),((v1 * p) + ((- (seq,p,m)) * m))) is complex Element of COMPLEX
[((v1 * p) + ((- (seq,p,m)) * m)),((v1 * p) + ((- (seq,p,m)) * m))] is set
{((v1 * p) + ((- (seq,p,m)) * m)),((v1 * p) + ((- (seq,p,m)) * m))} is non empty set
{((v1 * p) + ((- (seq,p,m)) * m))} is non empty set
{{((v1 * p) + ((- (seq,p,m)) * m)),((v1 * p) + ((- (seq,p,m)) * m))},{((v1 * p) + ((- (seq,p,m)) * m))}} is non empty set
the of seq . [((v1 * p) + ((- (seq,p,m)) * m)),((v1 * p) + ((- (seq,p,m)) * m))] is complex set
v1 *' is complex Element of COMPLEX
v1 * (v1 *') is complex Element of COMPLEX
(v1 * (v1 *')) * (seq,p,p) is complex set
(- (seq,p,m)) *' is complex Element of COMPLEX
v1 * ((- (seq,p,m)) *') is complex Element of COMPLEX
(v1 * ((- (seq,p,m)) *')) * (seq,p,m) is complex set
((v1 * (v1 *')) * (seq,p,p)) + ((v1 * ((- (seq,p,m)) *')) * (seq,p,m)) is complex set
(v1 *') * (- (seq,p,m)) is complex set
((v1 *') * (- (seq,p,m))) * (seq,m,p) is complex set
(((v1 * (v1 *')) * (seq,p,p)) + ((v1 * ((- (seq,p,m)) *')) * (seq,p,m))) + (((v1 *') * (- (seq,p,m))) * (seq,m,p)) is complex set
(- (seq,p,m)) * ((- (seq,p,m)) *') is complex set
((- (seq,p,m)) * ((- (seq,p,m)) *')) * (seq,m,m) is complex set
((((v1 * (v1 *')) * (seq,p,p)) + ((v1 * ((- (seq,p,m)) *')) * (seq,p,m))) + (((v1 *') * (- (seq,p,m))) * (seq,m,p))) + (((- (seq,p,m)) * ((- (seq,p,m)) *')) * (seq,m,m)) is complex set
(v1 *') * (seq,p,p) is complex set
v1 * ((v1 *') * (seq,p,p)) is complex set
((- (seq,p,m)) *') * (seq,p,m) is complex set
v1 * (((- (seq,p,m)) *') * (seq,p,m)) is complex set
(v1 * ((v1 *') * (seq,p,p))) + (v1 * (((- (seq,p,m)) *') * (seq,p,m))) is complex set
(v1 *') * ((- (seq,p,m)) * (seq,m,p)) is complex set
((v1 * ((v1 *') * (seq,p,p))) + (v1 * (((- (seq,p,m)) *') * (seq,p,m)))) + ((v1 *') * ((- (seq,p,m)) * (seq,m,p))) is complex set
v1 * ((- (seq,p,m)) * ((- (seq,p,m)) *')) is complex set
(((v1 * ((v1 *') * (seq,p,p))) + (v1 * (((- (seq,p,m)) *') * (seq,p,m)))) + ((v1 *') * ((- (seq,p,m)) * (seq,m,p)))) + (v1 * ((- (seq,p,m)) * ((- (seq,p,m)) *'))) is complex set
((v1 *') * (seq,p,p)) + (((- (seq,p,m)) *') * (seq,p,m)) is complex set
v1 * (((v1 *') * (seq,p,p)) + (((- (seq,p,m)) *') * (seq,p,m))) is complex set
v1 * ((- (seq,p,m)) * (seq,m,p)) is complex set
(v1 * (((v1 *') * (seq,p,p)) + (((- (seq,p,m)) *') * (seq,p,m)))) + (v1 * ((- (seq,p,m)) * (seq,m,p))) is complex set
((v1 * (((v1 *') * (seq,p,p)) + (((- (seq,p,m)) *') * (seq,p,m)))) + (v1 * ((- (seq,p,m)) * (seq,m,p)))) + (v1 * ((- (seq,p,m)) * ((- (seq,p,m)) *'))) is complex set
(((v1 *') * (seq,p,p)) + (((- (seq,p,m)) *') * (seq,p,m))) + ((- (seq,p,m)) * (seq,m,p)) is complex set
((((v1 *') * (seq,p,p)) + (((- (seq,p,m)) *') * (seq,p,m))) + ((- (seq,p,m)) * (seq,m,p))) + ((- (seq,p,m)) * ((- (seq,p,m)) *')) is complex set
v1 * (((((v1 *') * (seq,p,p)) + (((- (seq,p,m)) *') * (seq,p,m))) + ((- (seq,p,m)) * (seq,m,p))) + ((- (seq,p,m)) * ((- (seq,p,m)) *'))) is complex set
(seq,p,m) * ((- (seq,p,m)) *') is complex set
(v1 * (seq,p,p)) + ((seq,p,m) * ((- (seq,p,m)) *')) is complex set
((v1 * (seq,p,p)) + ((seq,p,m) * ((- (seq,p,m)) *'))) + ((- (seq,p,m)) * (seq,m,p)) is complex set
(((v1 * (seq,p,p)) + ((seq,p,m) * ((- (seq,p,m)) *'))) + ((- (seq,p,m)) * (seq,m,p))) + ((- (seq,p,m)) * ((- (seq,p,m)) *')) is complex set
v1 * ((((v1 * (seq,p,p)) + ((seq,p,m) * ((- (seq,p,m)) *'))) + ((- (seq,p,m)) * (seq,m,p))) + ((- (seq,p,m)) * ((- (seq,p,m)) *'))) is complex set
Re (v1 * (seq,p,p)) is complex V34() ext-real Element of REAL
(Re (v1 * (seq,p,p))) + (Re ((- (seq,p,m)) * (seq,m,p))) is complex V34() ext-real Element of REAL
(Re (v1 * (seq,p,p))) - (Re ((seq,p,m) * ((seq,p,m) *'))) is complex V34() ext-real Element of REAL
(Re ((seq,p,m) * ((seq,p,m) *'))) + 0 is complex V34() ext-real Element of REAL
Im (seq,p,p) is complex V34() ext-real Element of REAL
Im (seq,p,m) is complex V34() ext-real Element of REAL
(Im (seq,p,m)) ^2 is complex V34() ext-real Element of REAL
(Im (seq,p,m)) * (Im (seq,p,m)) is complex set
Im (v1 * (seq,p,p)) is complex V34() ext-real Element of REAL
(Re v1) * 0 is complex V34() ext-real Element of REAL
Re (seq,p,p) is complex V34() ext-real Element of REAL
(Re (seq,p,p)) * 0 is complex V34() ext-real Element of REAL
((Re v1) * 0) + ((Re (seq,p,p)) * 0) is complex V34() ext-real Element of REAL
|.(v1 * (seq,p,p)).| is complex V34() ext-real Element of REAL
abs (Re (v1 * (seq,p,p))) is complex V34() ext-real Element of REAL
((Re (seq,p,m)) ^2) + ((Im (seq,p,m)) ^2) is complex V34() ext-real Element of REAL
0 + 0 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
abs (Re ((seq,p,m) * ((seq,p,m) *'))) is complex V34() ext-real Element of REAL
|.((seq,p,m) * ((seq,p,m) *')).| is complex V34() ext-real Element of REAL
|.(seq,p,p).| * |.(seq,m,m).| is complex V34() ext-real Element of REAL
|.((seq,p,m) *').| is complex V34() ext-real Element of REAL
|.(seq,p,m).| * |.((seq,p,m) *').| is complex V34() ext-real Element of REAL
|.(seq,p,m).| * |.(seq,p,m).| is complex V34() ext-real Element of REAL
|.(seq,p,m).| ^2 is complex V34() ext-real Element of REAL
|.(seq,p,m).| * |.(seq,p,m).| is complex set
sqrt (|.(seq,p,m).| ^2) is complex V34() ext-real Element of REAL
sqrt (|.(seq,p,p).| * |.(seq,m,m).|) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
v is right_complementable Element of the carrier of seq
v1 is right_complementable Element of the carrier of seq
(seq,v,v1) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (v,v1) is complex Element of COMPLEX
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
the of seq . [v,v1] is complex set
(seq,v1,v) is complex set
the of seq . (v1,v) is complex Element of COMPLEX
[v1,v] is set
{v1,v} is non empty set
{v1} is non empty set
{{v1,v},{v1}} is non empty set
the of seq . [v1,v] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
(seq,p,m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
- (seq,p,m) is complex set
- 0 is complex V34() ext-real Element of REAL
(seq,p,(- m)) is complex set
the of seq . (p,(- m)) is complex Element of COMPLEX
[p,(- m)] is set
{p,(- m)} is non empty set
{{p,(- m)},{p}} is non empty set
the of seq . [p,(- m)] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
- (seq,p,m) is complex set
- 0 is complex V34() ext-real Element of REAL
(seq,(- p),m) is complex set
the of seq . ((- p),m) is complex Element of COMPLEX
[(- p),m] is set
{(- p),m} is non empty set
{(- p)} is non empty set
{{(- p),m},{(- p)}} is non empty set
the of seq . [(- p),m] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
(seq,p,m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
(seq,(- p),(- m)) is complex set
the of seq . ((- p),(- m)) is complex Element of COMPLEX
[(- p),(- m)] is set
{(- p),(- m)} is non empty set
{(- p)} is non empty set
{{(- p),(- m)},{(- p)}} is non empty set
the of seq . [(- p),(- m)] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
p is right_complementable Element of the carrier of seq
(seq,(0. seq),p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((0. seq),p) is complex Element of COMPLEX
[(0. seq),p] is set
{(0. seq),p} is non empty set
{(0. seq)} is non empty set
{{(0. seq),p},{(0. seq)}} is non empty set
the of seq . [(0. seq),p] is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
m is right_complementable Element of the carrier of seq
p + m is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,m) is right_complementable Element of the carrier of seq
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the addF of seq . [p,m] is set
(seq,(p + m),(p + m)) is complex set
the of seq . ((p + m),(p + m)) is complex Element of COMPLEX
[(p + m),(p + m)] is set
{(p + m),(p + m)} is non empty set
{(p + m)} is non empty set
{{(p + m),(p + m)},{(p + m)}} is non empty set
the of seq . [(p + m),(p + m)] is complex set
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
(seq,p,p) + (seq,m,m) is complex set
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
the of seq . [p,m] is complex set
(seq,p,p) + 0c is complex set
((seq,p,p) + 0c) + (seq,m,m) is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m),(p - m)) is complex set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
(seq,p,p) + (seq,m,m) is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
(seq,p,p) - (seq,p,m) is complex set
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
((seq,p,p) - (seq,p,m)) - (seq,m,p) is complex set
(((seq,p,p) - (seq,p,m)) - (seq,m,p)) + (seq,m,m) is complex set
((seq,p,p) + (seq,m,m)) - 0 is complex set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
p is right_complementable Element of the carrier of seq
(seq,p) is complex V34() ext-real Element of REAL
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
Re (seq,p,p) is complex V34() ext-real Element of REAL
seq is complex set
|.seq.| is complex V34() ext-real Element of REAL
p is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of p is non empty set
m is right_complementable Element of the carrier of p
seq * m is right_complementable Element of the carrier of p
the Mult of p is Relation-like [:COMPLEX, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([:COMPLEX, the carrier of p:]) quasi_total Element of bool [:[:COMPLEX, the carrier of p:], the carrier of p:]
[:COMPLEX, the carrier of p:] is non empty set
[:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
bool [:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
[seq,m] is set
{seq,m} is non empty set
{seq} is non empty V64() set
{{seq,m},{seq}} is non empty set
the Mult of p . [seq,m] is set
(p,(seq * m)) is complex V34() ext-real Element of REAL
(p,(seq * m),(seq * m)) is complex set
the of p is Relation-like [: the carrier of p, the carrier of p:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of p, the carrier of p:]) quasi_total V38() Element of bool [:[: the carrier of p, the carrier of p:],COMPLEX:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of p, the carrier of p:],COMPLEX:] is non empty set
the of p . ((seq * m),(seq * m)) is complex Element of COMPLEX
[(seq * m),(seq * m)] is set
{(seq * m),(seq * m)} is non empty set
{(seq * m)} is non empty set
{{(seq * m),(seq * m)},{(seq * m)}} is non empty set
the of p . [(seq * m),(seq * m)] is complex set
|.(p,(seq * m),(seq * m)).| is complex V34() ext-real Element of REAL
sqrt |.(p,(seq * m),(seq * m)).| is complex V34() ext-real Element of REAL
(p,m) is complex V34() ext-real Element of REAL
(p,m,m) is complex set
the of p . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of p . [m,m] is complex set
|.(p,m,m).| is complex V34() ext-real Element of REAL
sqrt |.(p,m,m).| is complex V34() ext-real Element of REAL
|.seq.| * (p,m) is complex V34() ext-real Element of REAL
seq * seq is complex set
|.(seq * seq).| is complex V34() ext-real Element of REAL
Re (p,m,m) is complex V34() ext-real Element of REAL
(p,m,(seq * m)) is complex set
the of p . (m,(seq * m)) is complex Element of COMPLEX
[m,(seq * m)] is set
{m,(seq * m)} is non empty set
{{m,(seq * m)},{m}} is non empty set
the of p . [m,(seq * m)] is complex set
seq * (p,m,(seq * m)) is complex set
|.(seq * (p,m,(seq * m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq * (p,m,(seq * m))).| is complex V34() ext-real Element of REAL
seq *' is complex Element of COMPLEX
(seq *') * (p,m,m) is complex set
seq * ((seq *') * (p,m,m)) is complex set
|.(seq * ((seq *') * (p,m,m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq * ((seq *') * (p,m,m))).| is complex V34() ext-real Element of REAL
seq * (seq *') is complex set
(seq * (seq *')) * (p,m,m) is complex set
|.((seq * (seq *')) * (p,m,m)).| is complex V34() ext-real Element of REAL
sqrt |.((seq * (seq *')) * (p,m,m)).| is complex V34() ext-real Element of REAL
|.(seq * (seq *')).| is complex V34() ext-real Element of REAL
|.(seq * (seq *')).| * |.(p,m,m).| is complex V34() ext-real Element of REAL
sqrt (|.(seq * (seq *')).| * |.(p,m,m).|) is complex V34() ext-real Element of REAL
|.(seq * seq).| * |.(p,m,m).| is complex V34() ext-real Element of REAL
sqrt (|.(seq * seq).| * |.(p,m,m).|) is complex V34() ext-real Element of REAL
sqrt |.(seq * seq).| is complex V34() ext-real Element of REAL
(sqrt |.(seq * seq).|) * (sqrt |.(p,m,m).|) is complex V34() ext-real Element of REAL
|.seq.| ^2 is complex V34() ext-real Element of REAL
|.seq.| * |.seq.| is complex set
sqrt (|.seq.| ^2) is complex V34() ext-real Element of REAL
(sqrt (|.seq.| ^2)) * (sqrt |.(p,m,m).|) is complex V34() ext-real Element of REAL
|.seq.| * (sqrt |.(p,m,m).|) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p) is complex V34() ext-real Element of REAL
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
Re (seq,p,p) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,m) is complex Element of COMPLEX
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the of seq . [p,m] is complex set
|.(seq,p,m).| is complex V34() ext-real Element of REAL
(seq,p) is complex V34() ext-real Element of REAL
(seq,p,p) is complex set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
(seq,m) is complex V34() ext-real Element of REAL
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
|.(seq,m,m).| is complex V34() ext-real Element of REAL
sqrt |.(seq,m,m).| is complex V34() ext-real Element of REAL
(seq,p) * (seq,m) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p) is complex V34() ext-real Element of REAL
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
m is right_complementable Element of the carrier of seq
p + m is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,m) is right_complementable Element of the carrier of seq
[p,m] is set
{p,m} is non empty set
{{p,m},{p}} is non empty set
the addF of seq . [p,m] is set
(seq,(p + m)) is complex V34() ext-real Element of REAL
(seq,(p + m),(p + m)) is complex set
the of seq . ((p + m),(p + m)) is complex Element of COMPLEX
[(p + m),(p + m)] is set
{(p + m),(p + m)} is non empty set
{(p + m)} is non empty set
{{(p + m),(p + m)},{(p + m)}} is non empty set
the of seq . [(p + m),(p + m)] is complex set
|.(seq,(p + m),(p + m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p + m),(p + m)).| is complex V34() ext-real Element of REAL
(seq,m) is complex V34() ext-real Element of REAL
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
|.(seq,m,m).| is complex V34() ext-real Element of REAL
sqrt |.(seq,m,m).| is complex V34() ext-real Element of REAL
(seq,p) + (seq,m) is complex V34() ext-real Element of REAL
(seq,(p + m)) ^2 is complex V34() ext-real Element of REAL
(seq,(p + m)) * (seq,(p + m)) is complex set
Re (seq,(p + m),(p + m)) is complex V34() ext-real Element of REAL
sqrt ((seq,(p + m)) ^2) is complex V34() ext-real Element of REAL
(seq,m) ^2 is complex V34() ext-real Element of REAL
(seq,m) * (seq,m) is complex set
(seq,p,m) is complex set
the of seq . (p,m) is complex Element of COMPLEX
the of seq . [p,m] is complex set
Im (seq,p,m) is complex V34() ext-real Element of REAL
- (Im (seq,p,m)) is complex V34() ext-real Element of REAL
(seq,p,m) *' is complex Element of COMPLEX
Im ((seq,p,m) *') is complex V34() ext-real Element of REAL
(seq,m,p) is complex set
the of seq . (m,p) is complex Element of COMPLEX
[m,p] is set
{m,p} is non empty set
{{m,p},{m}} is non empty set
the of seq . [m,p] is complex set
Im (seq,m,p) is complex V34() ext-real Element of REAL
(seq,p,p) + (seq,p,m) is complex set
((seq,p,p) + (seq,p,m)) + (seq,m,p) is complex set
(((seq,p,p) + (seq,p,m)) + (seq,m,p)) + (seq,m,m) is complex set
Im ((((seq,p,p) + (seq,p,m)) + (seq,m,p)) + (seq,m,m)) is complex V34() ext-real Element of REAL
Im (((seq,p,p) + (seq,p,m)) + (seq,m,p)) is complex V34() ext-real Element of REAL
Im (seq,m,m) is complex V34() ext-real Element of REAL
(Im (((seq,p,p) + (seq,p,m)) + (seq,m,p))) + (Im (seq,m,m)) is complex V34() ext-real Element of REAL
Im ((seq,p,p) + (seq,p,m)) is complex V34() ext-real Element of REAL
(Im ((seq,p,p) + (seq,p,m))) + (Im (seq,m,p)) is complex V34() ext-real Element of REAL
((Im ((seq,p,p) + (seq,p,m))) + (Im (seq,m,p))) + (Im (seq,m,m)) is complex V34() ext-real Element of REAL
Im (seq,p,p) is complex V34() ext-real Element of REAL
(Im (seq,p,p)) + (Im (seq,p,m)) is complex V34() ext-real Element of REAL
((Im (seq,p,p)) + (Im (seq,p,m))) + (Im (seq,m,p)) is complex V34() ext-real Element of REAL
(((Im (seq,p,p)) + (Im (seq,p,m))) + (Im (seq,m,p))) + (Im (seq,m,m)) is complex V34() ext-real Element of REAL
0 + (Im (seq,p,m)) is complex V34() ext-real Element of REAL
(0 + (Im (seq,p,m))) + (Im (seq,m,p)) is complex V34() ext-real Element of REAL
((0 + (Im (seq,p,m))) + (Im (seq,m,p))) + (Im (seq,m,m)) is complex V34() ext-real Element of REAL
(Im (seq,p,m)) + (Im (seq,m,p)) is complex V34() ext-real Element of REAL
((Im (seq,p,m)) + (Im (seq,m,p))) + 0 is complex V34() ext-real Element of REAL
Re ((((seq,p,p) + (seq,p,m)) + (seq,m,p)) + (seq,m,m)) is complex V34() ext-real Element of REAL
0 * <i> is complex set
(Re ((((seq,p,p) + (seq,p,m)) + (seq,m,p)) + (seq,m,m))) + (0 * <i>) is complex set
Re (seq,p,m) is complex V34() ext-real Element of REAL
Re ((seq,p,m) *') is complex V34() ext-real Element of REAL
Re (seq,m,p) is complex V34() ext-real Element of REAL
|.(seq,p,m).| is complex V34() ext-real Element of REAL
(seq,p) * (seq,m) is complex V34() ext-real Element of REAL
2 is non empty V26() V27() V28() V32() complex V34() ext-real positive non negative V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
2 * (Re (seq,p,m)) is complex V34() ext-real Element of REAL
2 * ((seq,p) * (seq,m)) is complex V34() ext-real Element of REAL
Re (((seq,p,p) + (seq,p,m)) + (seq,m,p)) is complex V34() ext-real Element of REAL
Re (seq,m,m) is complex V34() ext-real Element of REAL
(Re (((seq,p,p) + (seq,p,m)) + (seq,m,p))) + (Re (seq,m,m)) is complex V34() ext-real Element of REAL
Re ((seq,p,p) + (seq,p,m)) is complex V34() ext-real Element of REAL
(Re ((seq,p,p) + (seq,p,m))) + (Re (seq,m,p)) is complex V34() ext-real Element of REAL
((Re ((seq,p,p) + (seq,p,m))) + (Re (seq,m,p))) + (Re (seq,m,m)) is complex V34() ext-real Element of REAL
Re (seq,p,p) is complex V34() ext-real Element of REAL
(Re (seq,p,p)) + (Re (seq,p,m)) is complex V34() ext-real Element of REAL
((Re (seq,p,p)) + (Re (seq,p,m))) + (Re (seq,m,p)) is complex V34() ext-real Element of REAL
(((Re (seq,p,p)) + (Re (seq,p,m))) + (Re (seq,m,p))) + (Re (seq,m,m)) is complex V34() ext-real Element of REAL
|.(seq,p,p).| + (Re (seq,p,m)) is complex V34() ext-real Element of REAL
(|.(seq,p,p).| + (Re (seq,p,m))) + (Re (seq,m,p)) is complex V34() ext-real Element of REAL
((|.(seq,p,p).| + (Re (seq,p,m))) + (Re (seq,m,p))) + (Re (seq,m,m)) is complex V34() ext-real Element of REAL
((|.(seq,p,p).| + (Re (seq,p,m))) + (Re (seq,m,p))) + |.(seq,m,m).| is complex V34() ext-real Element of REAL
|.((((seq,p,p) + (seq,p,m)) + (seq,m,p)) + (seq,m,m)).| is complex V34() ext-real Element of REAL
|.(seq,p,p).| + (2 * (Re (seq,p,m))) is complex V34() ext-real Element of REAL
(|.(seq,p,p).| + (2 * (Re (seq,p,m)))) + |.(seq,m,m).| is complex V34() ext-real Element of REAL
|.(seq,p,p).| + |.(seq,m,m).| is complex V34() ext-real Element of REAL
(2 * (Re (seq,p,m))) + (|.(seq,p,p).| + |.(seq,m,m).|) is complex V34() ext-real Element of REAL
(sqrt |.(seq,p,p).|) ^2 is complex V34() ext-real Element of REAL
(sqrt |.(seq,p,p).|) * (sqrt |.(seq,p,p).|) is complex set
(seq,p) ^2 is complex V34() ext-real Element of REAL
(seq,p) * (seq,p) is complex set
((seq,p) ^2) + |.(seq,m,m).| is complex V34() ext-real Element of REAL
(2 * ((seq,p) * (seq,m))) + (((seq,p) ^2) + |.(seq,m,m).|) is complex V34() ext-real Element of REAL
((seq,p) + (seq,m)) ^2 is complex V34() ext-real Element of REAL
((seq,p) + (seq,m)) * ((seq,p) + (seq,m)) is complex set
0 + 0 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
(seq,(- p)) is complex V34() ext-real Element of REAL
(seq,(- p),(- p)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((- p),(- p)) is complex Element of COMPLEX
[(- p),(- p)] is set
{(- p),(- p)} is non empty set
{(- p)} is non empty set
{{(- p),(- p)},{(- p)}} is non empty set
the of seq . [(- p),(- p)] is complex set
|.(seq,(- p),(- p)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(- p),(- p)).| is complex V34() ext-real Element of REAL
(seq,p) is complex V34() ext-real Element of REAL
(seq,p,p) is complex set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
(- 1r) * p is right_complementable Element of the carrier of seq
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([:COMPLEX, the carrier of seq:]) quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is non empty set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
[(- 1r),p] is set
{(- 1r),p} is non empty set
{(- 1r)} is non empty V64() set
{{(- 1r),p},{(- 1r)}} is non empty set
the Mult of seq . [(- 1r),p] is set
(seq,((- 1r) * p)) is complex V34() ext-real Element of REAL
(seq,((- 1r) * p),((- 1r) * p)) is complex set
the of seq . (((- 1r) * p),((- 1r) * p)) is complex Element of COMPLEX
[((- 1r) * p),((- 1r) * p)] is set
{((- 1r) * p),((- 1r) * p)} is non empty set
{((- 1r) * p)} is non empty set
{{((- 1r) * p),((- 1r) * p)},{((- 1r) * p)}} is non empty set
the of seq . [((- 1r) * p),((- 1r) * p)] is complex set
|.(seq,((- 1r) * p),((- 1r) * p)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((- 1r) * p),((- 1r) * p)).| is complex V34() ext-real Element of REAL
|.(- 1r).| is complex V34() ext-real Element of REAL
|.(- 1r).| * (seq,p) is complex V34() ext-real Element of REAL
|.1r.| * (seq,p) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p) is complex V34() ext-real Element of REAL
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
m is right_complementable Element of the carrier of seq
(seq,m) is complex V34() ext-real Element of REAL
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
|.(seq,m,m).| is complex V34() ext-real Element of REAL
sqrt |.(seq,m,m).| is complex V34() ext-real Element of REAL
(seq,p) - (seq,m) is complex V34() ext-real Element of REAL
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
(p - m) + m is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),m) is right_complementable Element of the carrier of seq
[(p - m),m] is set
{(p - m),m} is non empty set
{{(p - m),m},{(p - m)}} is non empty set
the addF of seq . [(p - m),m] is set
m - m is right_complementable Element of the carrier of seq
m + (- m) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- m)) is right_complementable Element of the carrier of seq
[m,(- m)] is set
{m,(- m)} is non empty set
{{m,(- m)},{m}} is non empty set
the addF of seq . [m,(- m)] is set
p - (m - m) is right_complementable Element of the carrier of seq
- (m - m) is right_complementable Element of the carrier of seq
p + (- (m - m)) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- (m - m))) is right_complementable Element of the carrier of seq
[p,(- (m - m))] is set
{p,(- (m - m))} is non empty set
{{p,(- (m - m))},{p}} is non empty set
the addF of seq . [p,(- (m - m))] is set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
p - H₁(seq) is right_complementable Element of the carrier of seq
- (0. seq) is right_complementable Element of the carrier of seq
p + (- (0. seq)) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- (0. seq))) is right_complementable Element of the carrier of seq
[p,(- (0. seq))] is set
{p,(- (0. seq))} is non empty set
{{p,(- (0. seq))},{p}} is non empty set
the addF of seq . [p,(- (0. seq))] is set
(seq,(p - m)) + (seq,m) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p) is complex V34() ext-real Element of REAL
(seq,p,p) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (p,p) is complex Element of COMPLEX
[p,p] is set
{p,p} is non empty set
{p} is non empty set
{{p,p},{p}} is non empty set
the of seq . [p,p] is complex set
|.(seq,p,p).| is complex V34() ext-real Element of REAL
sqrt |.(seq,p,p).| is complex V34() ext-real Element of REAL
m is right_complementable Element of the carrier of seq
(seq,m) is complex V34() ext-real Element of REAL
(seq,m,m) is complex set
the of seq . (m,m) is complex Element of COMPLEX
[m,m] is set
{m,m} is non empty set
{m} is non empty set
{{m,m},{m}} is non empty set
the of seq . [m,m] is complex set
|.(seq,m,m).| is complex V34() ext-real Element of REAL
sqrt |.(seq,m,m).| is complex V34() ext-real Element of REAL
(seq,p) - (seq,m) is complex V34() ext-real Element of REAL
abs ((seq,p) - (seq,m)) is complex V34() ext-real Element of REAL
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
m - p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m + (- p) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- p)) is right_complementable Element of the carrier of seq
[m,(- p)] is set
{m,(- p)} is non empty set
{{m,(- p)},{m}} is non empty set
the addF of seq . [m,(- p)] is set
(m - p) + p is right_complementable Element of the carrier of seq
the addF of seq . ((m - p),p) is right_complementable Element of the carrier of seq
[(m - p),p] is set
{(m - p),p} is non empty set
{(m - p)} is non empty set
{{(m - p),p},{(m - p)}} is non empty set
the addF of seq . [(m - p),p] is set
p - p is right_complementable Element of the carrier of seq
p + (- p) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- p)) is right_complementable Element of the carrier of seq
[p,(- p)] is set
{p,(- p)} is non empty set
{{p,(- p)},{p}} is non empty set
the addF of seq . [p,(- p)] is set
m - (p - p) is right_complementable Element of the carrier of seq
- (p - p) is right_complementable Element of the carrier of seq
m + (- (p - p)) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- (p - p))) is right_complementable Element of the carrier of seq
[m,(- (p - p))] is set
{m,(- (p - p))} is non empty set
{{m,(- (p - p))},{m}} is non empty set
the addF of seq . [m,(- (p - p))] is set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
m - H₁(seq) is right_complementable Element of the carrier of seq
- (0. seq) is right_complementable Element of the carrier of seq
m + (- (0. seq)) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- (0. seq))) is right_complementable Element of the carrier of seq
[m,(- (0. seq))] is set
{m,(- (0. seq))} is non empty set
{{m,(- (0. seq))},{m}} is non empty set
the addF of seq . [m,(- (0. seq))] is set
(seq,(m - p)) is complex V34() ext-real Element of REAL
(seq,(m - p),(m - p)) is complex set
the of seq . ((m - p),(m - p)) is complex Element of COMPLEX
[(m - p),(m - p)] is set
{(m - p),(m - p)} is non empty set
{{(m - p),(m - p)},{(m - p)}} is non empty set
the of seq . [(m - p),(m - p)] is complex set
|.(seq,(m - p),(m - p)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(m - p),(m - p)).| is complex V34() ext-real Element of REAL
(seq,(m - p)) + (seq,p) is complex V34() ext-real Element of REAL
(seq,m) - (seq,p) is complex V34() ext-real Element of REAL
- (p - m) is right_complementable Element of the carrier of seq
(seq,(- (p - m))) is complex V34() ext-real Element of REAL
(seq,(- (p - m)),(- (p - m))) is complex set
the of seq . ((- (p - m)),(- (p - m))) is complex Element of COMPLEX
[(- (p - m)),(- (p - m))] is set
{(- (p - m)),(- (p - m))} is non empty set
{(- (p - m))} is non empty set
{{(- (p - m)),(- (p - m))},{(- (p - m))}} is non empty set
the of seq . [(- (p - m)),(- (p - m))] is complex set
|.(seq,(- (p - m)),(- (p - m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(- (p - m)),(- (p - m))).| is complex V34() ext-real Element of REAL
- (seq,(p - m)) is complex V34() ext-real Element of REAL
- ((seq,m) - (seq,p)) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
v is right_complementable Element of the carrier of seq
v1 is right_complementable Element of the carrier of seq
(seq,v,v1) is complex V34() ext-real Element of REAL
v - v1 is right_complementable Element of the carrier of seq
- v1 is right_complementable Element of the carrier of seq
v + (- v1) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (v,(- v1)) is right_complementable Element of the carrier of seq
[v,(- v1)] is set
{v,(- v1)} is non empty set
{v} is non empty set
{{v,(- v1)},{v}} is non empty set
the addF of seq . [v,(- v1)] is set
(seq,(v - v1)) is complex V34() ext-real Element of REAL
(seq,(v - v1),(v - v1)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((v - v1),(v - v1)) is complex Element of COMPLEX
[(v - v1),(v - v1)] is set
{(v - v1),(v - v1)} is non empty set
{(v - v1)} is non empty set
{{(v - v1),(v - v1)},{(v - v1)}} is non empty set
the of seq . [(v - v1),(v - v1)] is complex set
|.(seq,(v - v1),(v - v1)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(v - v1),(v - v1)).| is complex V34() ext-real Element of REAL
(seq,v1,v) is complex V34() ext-real Element of REAL
v1 - v is right_complementable Element of the carrier of seq
- v is right_complementable Element of the carrier of seq
v1 + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (v1,(- v)) is right_complementable Element of the carrier of seq
[v1,(- v)] is set
{v1,(- v)} is non empty set
{v1} is non empty set
{{v1,(- v)},{v1}} is non empty set
the addF of seq . [v1,(- v)] is set
(seq,(v1 - v)) is complex V34() ext-real Element of REAL
(seq,(v1 - v),(v1 - v)) is complex set
the of seq . ((v1 - v),(v1 - v)) is complex Element of COMPLEX
[(v1 - v),(v1 - v)] is set
{(v1 - v),(v1 - v)} is non empty set
{(v1 - v)} is non empty set
{{(v1 - v),(v1 - v)},{(v1 - v)}} is non empty set
the of seq . [(v1 - v),(v1 - v)] is complex set
|.(seq,(v1 - v),(v1 - v)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(v1 - v),(v1 - v)).| is complex V34() ext-real Element of REAL
- (v1 - v) is right_complementable Element of the carrier of seq
(seq,(- (v1 - v))) is complex V34() ext-real Element of REAL
(seq,(- (v1 - v)),(- (v1 - v))) is complex set
the of seq . ((- (v1 - v)),(- (v1 - v))) is complex Element of COMPLEX
[(- (v1 - v)),(- (v1 - v))] is set
{(- (v1 - v)),(- (v1 - v))} is non empty set
{(- (v1 - v))} is non empty set
{{(- (v1 - v)),(- (v1 - v))},{(- (v1 - v))}} is non empty set
the of seq . [(- (v1 - v)),(- (v1 - v))] is complex set
|.(seq,(- (v1 - v)),(- (v1 - v))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(- (v1 - v)),(- (v1 - v))).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
(seq,p,p) is complex V34() ext-real Element of REAL
p - p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
p + (- p) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- p)) is right_complementable Element of the carrier of seq
[p,(- p)] is set
{p,(- p)} is non empty set
{p} is non empty set
{{p,(- p)},{p}} is non empty set
the addF of seq . [p,(- p)] is set
(seq,(p - p)) is complex V34() ext-real Element of REAL
(seq,(p - p),(p - p)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - p),(p - p)) is complex Element of COMPLEX
[(p - p),(p - p)] is set
{(p - p),(p - p)} is non empty set
{(p - p)} is non empty set
{{(p - p),(p - p)},{(p - p)}} is non empty set
the of seq . [(p - p),(p - p)] is complex set
|.(seq,(p - p),(p - p)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - p),(p - p)).| is complex V34() ext-real Element of REAL
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
(seq,H₁(seq)) is complex V34() ext-real Element of REAL
(seq,(0. seq),(0. seq)) is complex set
the of seq . ((0. seq),(0. seq)) is complex Element of COMPLEX
[(0. seq),(0. seq)] is set
{(0. seq),(0. seq)} is non empty set
{(0. seq)} is non empty set
{{(0. seq),(0. seq)},{(0. seq)}} is non empty set
the of seq . [(0. seq),(0. seq)] is complex set
|.(seq,(0. seq),(0. seq)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(0. seq),(0. seq)).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex V34() ext-real Element of REAL
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
v is right_complementable Element of the carrier of seq
(seq,p,v) is complex V34() ext-real Element of REAL
p - v is right_complementable Element of the carrier of seq
- v is right_complementable Element of the carrier of seq
p + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- v)) is right_complementable Element of the carrier of seq
[p,(- v)] is set
{p,(- v)} is non empty set
{{p,(- v)},{p}} is non empty set
the addF of seq . [p,(- v)] is set
(seq,(p - v)) is complex V34() ext-real Element of REAL
(seq,(p - v),(p - v)) is complex set
the of seq . ((p - v),(p - v)) is complex Element of COMPLEX
[(p - v),(p - v)] is set
{(p - v),(p - v)} is non empty set
{(p - v)} is non empty set
{{(p - v),(p - v)},{(p - v)}} is non empty set
the of seq . [(p - v),(p - v)] is complex set
|.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
(seq,v,m) is complex V34() ext-real Element of REAL
v - m is right_complementable Element of the carrier of seq
v + (- m) is right_complementable Element of the carrier of seq
the addF of seq . (v,(- m)) is right_complementable Element of the carrier of seq
[v,(- m)] is set
{v,(- m)} is non empty set
{v} is non empty set
{{v,(- m)},{v}} is non empty set
the addF of seq . [v,(- m)] is set
(seq,(v - m)) is complex V34() ext-real Element of REAL
(seq,(v - m),(v - m)) is complex set
the of seq . ((v - m),(v - m)) is complex Element of COMPLEX
[(v - m),(v - m)] is set
{(v - m),(v - m)} is non empty set
{(v - m)} is non empty set
{{(v - m),(v - m)},{(v - m)}} is non empty set
the of seq . [(v - m),(v - m)] is complex set
|.(seq,(v - m),(v - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(v - m),(v - m)).| is complex V34() ext-real Element of REAL
(seq,p,v) + (seq,v,m) is complex V34() ext-real Element of REAL
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
(p - m) + H₁(seq) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(0. seq)) is right_complementable Element of the carrier of seq
[(p - m),(0. seq)] is set
{(p - m),(0. seq)} is non empty set
{{(p - m),(0. seq)},{(p - m)}} is non empty set
the addF of seq . [(p - m),(0. seq)] is set
(seq,((p - m) + H₁(seq))) is complex V34() ext-real Element of REAL
(seq,((p - m) + H₁(seq)),((p - m) + H₁(seq))) is complex set
the of seq . (((p - m) + H₁(seq)),((p - m) + H₁(seq))) is complex Element of COMPLEX
[((p - m) + H₁(seq)),((p - m) + H₁(seq))] is set
{((p - m) + H₁(seq)),((p - m) + H₁(seq))} is non empty set
{((p - m) + H₁(seq))} is non empty set
{{((p - m) + H₁(seq)),((p - m) + H₁(seq))},{((p - m) + H₁(seq))}} is non empty set
the of seq . [((p - m) + H₁(seq)),((p - m) + H₁(seq))] is complex set
|.(seq,((p - m) + H₁(seq)),((p - m) + H₁(seq))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - m) + H₁(seq)),((p - m) + H₁(seq))).| is complex V34() ext-real Element of REAL
v - v is right_complementable Element of the carrier of seq
v + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (v,(- v)) is right_complementable Element of the carrier of seq
[v,(- v)] is set
{v,(- v)} is non empty set
{{v,(- v)},{v}} is non empty set
the addF of seq . [v,(- v)] is set
(p - m) + (v - v) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(v - v)) is right_complementable Element of the carrier of seq
[(p - m),(v - v)] is set
{(p - m),(v - v)} is non empty set
{{(p - m),(v - v)},{(p - m)}} is non empty set
the addF of seq . [(p - m),(v - v)] is set
(seq,((p - m) + (v - v))) is complex V34() ext-real Element of REAL
(seq,((p - m) + (v - v)),((p - m) + (v - v))) is complex set
the of seq . (((p - m) + (v - v)),((p - m) + (v - v))) is complex Element of COMPLEX
[((p - m) + (v - v)),((p - m) + (v - v))] is set
{((p - m) + (v - v)),((p - m) + (v - v))} is non empty set
{((p - m) + (v - v))} is non empty set
{{((p - m) + (v - v)),((p - m) + (v - v))},{((p - m) + (v - v))}} is non empty set
the of seq . [((p - m) + (v - v)),((p - m) + (v - v))] is complex set
|.(seq,((p - m) + (v - v)),((p - m) + (v - v))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - m) + (v - v)),((p - m) + (v - v))).| is complex V34() ext-real Element of REAL
m - (v - v) is right_complementable Element of the carrier of seq
- (v - v) is right_complementable Element of the carrier of seq
m + (- (v - v)) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- (v - v))) is right_complementable Element of the carrier of seq
[m,(- (v - v))] is set
{m,(- (v - v))} is non empty set
{m} is non empty set
{{m,(- (v - v))},{m}} is non empty set
the addF of seq . [m,(- (v - v))] is set
p - (m - (v - v)) is right_complementable Element of the carrier of seq
- (m - (v - v)) is right_complementable Element of the carrier of seq
p + (- (m - (v - v))) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- (m - (v - v)))) is right_complementable Element of the carrier of seq
[p,(- (m - (v - v)))] is set
{p,(- (m - (v - v)))} is non empty set
{{p,(- (m - (v - v)))},{p}} is non empty set
the addF of seq . [p,(- (m - (v - v)))] is set
(seq,(p - (m - (v - v)))) is complex V34() ext-real Element of REAL
(seq,(p - (m - (v - v))),(p - (m - (v - v)))) is complex set
the of seq . ((p - (m - (v - v))),(p - (m - (v - v)))) is complex Element of COMPLEX
[(p - (m - (v - v))),(p - (m - (v - v)))] is set
{(p - (m - (v - v))),(p - (m - (v - v)))} is non empty set
{(p - (m - (v - v)))} is non empty set
{{(p - (m - (v - v))),(p - (m - (v - v)))},{(p - (m - (v - v)))}} is non empty set
the of seq . [(p - (m - (v - v))),(p - (m - (v - v)))] is complex set
|.(seq,(p - (m - (v - v))),(p - (m - (v - v)))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - (m - (v - v))),(p - (m - (v - v)))).| is complex V34() ext-real Element of REAL
m - v is right_complementable Element of the carrier of seq
m + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- v)) is right_complementable Element of the carrier of seq
[m,(- v)] is set
{m,(- v)} is non empty set
{{m,(- v)},{m}} is non empty set
the addF of seq . [m,(- v)] is set
v + (m - v) is right_complementable Element of the carrier of seq
the addF of seq . (v,(m - v)) is right_complementable Element of the carrier of seq
[v,(m - v)] is set
{v,(m - v)} is non empty set
{{v,(m - v)},{v}} is non empty set
the addF of seq . [v,(m - v)] is set
p - (v + (m - v)) is right_complementable Element of the carrier of seq
- (v + (m - v)) is right_complementable Element of the carrier of seq
p + (- (v + (m - v))) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- (v + (m - v)))) is right_complementable Element of the carrier of seq
[p,(- (v + (m - v)))] is set
{p,(- (v + (m - v)))} is non empty set
{{p,(- (v + (m - v)))},{p}} is non empty set
the addF of seq . [p,(- (v + (m - v)))] is set
(seq,(p - (v + (m - v)))) is complex V34() ext-real Element of REAL
(seq,(p - (v + (m - v))),(p - (v + (m - v)))) is complex set
the of seq . ((p - (v + (m - v))),(p - (v + (m - v)))) is complex Element of COMPLEX
[(p - (v + (m - v))),(p - (v + (m - v)))] is set
{(p - (v + (m - v))),(p - (v + (m - v)))} is non empty set
{(p - (v + (m - v)))} is non empty set
{{(p - (v + (m - v))),(p - (v + (m - v)))},{(p - (v + (m - v)))}} is non empty set
the of seq . [(p - (v + (m - v))),(p - (v + (m - v)))] is complex set
|.(seq,(p - (v + (m - v))),(p - (v + (m - v)))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - (v + (m - v))),(p - (v + (m - v)))).| is complex V34() ext-real Element of REAL
(p - v) - (m - v) is right_complementable Element of the carrier of seq
- (m - v) is right_complementable Element of the carrier of seq
(p - v) + (- (m - v)) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(- (m - v))) is right_complementable Element of the carrier of seq
[(p - v),(- (m - v))] is set
{(p - v),(- (m - v))} is non empty set
{{(p - v),(- (m - v))},{(p - v)}} is non empty set
the addF of seq . [(p - v),(- (m - v))] is set
(seq,((p - v) - (m - v))) is complex V34() ext-real Element of REAL
(seq,((p - v) - (m - v)),((p - v) - (m - v))) is complex set
the of seq . (((p - v) - (m - v)),((p - v) - (m - v))) is complex Element of COMPLEX
[((p - v) - (m - v)),((p - v) - (m - v))] is set
{((p - v) - (m - v)),((p - v) - (m - v))} is non empty set
{((p - v) - (m - v))} is non empty set
{{((p - v) - (m - v)),((p - v) - (m - v))},{((p - v) - (m - v))}} is non empty set
the of seq . [((p - v) - (m - v)),((p - v) - (m - v))] is complex set
|.(seq,((p - v) - (m - v)),((p - v) - (m - v))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - v) - (m - v)),((p - v) - (m - v))).| is complex V34() ext-real Element of REAL
(p - v) + (v - m) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(v - m)) is right_complementable Element of the carrier of seq
[(p - v),(v - m)] is set
{(p - v),(v - m)} is non empty set
{{(p - v),(v - m)},{(p - v)}} is non empty set
the addF of seq . [(p - v),(v - m)] is set
(seq,((p - v) + (v - m))) is complex V34() ext-real Element of REAL
(seq,((p - v) + (v - m)),((p - v) + (v - m))) is complex set
the of seq . (((p - v) + (v - m)),((p - v) + (v - m))) is complex Element of COMPLEX
[((p - v) + (v - m)),((p - v) + (v - m))] is set
{((p - v) + (v - m)),((p - v) + (v - m))} is non empty set
{((p - v) + (v - m))} is non empty set
{{((p - v) + (v - m)),((p - v) + (v - m))},{((p - v) + (v - m))}} is non empty set
the of seq . [((p - v) + (v - m)),((p - v) + (v - m))] is complex set
|.(seq,((p - v) + (v - m)),((p - v) + (v - m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - v) + (v - m)),((p - v) + (v - m))).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex V34() ext-real Element of REAL
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex V34() ext-real Element of REAL
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex V34() ext-real Element of REAL
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
(seq,p,m) is complex V34() ext-real Element of REAL
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,(p - m)) is complex V34() ext-real Element of REAL
(seq,(p - m),(p - m)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - m),(p - m)) is complex Element of COMPLEX
[(p - m),(p - m)] is set
{(p - m),(p - m)} is non empty set
{(p - m)} is non empty set
{{(p - m),(p - m)},{(p - m)}} is non empty set
the of seq . [(p - m),(p - m)] is complex set
|.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - m),(p - m)).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
p + m is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,m) is right_complementable Element of the carrier of seq
[p,m] is set
{p,m} is non empty set
{p} is non empty set
{{p,m},{p}} is non empty set
the addF of seq . [p,m] is set
v is right_complementable Element of the carrier of seq
(seq,p,v) is complex V34() ext-real Element of REAL
p - v is right_complementable Element of the carrier of seq
- v is right_complementable Element of the carrier of seq
p + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- v)) is right_complementable Element of the carrier of seq
[p,(- v)] is set
{p,(- v)} is non empty set
{{p,(- v)},{p}} is non empty set
the addF of seq . [p,(- v)] is set
(seq,(p - v)) is complex V34() ext-real Element of REAL
(seq,(p - v),(p - v)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - v),(p - v)) is complex Element of COMPLEX
[(p - v),(p - v)] is set
{(p - v),(p - v)} is non empty set
{(p - v)} is non empty set
{{(p - v),(p - v)},{(p - v)}} is non empty set
the of seq . [(p - v),(p - v)] is complex set
|.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
v1 is right_complementable Element of the carrier of seq
v + v1 is right_complementable Element of the carrier of seq
the addF of seq . (v,v1) is right_complementable Element of the carrier of seq
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
the addF of seq . [v,v1] is set
(seq,(p + m),(v + v1)) is complex V34() ext-real Element of REAL
(p + m) - (v + v1) is right_complementable Element of the carrier of seq
- (v + v1) is right_complementable Element of the carrier of seq
(p + m) + (- (v + v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((p + m),(- (v + v1))) is right_complementable Element of the carrier of seq
[(p + m),(- (v + v1))] is set
{(p + m),(- (v + v1))} is non empty set
{(p + m)} is non empty set
{{(p + m),(- (v + v1))},{(p + m)}} is non empty set
the addF of seq . [(p + m),(- (v + v1))] is set
(seq,((p + m) - (v + v1))) is complex V34() ext-real Element of REAL
(seq,((p + m) - (v + v1)),((p + m) - (v + v1))) is complex set
the of seq . (((p + m) - (v + v1)),((p + m) - (v + v1))) is complex Element of COMPLEX
[((p + m) - (v + v1)),((p + m) - (v + v1))] is set
{((p + m) - (v + v1)),((p + m) - (v + v1))} is non empty set
{((p + m) - (v + v1))} is non empty set
{{((p + m) - (v + v1)),((p + m) - (v + v1))},{((p + m) - (v + v1))}} is non empty set
the of seq . [((p + m) - (v + v1)),((p + m) - (v + v1))] is complex set
|.(seq,((p + m) - (v + v1)),((p + m) - (v + v1))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p + m) - (v + v1)),((p + m) - (v + v1))).| is complex V34() ext-real Element of REAL
(seq,m,v1) is complex V34() ext-real Element of REAL
m - v1 is right_complementable Element of the carrier of seq
- v1 is right_complementable Element of the carrier of seq
m + (- v1) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- v1)) is right_complementable Element of the carrier of seq
[m,(- v1)] is set
{m,(- v1)} is non empty set
{m} is non empty set
{{m,(- v1)},{m}} is non empty set
the addF of seq . [m,(- v1)] is set
(seq,(m - v1)) is complex V34() ext-real Element of REAL
(seq,(m - v1),(m - v1)) is complex set
the of seq . ((m - v1),(m - v1)) is complex Element of COMPLEX
[(m - v1),(m - v1)] is set
{(m - v1),(m - v1)} is non empty set
{(m - v1)} is non empty set
{{(m - v1),(m - v1)},{(m - v1)}} is non empty set
the of seq . [(m - v1),(m - v1)] is complex set
|.(seq,(m - v1),(m - v1)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(m - v1),(m - v1)).| is complex V34() ext-real Element of REAL
(seq,p,v) + (seq,m,v1) is complex V34() ext-real Element of REAL
(- v) + (- v1) is right_complementable Element of the carrier of seq
the addF of seq . ((- v),(- v1)) is right_complementable Element of the carrier of seq
[(- v),(- v1)] is set
{(- v),(- v1)} is non empty set
{(- v)} is non empty set
{{(- v),(- v1)},{(- v)}} is non empty set
the addF of seq . [(- v),(- v1)] is set
((- v) + (- v1)) + (p + m) is right_complementable Element of the carrier of seq
the addF of seq . (((- v) + (- v1)),(p + m)) is right_complementable Element of the carrier of seq
[((- v) + (- v1)),(p + m)] is set
{((- v) + (- v1)),(p + m)} is non empty set
{((- v) + (- v1))} is non empty set
{{((- v) + (- v1)),(p + m)},{((- v) + (- v1))}} is non empty set
the addF of seq . [((- v) + (- v1)),(p + m)] is set
(seq,(((- v) + (- v1)) + (p + m))) is complex V34() ext-real Element of REAL
(seq,(((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))) is complex set
the of seq . ((((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))) is complex Element of COMPLEX
[(((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))] is set
{(((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))} is non empty set
{(((- v) + (- v1)) + (p + m))} is non empty set
{{(((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))},{(((- v) + (- v1)) + (p + m))}} is non empty set
the of seq . [(((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))] is complex set
|.(seq,(((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(((- v) + (- v1)) + (p + m)),(((- v) + (- v1)) + (p + m))).| is complex V34() ext-real Element of REAL
p + ((- v) + (- v1)) is right_complementable Element of the carrier of seq
the addF of seq . (p,((- v) + (- v1))) is right_complementable Element of the carrier of seq
[p,((- v) + (- v1))] is set
{p,((- v) + (- v1))} is non empty set
{{p,((- v) + (- v1))},{p}} is non empty set
the addF of seq . [p,((- v) + (- v1))] is set
(p + ((- v) + (- v1))) + m is right_complementable Element of the carrier of seq
the addF of seq . ((p + ((- v) + (- v1))),m) is right_complementable Element of the carrier of seq
[(p + ((- v) + (- v1))),m] is set
{(p + ((- v) + (- v1))),m} is non empty set
{(p + ((- v) + (- v1)))} is non empty set
{{(p + ((- v) + (- v1))),m},{(p + ((- v) + (- v1)))}} is non empty set
the addF of seq . [(p + ((- v) + (- v1))),m] is set
(seq,((p + ((- v) + (- v1))) + m)) is complex V34() ext-real Element of REAL
(seq,((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)) is complex set
the of seq . (((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)) is complex Element of COMPLEX
[((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)] is set
{((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)} is non empty set
{((p + ((- v) + (- v1))) + m)} is non empty set
{{((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)},{((p + ((- v) + (- v1))) + m)}} is non empty set
the of seq . [((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)] is complex set
|.(seq,((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p + ((- v) + (- v1))) + m),((p + ((- v) + (- v1))) + m)).| is complex V34() ext-real Element of REAL
(p - v) + (- v1) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(- v1)) is right_complementable Element of the carrier of seq
[(p - v),(- v1)] is set
{(p - v),(- v1)} is non empty set
{{(p - v),(- v1)},{(p - v)}} is non empty set
the addF of seq . [(p - v),(- v1)] is set
((p - v) + (- v1)) + m is right_complementable Element of the carrier of seq
the addF of seq . (((p - v) + (- v1)),m) is right_complementable Element of the carrier of seq
[((p - v) + (- v1)),m] is set
{((p - v) + (- v1)),m} is non empty set
{((p - v) + (- v1))} is non empty set
{{((p - v) + (- v1)),m},{((p - v) + (- v1))}} is non empty set
the addF of seq . [((p - v) + (- v1)),m] is set
(seq,(((p - v) + (- v1)) + m)) is complex V34() ext-real Element of REAL
(seq,(((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)) is complex set
the of seq . ((((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)) is complex Element of COMPLEX
[(((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)] is set
{(((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)} is non empty set
{(((p - v) + (- v1)) + m)} is non empty set
{{(((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)},{(((p - v) + (- v1)) + m)}} is non empty set
the of seq . [(((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)] is complex set
|.(seq,(((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(((p - v) + (- v1)) + m),(((p - v) + (- v1)) + m)).| is complex V34() ext-real Element of REAL
(p - v) + (m - v1) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(m - v1)) is right_complementable Element of the carrier of seq
[(p - v),(m - v1)] is set
{(p - v),(m - v1)} is non empty set
{{(p - v),(m - v1)},{(p - v)}} is non empty set
the addF of seq . [(p - v),(m - v1)] is set
(seq,((p - v) + (m - v1))) is complex V34() ext-real Element of REAL
(seq,((p - v) + (m - v1)),((p - v) + (m - v1))) is complex set
the of seq . (((p - v) + (m - v1)),((p - v) + (m - v1))) is complex Element of COMPLEX
[((p - v) + (m - v1)),((p - v) + (m - v1))] is set
{((p - v) + (m - v1)),((p - v) + (m - v1))} is non empty set
{((p - v) + (m - v1))} is non empty set
{{((p - v) + (m - v1)),((p - v) + (m - v1))},{((p - v) + (m - v1))}} is non empty set
the of seq . [((p - v) + (m - v1)),((p - v) + (m - v1))] is complex set
|.(seq,((p - v) + (m - v1)),((p - v) + (m - v1))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - v) + (m - v1)),((p - v) + (m - v1))).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
v is right_complementable Element of the carrier of seq
(seq,p,v) is complex V34() ext-real Element of REAL
p - v is right_complementable Element of the carrier of seq
- v is right_complementable Element of the carrier of seq
p + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- v)) is right_complementable Element of the carrier of seq
[p,(- v)] is set
{p,(- v)} is non empty set
{{p,(- v)},{p}} is non empty set
the addF of seq . [p,(- v)] is set
(seq,(p - v)) is complex V34() ext-real Element of REAL
(seq,(p - v),(p - v)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((p - v),(p - v)) is complex Element of COMPLEX
[(p - v),(p - v)] is set
{(p - v),(p - v)} is non empty set
{(p - v)} is non empty set
{{(p - v),(p - v)},{(p - v)}} is non empty set
the of seq . [(p - v),(p - v)] is complex set
|.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
v1 is right_complementable Element of the carrier of seq
v - v1 is right_complementable Element of the carrier of seq
- v1 is right_complementable Element of the carrier of seq
v + (- v1) is right_complementable Element of the carrier of seq
the addF of seq . (v,(- v1)) is right_complementable Element of the carrier of seq
[v,(- v1)] is set
{v,(- v1)} is non empty set
{v} is non empty set
{{v,(- v1)},{v}} is non empty set
the addF of seq . [v,(- v1)] is set
(seq,(p - m),(v - v1)) is complex V34() ext-real Element of REAL
(p - m) - (v - v1) is right_complementable Element of the carrier of seq
- (v - v1) is right_complementable Element of the carrier of seq
(p - m) + (- (v - v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(- (v - v1))) is right_complementable Element of the carrier of seq
[(p - m),(- (v - v1))] is set
{(p - m),(- (v - v1))} is non empty set
{(p - m)} is non empty set
{{(p - m),(- (v - v1))},{(p - m)}} is non empty set
the addF of seq . [(p - m),(- (v - v1))] is set
(seq,((p - m) - (v - v1))) is complex V34() ext-real Element of REAL
(seq,((p - m) - (v - v1)),((p - m) - (v - v1))) is complex set
the of seq . (((p - m) - (v - v1)),((p - m) - (v - v1))) is complex Element of COMPLEX
[((p - m) - (v - v1)),((p - m) - (v - v1))] is set
{((p - m) - (v - v1)),((p - m) - (v - v1))} is non empty set
{((p - m) - (v - v1))} is non empty set
{{((p - m) - (v - v1)),((p - m) - (v - v1))},{((p - m) - (v - v1))}} is non empty set
the of seq . [((p - m) - (v - v1)),((p - m) - (v - v1))] is complex set
|.(seq,((p - m) - (v - v1)),((p - m) - (v - v1))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - m) - (v - v1)),((p - m) - (v - v1))).| is complex V34() ext-real Element of REAL
(seq,m,v1) is complex V34() ext-real Element of REAL
m - v1 is right_complementable Element of the carrier of seq
m + (- v1) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- v1)) is right_complementable Element of the carrier of seq
[m,(- v1)] is set
{m,(- v1)} is non empty set
{m} is non empty set
{{m,(- v1)},{m}} is non empty set
the addF of seq . [m,(- v1)] is set
(seq,(m - v1)) is complex V34() ext-real Element of REAL
(seq,(m - v1),(m - v1)) is complex set
the of seq . ((m - v1),(m - v1)) is complex Element of COMPLEX
[(m - v1),(m - v1)] is set
{(m - v1),(m - v1)} is non empty set
{(m - v1)} is non empty set
{{(m - v1),(m - v1)},{(m - v1)}} is non empty set
the of seq . [(m - v1),(m - v1)] is complex set
|.(seq,(m - v1),(m - v1)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(m - v1),(m - v1)).| is complex V34() ext-real Element of REAL
(seq,p,v) + (seq,m,v1) is complex V34() ext-real Element of REAL
(p - m) - v is right_complementable Element of the carrier of seq
(p - m) + (- v) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(- v)) is right_complementable Element of the carrier of seq
[(p - m),(- v)] is set
{(p - m),(- v)} is non empty set
{{(p - m),(- v)},{(p - m)}} is non empty set
the addF of seq . [(p - m),(- v)] is set
((p - m) - v) + v1 is right_complementable Element of the carrier of seq
the addF of seq . (((p - m) - v),v1) is right_complementable Element of the carrier of seq
[((p - m) - v),v1] is set
{((p - m) - v),v1} is non empty set
{((p - m) - v)} is non empty set
{{((p - m) - v),v1},{((p - m) - v)}} is non empty set
the addF of seq . [((p - m) - v),v1] is set
(seq,(((p - m) - v) + v1)) is complex V34() ext-real Element of REAL
(seq,(((p - m) - v) + v1),(((p - m) - v) + v1)) is complex set
the of seq . ((((p - m) - v) + v1),(((p - m) - v) + v1)) is complex Element of COMPLEX
[(((p - m) - v) + v1),(((p - m) - v) + v1)] is set
{(((p - m) - v) + v1),(((p - m) - v) + v1)} is non empty set
{(((p - m) - v) + v1)} is non empty set
{{(((p - m) - v) + v1),(((p - m) - v) + v1)},{(((p - m) - v) + v1)}} is non empty set
the of seq . [(((p - m) - v) + v1),(((p - m) - v) + v1)] is complex set
|.(seq,(((p - m) - v) + v1),(((p - m) - v) + v1)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(((p - m) - v) + v1),(((p - m) - v) + v1)).| is complex V34() ext-real Element of REAL
v + m is right_complementable Element of the carrier of seq
the addF of seq . (v,m) is right_complementable Element of the carrier of seq
[v,m] is set
{v,m} is non empty set
{{v,m},{v}} is non empty set
the addF of seq . [v,m] is set
p - (v + m) is right_complementable Element of the carrier of seq
- (v + m) is right_complementable Element of the carrier of seq
p + (- (v + m)) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- (v + m))) is right_complementable Element of the carrier of seq
[p,(- (v + m))] is set
{p,(- (v + m))} is non empty set
{{p,(- (v + m))},{p}} is non empty set
the addF of seq . [p,(- (v + m))] is set
(p - (v + m)) + v1 is right_complementable Element of the carrier of seq
the addF of seq . ((p - (v + m)),v1) is right_complementable Element of the carrier of seq
[(p - (v + m)),v1] is set
{(p - (v + m)),v1} is non empty set
{(p - (v + m))} is non empty set
{{(p - (v + m)),v1},{(p - (v + m))}} is non empty set
the addF of seq . [(p - (v + m)),v1] is set
(seq,((p - (v + m)) + v1)) is complex V34() ext-real Element of REAL
(seq,((p - (v + m)) + v1),((p - (v + m)) + v1)) is complex set
the of seq . (((p - (v + m)) + v1),((p - (v + m)) + v1)) is complex Element of COMPLEX
[((p - (v + m)) + v1),((p - (v + m)) + v1)] is set
{((p - (v + m)) + v1),((p - (v + m)) + v1)} is non empty set
{((p - (v + m)) + v1)} is non empty set
{{((p - (v + m)) + v1),((p - (v + m)) + v1)},{((p - (v + m)) + v1)}} is non empty set
the of seq . [((p - (v + m)) + v1),((p - (v + m)) + v1)] is complex set
|.(seq,((p - (v + m)) + v1),((p - (v + m)) + v1)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - (v + m)) + v1),((p - (v + m)) + v1)).| is complex V34() ext-real Element of REAL
(p - v) - m is right_complementable Element of the carrier of seq
(p - v) + (- m) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(- m)) is right_complementable Element of the carrier of seq
[(p - v),(- m)] is set
{(p - v),(- m)} is non empty set
{{(p - v),(- m)},{(p - v)}} is non empty set
the addF of seq . [(p - v),(- m)] is set
((p - v) - m) + v1 is right_complementable Element of the carrier of seq
the addF of seq . (((p - v) - m),v1) is right_complementable Element of the carrier of seq
[((p - v) - m),v1] is set
{((p - v) - m),v1} is non empty set
{((p - v) - m)} is non empty set
{{((p - v) - m),v1},{((p - v) - m)}} is non empty set
the addF of seq . [((p - v) - m),v1] is set
(seq,(((p - v) - m) + v1)) is complex V34() ext-real Element of REAL
(seq,(((p - v) - m) + v1),(((p - v) - m) + v1)) is complex set
the of seq . ((((p - v) - m) + v1),(((p - v) - m) + v1)) is complex Element of COMPLEX
[(((p - v) - m) + v1),(((p - v) - m) + v1)] is set
{(((p - v) - m) + v1),(((p - v) - m) + v1)} is non empty set
{(((p - v) - m) + v1)} is non empty set
{{(((p - v) - m) + v1),(((p - v) - m) + v1)},{(((p - v) - m) + v1)}} is non empty set
the of seq . [(((p - v) - m) + v1),(((p - v) - m) + v1)] is complex set
|.(seq,(((p - v) - m) + v1),(((p - v) - m) + v1)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(((p - v) - m) + v1),(((p - v) - m) + v1)).| is complex V34() ext-real Element of REAL
(p - v) - (m - v1) is right_complementable Element of the carrier of seq
- (m - v1) is right_complementable Element of the carrier of seq
(p - v) + (- (m - v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(- (m - v1))) is right_complementable Element of the carrier of seq
[(p - v),(- (m - v1))] is set
{(p - v),(- (m - v1))} is non empty set
{{(p - v),(- (m - v1))},{(p - v)}} is non empty set
the addF of seq . [(p - v),(- (m - v1))] is set
(seq,((p - v) - (m - v1))) is complex V34() ext-real Element of REAL
(seq,((p - v) - (m - v1)),((p - v) - (m - v1))) is complex set
the of seq . (((p - v) - (m - v1)),((p - v) - (m - v1))) is complex Element of COMPLEX
[((p - v) - (m - v1)),((p - v) - (m - v1))] is set
{((p - v) - (m - v1)),((p - v) - (m - v1))} is non empty set
{((p - v) - (m - v1))} is non empty set
{{((p - v) - (m - v1)),((p - v) - (m - v1))},{((p - v) - (m - v1))}} is non empty set
the of seq . [((p - v) - (m - v1)),((p - v) - (m - v1))] is complex set
|.(seq,((p - v) - (m - v1)),((p - v) - (m - v1))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - v) - (m - v1)),((p - v) - (m - v1))).| is complex V34() ext-real Element of REAL
(p - v) + (- (m - v1)) is right_complementable Element of the carrier of seq
(seq,((p - v) + (- (m - v1)))) is complex V34() ext-real Element of REAL
(seq,((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))) is complex set
the of seq . (((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))) is complex Element of COMPLEX
[((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))] is set
{((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))} is non empty set
{((p - v) + (- (m - v1)))} is non empty set
{{((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))},{((p - v) + (- (m - v1)))}} is non empty set
the of seq . [((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))] is complex set
|.(seq,((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - v) + (- (m - v1))),((p - v) + (- (m - v1)))).| is complex V34() ext-real Element of REAL
(seq,(- (m - v1))) is complex V34() ext-real Element of REAL
(seq,(- (m - v1)),(- (m - v1))) is complex set
the of seq . ((- (m - v1)),(- (m - v1))) is complex Element of COMPLEX
[(- (m - v1)),(- (m - v1))] is set
{(- (m - v1)),(- (m - v1))} is non empty set
{(- (m - v1))} is non empty set
{{(- (m - v1)),(- (m - v1))},{(- (m - v1))}} is non empty set
the of seq . [(- (m - v1)),(- (m - v1))] is complex set
|.(seq,(- (m - v1)),(- (m - v1))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(- (m - v1)),(- (m - v1))).| is complex V34() ext-real Element of REAL
(seq,(p - v)) + (seq,(- (m - v1))) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
v is right_complementable Element of the carrier of seq
v - m is right_complementable Element of the carrier of seq
v + (- m) is right_complementable Element of the carrier of seq
the addF of seq . (v,(- m)) is right_complementable Element of the carrier of seq
[v,(- m)] is set
{v,(- m)} is non empty set
{v} is non empty set
{{v,(- m)},{v}} is non empty set
the addF of seq . [v,(- m)] is set
(seq,(p - m),(v - m)) is complex V34() ext-real Element of REAL
(p - m) - (v - m) is right_complementable Element of the carrier of seq
- (v - m) is right_complementable Element of the carrier of seq
(p - m) + (- (v - m)) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(- (v - m))) is right_complementable Element of the carrier of seq
[(p - m),(- (v - m))] is set
{(p - m),(- (v - m))} is non empty set
{(p - m)} is non empty set
{{(p - m),(- (v - m))},{(p - m)}} is non empty set
the addF of seq . [(p - m),(- (v - m))] is set
(seq,((p - m) - (v - m))) is complex V34() ext-real Element of REAL
(seq,((p - m) - (v - m)),((p - m) - (v - m))) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . (((p - m) - (v - m)),((p - m) - (v - m))) is complex Element of COMPLEX
[((p - m) - (v - m)),((p - m) - (v - m))] is set
{((p - m) - (v - m)),((p - m) - (v - m))} is non empty set
{((p - m) - (v - m))} is non empty set
{{((p - m) - (v - m)),((p - m) - (v - m))},{((p - m) - (v - m))}} is non empty set
the of seq . [((p - m) - (v - m)),((p - m) - (v - m))] is complex set
|.(seq,((p - m) - (v - m)),((p - m) - (v - m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - m) - (v - m)),((p - m) - (v - m))).| is complex V34() ext-real Element of REAL
(seq,p,v) is complex V34() ext-real Element of REAL
p - v is right_complementable Element of the carrier of seq
- v is right_complementable Element of the carrier of seq
p + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- v)) is right_complementable Element of the carrier of seq
[p,(- v)] is set
{p,(- v)} is non empty set
{{p,(- v)},{p}} is non empty set
the addF of seq . [p,(- v)] is set
(seq,(p - v)) is complex V34() ext-real Element of REAL
(seq,(p - v),(p - v)) is complex set
the of seq . ((p - v),(p - v)) is complex Element of COMPLEX
[(p - v),(p - v)] is set
{(p - v),(p - v)} is non empty set
{(p - v)} is non empty set
{{(p - v),(p - v)},{(p - v)}} is non empty set
the of seq . [(p - v),(p - v)] is complex set
|.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(p - v),(p - v)).| is complex V34() ext-real Element of REAL
(p - m) - v is right_complementable Element of the carrier of seq
(p - m) + (- v) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(- v)) is right_complementable Element of the carrier of seq
[(p - m),(- v)] is set
{(p - m),(- v)} is non empty set
{{(p - m),(- v)},{(p - m)}} is non empty set
the addF of seq . [(p - m),(- v)] is set
((p - m) - v) + m is right_complementable Element of the carrier of seq
the addF of seq . (((p - m) - v),m) is right_complementable Element of the carrier of seq
[((p - m) - v),m] is set
{((p - m) - v),m} is non empty set
{((p - m) - v)} is non empty set
{{((p - m) - v),m},{((p - m) - v)}} is non empty set
the addF of seq . [((p - m) - v),m] is set
(seq,(((p - m) - v) + m)) is complex V34() ext-real Element of REAL
(seq,(((p - m) - v) + m),(((p - m) - v) + m)) is complex set
the of seq . ((((p - m) - v) + m),(((p - m) - v) + m)) is complex Element of COMPLEX
[(((p - m) - v) + m),(((p - m) - v) + m)] is set
{(((p - m) - v) + m),(((p - m) - v) + m)} is non empty set
{(((p - m) - v) + m)} is non empty set
{{(((p - m) - v) + m),(((p - m) - v) + m)},{(((p - m) - v) + m)}} is non empty set
the of seq . [(((p - m) - v) + m),(((p - m) - v) + m)] is complex set
|.(seq,(((p - m) - v) + m),(((p - m) - v) + m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(((p - m) - v) + m),(((p - m) - v) + m)).| is complex V34() ext-real Element of REAL
v + m is right_complementable Element of the carrier of seq
the addF of seq . (v,m) is right_complementable Element of the carrier of seq
[v,m] is set
{v,m} is non empty set
{{v,m},{v}} is non empty set
the addF of seq . [v,m] is set
p - (v + m) is right_complementable Element of the carrier of seq
- (v + m) is right_complementable Element of the carrier of seq
p + (- (v + m)) is right_complementable Element of the carrier of seq
the addF of seq . (p,(- (v + m))) is right_complementable Element of the carrier of seq
[p,(- (v + m))] is set
{p,(- (v + m))} is non empty set
{{p,(- (v + m))},{p}} is non empty set
the addF of seq . [p,(- (v + m))] is set
(p - (v + m)) + m is right_complementable Element of the carrier of seq
the addF of seq . ((p - (v + m)),m) is right_complementable Element of the carrier of seq
[(p - (v + m)),m] is set
{(p - (v + m)),m} is non empty set
{(p - (v + m))} is non empty set
{{(p - (v + m)),m},{(p - (v + m))}} is non empty set
the addF of seq . [(p - (v + m)),m] is set
(seq,((p - (v + m)) + m)) is complex V34() ext-real Element of REAL
(seq,((p - (v + m)) + m),((p - (v + m)) + m)) is complex set
the of seq . (((p - (v + m)) + m),((p - (v + m)) + m)) is complex Element of COMPLEX
[((p - (v + m)) + m),((p - (v + m)) + m)] is set
{((p - (v + m)) + m),((p - (v + m)) + m)} is non empty set
{((p - (v + m)) + m)} is non empty set
{{((p - (v + m)) + m),((p - (v + m)) + m)},{((p - (v + m)) + m)}} is non empty set
the of seq . [((p - (v + m)) + m),((p - (v + m)) + m)] is complex set
|.(seq,((p - (v + m)) + m),((p - (v + m)) + m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - (v + m)) + m),((p - (v + m)) + m)).| is complex V34() ext-real Element of REAL
(p - v) - m is right_complementable Element of the carrier of seq
(p - v) + (- m) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(- m)) is right_complementable Element of the carrier of seq
[(p - v),(- m)] is set
{(p - v),(- m)} is non empty set
{{(p - v),(- m)},{(p - v)}} is non empty set
the addF of seq . [(p - v),(- m)] is set
((p - v) - m) + m is right_complementable Element of the carrier of seq
the addF of seq . (((p - v) - m),m) is right_complementable Element of the carrier of seq
[((p - v) - m),m] is set
{((p - v) - m),m} is non empty set
{((p - v) - m)} is non empty set
{{((p - v) - m),m},{((p - v) - m)}} is non empty set
the addF of seq . [((p - v) - m),m] is set
(seq,(((p - v) - m) + m)) is complex V34() ext-real Element of REAL
(seq,(((p - v) - m) + m),(((p - v) - m) + m)) is complex set
the of seq . ((((p - v) - m) + m),(((p - v) - m) + m)) is complex Element of COMPLEX
[(((p - v) - m) + m),(((p - v) - m) + m)] is set
{(((p - v) - m) + m),(((p - v) - m) + m)} is non empty set
{(((p - v) - m) + m)} is non empty set
{{(((p - v) - m) + m),(((p - v) - m) + m)},{(((p - v) - m) + m)}} is non empty set
the of seq . [(((p - v) - m) + m),(((p - v) - m) + m)] is complex set
|.(seq,(((p - v) - m) + m),(((p - v) - m) + m)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(((p - v) - m) + m),(((p - v) - m) + m)).| is complex V34() ext-real Element of REAL
m - m is right_complementable Element of the carrier of seq
m + (- m) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- m)) is right_complementable Element of the carrier of seq
[m,(- m)] is set
{m,(- m)} is non empty set
{m} is non empty set
{{m,(- m)},{m}} is non empty set
the addF of seq . [m,(- m)] is set
(p - v) - (m - m) is right_complementable Element of the carrier of seq
- (m - m) is right_complementable Element of the carrier of seq
(p - v) + (- (m - m)) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(- (m - m))) is right_complementable Element of the carrier of seq
[(p - v),(- (m - m))] is set
{(p - v),(- (m - m))} is non empty set
{{(p - v),(- (m - m))},{(p - v)}} is non empty set
the addF of seq . [(p - v),(- (m - m))] is set
(seq,((p - v) - (m - m))) is complex V34() ext-real Element of REAL
(seq,((p - v) - (m - m)),((p - v) - (m - m))) is complex set
the of seq . (((p - v) - (m - m)),((p - v) - (m - m))) is complex Element of COMPLEX
[((p - v) - (m - m)),((p - v) - (m - m))] is set
{((p - v) - (m - m)),((p - v) - (m - m))} is non empty set
{((p - v) - (m - m))} is non empty set
{{((p - v) - (m - m)),((p - v) - (m - m))},{((p - v) - (m - m))}} is non empty set
the of seq . [((p - v) - (m - m)),((p - v) - (m - m))] is complex set
|.(seq,((p - v) - (m - m)),((p - v) - (m - m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - v) - (m - m)),((p - v) - (m - m))).| is complex V34() ext-real Element of REAL
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
(p - v) - H₁(seq) is right_complementable Element of the carrier of seq
- (0. seq) is right_complementable Element of the carrier of seq
(p - v) + (- (0. seq)) is right_complementable Element of the carrier of seq
the addF of seq . ((p - v),(- (0. seq))) is right_complementable Element of the carrier of seq
[(p - v),(- (0. seq))] is set
{(p - v),(- (0. seq))} is non empty set
{{(p - v),(- (0. seq))},{(p - v)}} is non empty set
the addF of seq . [(p - v),(- (0. seq))] is set
(seq,((p - v) - H₁(seq))) is complex V34() ext-real Element of REAL
(seq,((p - v) - H₁(seq)),((p - v) - H₁(seq))) is complex set
the of seq . (((p - v) - H₁(seq)),((p - v) - H₁(seq))) is complex Element of COMPLEX
[((p - v) - H₁(seq)),((p - v) - H₁(seq))] is set
{((p - v) - H₁(seq)),((p - v) - H₁(seq))} is non empty set
{((p - v) - H₁(seq))} is non empty set
{{((p - v) - H₁(seq)),((p - v) - H₁(seq))},{((p - v) - H₁(seq))}} is non empty set
the of seq . [((p - v) - H₁(seq)),((p - v) - H₁(seq))] is complex set
|.(seq,((p - v) - H₁(seq)),((p - v) - H₁(seq))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - v) - H₁(seq)),((p - v) - H₁(seq))).| is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
p is right_complementable Element of the carrier of seq
m is right_complementable Element of the carrier of seq
p - m is right_complementable Element of the carrier of seq
- m is right_complementable Element of the carrier of seq
p + (- m) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (p,(- m)) is right_complementable Element of the carrier of seq
[p,(- m)] is set
{p,(- m)} is non empty set
{p} is non empty set
{{p,(- m)},{p}} is non empty set
the addF of seq . [p,(- m)] is set
(seq,m,p) is complex V34() ext-real Element of REAL
m - p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m + (- p) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- p)) is right_complementable Element of the carrier of seq
[m,(- p)] is set
{m,(- p)} is non empty set
{m} is non empty set
{{m,(- p)},{m}} is non empty set
the addF of seq . [m,(- p)] is set
(seq,(m - p)) is complex V34() ext-real Element of REAL
(seq,(m - p),(m - p)) is complex set
the of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined COMPLEX -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total V38() Element of bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:]
[:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty V38() set
bool [:[: the carrier of seq, the carrier of seq:],COMPLEX:] is non empty set
the of seq . ((m - p),(m - p)) is complex Element of COMPLEX
[(m - p),(m - p)] is set
{(m - p),(m - p)} is non empty set
{(m - p)} is non empty set
{{(m - p),(m - p)},{(m - p)}} is non empty set
the of seq . [(m - p),(m - p)] is complex set
|.(seq,(m - p),(m - p)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(m - p),(m - p)).| is complex V34() ext-real Element of REAL
v is right_complementable Element of the carrier of seq
v - m is right_complementable Element of the carrier of seq
v + (- m) is right_complementable Element of the carrier of seq
the addF of seq . (v,(- m)) is right_complementable Element of the carrier of seq
[v,(- m)] is set
{v,(- m)} is non empty set
{v} is non empty set
{{v,(- m)},{v}} is non empty set
the addF of seq . [v,(- m)] is set
(seq,(p - m),(v - m)) is complex V34() ext-real Element of REAL
(p - m) - (v - m) is right_complementable Element of the carrier of seq
- (v - m) is right_complementable Element of the carrier of seq
(p - m) + (- (v - m)) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(- (v - m))) is right_complementable Element of the carrier of seq
[(p - m),(- (v - m))] is set
{(p - m),(- (v - m))} is non empty set
{(p - m)} is non empty set
{{(p - m),(- (v - m))},{(p - m)}} is non empty set
the addF of seq . [(p - m),(- (v - m))] is set
(seq,((p - m) - (v - m))) is complex V34() ext-real Element of REAL
(seq,((p - m) - (v - m)),((p - m) - (v - m))) is complex set
the of seq . (((p - m) - (v - m)),((p - m) - (v - m))) is complex Element of COMPLEX
[((p - m) - (v - m)),((p - m) - (v - m))] is set
{((p - m) - (v - m)),((p - m) - (v - m))} is non empty set
{((p - m) - (v - m))} is non empty set
{{((p - m) - (v - m)),((p - m) - (v - m))},{((p - m) - (v - m))}} is non empty set
the of seq . [((p - m) - (v - m)),((p - m) - (v - m))] is complex set
|.(seq,((p - m) - (v - m)),((p - m) - (v - m))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - m) - (v - m)),((p - m) - (v - m))).| is complex V34() ext-real Element of REAL
(seq,m,v) is complex V34() ext-real Element of REAL
m - v is right_complementable Element of the carrier of seq
- v is right_complementable Element of the carrier of seq
m + (- v) is right_complementable Element of the carrier of seq
the addF of seq . (m,(- v)) is right_complementable Element of the carrier of seq
[m,(- v)] is set
{m,(- v)} is non empty set
{{m,(- v)},{m}} is non empty set
the addF of seq . [m,(- v)] is set
(seq,(m - v)) is complex V34() ext-real Element of REAL
(seq,(m - v),(m - v)) is complex set
the of seq . ((m - v),(m - v)) is complex Element of COMPLEX
[(m - v),(m - v)] is set
{(m - v),(m - v)} is non empty set
{(m - v)} is non empty set
{{(m - v),(m - v)},{(m - v)}} is non empty set
the of seq . [(m - v),(m - v)] is complex set
|.(seq,(m - v),(m - v)).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(m - v),(m - v)).| is complex V34() ext-real Element of REAL
(seq,m,p) + (seq,m,v) is complex V34() ext-real Element of REAL
(p - m) + (m - v) is right_complementable Element of the carrier of seq
the addF of seq . ((p - m),(m - v)) is right_complementable Element of the carrier of seq
[(p - m),(m - v)] is set
{(p - m),(m - v)} is non empty set
{{(p - m),(m - v)},{(p - m)}} is non empty set
the addF of seq . [(p - m),(m - v)] is set
(seq,((p - m) + (m - v))) is complex V34() ext-real Element of REAL
(seq,((p - m) + (m - v)),((p - m) + (m - v))) is complex set
the of seq . (((p - m) + (m - v)),((p - m) + (m - v))) is complex Element of COMPLEX
[((p - m) + (m - v)),((p - m) + (m - v))] is set
{((p - m) + (m - v)),((p - m) + (m - v))} is non empty set
{((p - m) + (m - v))} is non empty set
{{((p - m) + (m - v)),((p - m) + (m - v))},{((p - m) + (m - v))}} is non empty set
the of seq . [((p - m) + (m - v)),((p - m) + (m - v))] is complex set
|.(seq,((p - m) + (m - v)),((p - m) + (m - v))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((p - m) + (m - v)),((p - m) + (m - v))).| is complex V34() ext-real Element of REAL
- (m - p) is right_complementable Element of the carrier of seq
(- (m - p)) + (m - v) is right_complementable Element of the carrier of seq
the addF of seq . ((- (m - p)),(m - v)) is right_complementable Element of the carrier of seq
[(- (m - p)),(m - v)] is set
{(- (m - p)),(m - v)} is non empty set
{(- (m - p))} is non empty set
{{(- (m - p)),(m - v)},{(- (m - p))}} is non empty set
the addF of seq . [(- (m - p)),(m - v)] is set
(seq,((- (m - p)) + (m - v))) is complex V34() ext-real Element of REAL
(seq,((- (m - p)) + (m - v)),((- (m - p)) + (m - v))) is complex set
the of seq . (((- (m - p)) + (m - v)),((- (m - p)) + (m - v))) is complex Element of COMPLEX
[((- (m - p)) + (m - v)),((- (m - p)) + (m - v))] is set
{((- (m - p)) + (m - v)),((- (m - p)) + (m - v))} is non empty set
{((- (m - p)) + (m - v))} is non empty set
{{((- (m - p)) + (m - v)),((- (m - p)) + (m - v))},{((- (m - p)) + (m - v))}} is non empty set
the of seq . [((- (m - p)) + (m - v)),((- (m - p)) + (m - v))] is complex set
|.(seq,((- (m - p)) + (m - v)),((- (m - p)) + (m - v))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,((- (m - p)) + (m - v)),((- (m - p)) + (m - v))).| is complex V34() ext-real Element of REAL
(seq,(- (m - p))) is complex V34() ext-real Element of REAL
(seq,(- (m - p)),(- (m - p))) is complex set
the of seq . ((- (m - p)),(- (m - p))) is complex Element of COMPLEX
[(- (m - p)),(- (m - p))] is set
{(- (m - p)),(- (m - p))} is non empty set
{{(- (m - p)),(- (m - p))},{(- (m - p))}} is non empty set
the of seq . [(- (m - p)),(- (m - p))] is complex set
|.(seq,(- (m - p)),(- (m - p))).| is complex V34() ext-real Element of REAL
sqrt |.(seq,(- (m - p)),(- (m - p))).| is complex V34() ext-real Element of REAL
(seq,(- (m - p))) + (seq,(m - v)) is complex V34() ext-real Element of REAL
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v + v1 is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 + v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
w1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(v + v1) . w1 is right_complementable Element of the carrier of seq
v1 . w1 is right_complementable Element of the carrier of seq
v . w1 is right_complementable Element of the carrier of seq
(v1 . w1) + (v . w1) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((v1 . w1),(v . w1)) is right_complementable Element of the carrier of seq
[(v1 . w1),(v . w1)] is set
{(v1 . w1),(v . w1)} is non empty set
{(v1 . w1)} is non empty set
{{(v1 . w1),(v . w1)},{(v1 . w1)}} is non empty set
the addF of seq . [(v1 . w1),(v . w1)] is set
(v1 + v) . w1 is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,p,m) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,m,v) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,p,(seq,m,v)) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,(seq,p,m),v) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(seq,p,(seq,m,v)) . v1 is right_complementable Element of the carrier of seq
p . v1 is right_complementable Element of the carrier of seq
(seq,m,v) . v1 is right_complementable Element of the carrier of seq
(p . v1) + ((seq,m,v) . v1) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p . v1),((seq,m,v) . v1)) is right_complementable Element of the carrier of seq
[(p . v1),((seq,m,v) . v1)] is set
{(p . v1),((seq,m,v) . v1)} is non empty set
{(p . v1)} is non empty set
{{(p . v1),((seq,m,v) . v1)},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),((seq,m,v) . v1)] is set
m . v1 is right_complementable Element of the carrier of seq
v . v1 is right_complementable Element of the carrier of seq
(m . v1) + (v . v1) is right_complementable Element of the carrier of seq
the addF of seq . ((m . v1),(v . v1)) is right_complementable Element of the carrier of seq
[(m . v1),(v . v1)] is set
{(m . v1),(v . v1)} is non empty set
{(m . v1)} is non empty set
{{(m . v1),(v . v1)},{(m . v1)}} is non empty set
the addF of seq . [(m . v1),(v . v1)] is set
(p . v1) + ((m . v1) + (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),((m . v1) + (v . v1))) is right_complementable Element of the carrier of seq
[(p . v1),((m . v1) + (v . v1))] is set
{(p . v1),((m . v1) + (v . v1))} is non empty set
{{(p . v1),((m . v1) + (v . v1))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),((m . v1) + (v . v1))] is set
(p . v1) + (m . v1) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),(m . v1)) is right_complementable Element of the carrier of seq
[(p . v1),(m . v1)] is set
{(p . v1),(m . v1)} is non empty set
{{(p . v1),(m . v1)},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(m . v1)] is set
((p . v1) + (m . v1)) + (v . v1) is right_complementable Element of the carrier of seq
the addF of seq . (((p . v1) + (m . v1)),(v . v1)) is right_complementable Element of the carrier of seq
[((p . v1) + (m . v1)),(v . v1)] is set
{((p . v1) + (m . v1)),(v . v1)} is non empty set
{((p . v1) + (m . v1))} is non empty set
{{((p . v1) + (m . v1)),(v . v1)},{((p . v1) + (m . v1))}} is non empty set
the addF of seq . [((p . v1) + (m . v1)),(v . v1)] is set
(seq,p,m) . v1 is right_complementable Element of the carrier of seq
((seq,p,m) . v1) + (v . v1) is right_complementable Element of the carrier of seq
the addF of seq . (((seq,p,m) . v1),(v . v1)) is right_complementable Element of the carrier of seq
[((seq,p,m) . v1),(v . v1)] is set
{((seq,p,m) . v1),(v . v1)} is non empty set
{((seq,p,m) . v1)} is non empty set
{{((seq,p,m) . v1),(v . v1)},{((seq,p,m) . v1)}} is non empty set
the addF of seq . [((seq,p,m) . v1),(v . v1)] is set
(seq,(seq,p,m),v) . v1 is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,p,m) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 is right_complementable Element of the carrier of seq
w1 is right_complementable Element of the carrier of seq
v1 + w1 is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (v1,w1) is right_complementable Element of the carrier of seq
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty set
{{v1,w1},{v1}} is non empty set
the addF of seq . [v1,w1] is set
w is right_complementable Element of the carrier of seq
c₁₁ is V26() V27() V28() V32() complex ext-real set
v . c₁₁ is set
v . c₁₁ is right_complementable Element of the carrier of seq
p . c₁₁ is right_complementable Element of the carrier of seq
m . c₁₁ is right_complementable Element of the carrier of seq
(p . c₁₁) + (m . c₁₁) is right_complementable Element of the carrier of seq
the addF of seq . ((p . c₁₁),(m . c₁₁)) is right_complementable Element of the carrier of seq
[(p . c₁₁),(m . c₁₁)] is set
{(p . c₁₁),(m . c₁₁)} is non empty set
{(p . c₁₁)} is non empty set
{{(p . c₁₁),(m . c₁₁)},{(p . c₁₁)}} is non empty set
the addF of seq . [(p . c₁₁),(m . c₁₁)] is set
v1 + (m . c₁₁) is right_complementable Element of the carrier of seq
the addF of seq . (v1,(m . c₁₁)) is right_complementable Element of the carrier of seq
[v1,(m . c₁₁)] is set
{v1,(m . c₁₁)} is non empty set
{{v1,(m . c₁₁)},{v1}} is non empty set
the addF of seq . [v1,(m . c₁₁)] is set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 is right_complementable Element of the carrier of seq
w1 is right_complementable Element of the carrier of seq
v1 - w1 is right_complementable Element of the carrier of seq
- w1 is right_complementable Element of the carrier of seq
v1 + (- w1) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (v1,(- w1)) is right_complementable Element of the carrier of seq
[v1,(- w1)] is set
{v1,(- w1)} is non empty set
{v1} is non empty set
{{v1,(- w1)},{v1}} is non empty set
the addF of seq . [v1,(- w1)] is set
w is right_complementable Element of the carrier of seq
c₁₁ is V26() V27() V28() V32() complex ext-real set
v . c₁₁ is set
v . c₁₁ is right_complementable Element of the carrier of seq
p . c₁₁ is right_complementable Element of the carrier of seq
m . c₁₁ is right_complementable Element of the carrier of seq
(p . c₁₁) - (m . c₁₁) is right_complementable Element of the carrier of seq
- (m . c₁₁) is right_complementable Element of the carrier of seq
(p . c₁₁) + (- (m . c₁₁)) is right_complementable Element of the carrier of seq
the addF of seq . ((p . c₁₁),(- (m . c₁₁))) is right_complementable Element of the carrier of seq
[(p . c₁₁),(- (m . c₁₁))] is set
{(p . c₁₁),(- (m . c₁₁))} is non empty set
{(p . c₁₁)} is non empty set
{{(p . c₁₁),(- (m . c₁₁))},{(p . c₁₁)}} is non empty set
the addF of seq . [(p . c₁₁),(- (m . c₁₁))] is set
v1 - (m . c₁₁) is right_complementable Element of the carrier of seq
v1 + (- (m . c₁₁)) is right_complementable Element of the carrier of seq
the addF of seq . (v1,(- (m . c₁₁))) is right_complementable Element of the carrier of seq
[v1,(- (m . c₁₁))] is set
{v1,(- (m . c₁₁))} is non empty set
{{v1,(- (m . c₁₁))},{v1}} is non empty set
the addF of seq . [v1,(- (m . c₁₁))] is set
seq is complex set
p is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of p is non empty set
[:NAT, the carrier of p:] is non empty set
bool [:NAT, the carrier of p:] is non empty set
m is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
seq * m is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
v is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
v1 is right_complementable Element of the carrier of p
seq * v1 is right_complementable Element of the carrier of p
the Mult of p is Relation-like [:COMPLEX, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([:COMPLEX, the carrier of p:]) quasi_total Element of bool [:[:COMPLEX, the carrier of p:], the carrier of p:]
[:COMPLEX, the carrier of p:] is non empty set
[:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
bool [:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
[seq,v1] is set
{seq,v1} is non empty set
{seq} is non empty V64() set
{{seq,v1},{seq}} is non empty set
the Mult of p . [seq,v1] is set
w1 is right_complementable Element of the carrier of p
w is V26() V27() V28() V32() complex ext-real set
v . w is set
v . w is right_complementable Element of the carrier of p
m . w is right_complementable Element of the carrier of p
seq * (m . w) is right_complementable Element of the carrier of p
[seq,(m . w)] is set
{seq,(m . w)} is non empty set
{{seq,(m . w)},{seq}} is non empty set
the Mult of p . [seq,(m . w)] is set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
- m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,p,(- m)) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(p - m) . v is right_complementable Element of the carrier of seq
p . v is right_complementable Element of the carrier of seq
m . v is right_complementable Element of the carrier of seq
(p . v) - (m . v) is right_complementable Element of the carrier of seq
- (m . v) is right_complementable Element of the carrier of seq
(p . v) + (- (m . v)) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p . v),(- (m . v))) is right_complementable Element of the carrier of seq
[(p . v),(- (m . v))] is set
{(p . v),(- (m . v))} is non empty set
{(p . v)} is non empty set
{{(p . v),(- (m . v))},{(p . v)}} is non empty set
the addF of seq . [(p . v),(- (m . v))] is set
(- m) . v is right_complementable Element of the carrier of seq
(p . v) + ((- m) . v) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v),((- m) . v)) is right_complementable Element of the carrier of seq
[(p . v),((- m) . v)] is set
{(p . v),((- m) . v)} is non empty set
{{(p . v),((- m) . v)},{(p . v)}} is non empty set
the addF of seq . [(p . v),((- m) . v)] is set
(seq,p,(- m)) . v is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p + (0. seq) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p + H₁(seq) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(p + H₁(seq)) . m is right_complementable Element of the carrier of seq
p . m is right_complementable Element of the carrier of seq
(p . m) + H₁(seq) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p . m),(0. seq)) is right_complementable Element of the carrier of seq
[(p . m),(0. seq)] is set
{(p . m),(0. seq)} is non empty set
{(p . m)} is non empty set
{{(p . m),(0. seq)},{(p . m)}} is non empty set
the addF of seq . [(p . m),(0. seq)] is set
seq is complex set
p is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of p is non empty set
[:NAT, the carrier of p:] is non empty set
bool [:NAT, the carrier of p:] is non empty set
m is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
seq * m is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
v is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
(p,m,v) is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
seq * (p,m,v) is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
seq * v is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
(p,(seq * m),(seq * v)) is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(seq * (p,m,v)) . v1 is right_complementable Element of the carrier of p
(p,m,v) . v1 is right_complementable Element of the carrier of p
seq * ((p,m,v) . v1) is right_complementable Element of the carrier of p
the Mult of p is Relation-like [:COMPLEX, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([:COMPLEX, the carrier of p:]) quasi_total Element of bool [:[:COMPLEX, the carrier of p:], the carrier of p:]
[:COMPLEX, the carrier of p:] is non empty set
[:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
bool [:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
[seq,((p,m,v) . v1)] is set
{seq,((p,m,v) . v1)} is non empty set
{seq} is non empty V64() set
{{seq,((p,m,v) . v1)},{seq}} is non empty set
the Mult of p . [seq,((p,m,v) . v1)] is set
m . v1 is right_complementable Element of the carrier of p
v . v1 is right_complementable Element of the carrier of p
(m . v1) + (v . v1) is right_complementable Element of the carrier of p
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([: the carrier of p, the carrier of p:]) quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the addF of p . ((m . v1),(v . v1)) is right_complementable Element of the carrier of p
[(m . v1),(v . v1)] is set
{(m . v1),(v . v1)} is non empty set
{(m . v1)} is non empty set
{{(m . v1),(v . v1)},{(m . v1)}} is non empty set
the addF of p . [(m . v1),(v . v1)] is set
seq * ((m . v1) + (v . v1)) is right_complementable Element of the carrier of p
[seq,((m . v1) + (v . v1))] is set
{seq,((m . v1) + (v . v1))} is non empty set
{{seq,((m . v1) + (v . v1))},{seq}} is non empty set
the Mult of p . [seq,((m . v1) + (v . v1))] is set
seq * (m . v1) is right_complementable Element of the carrier of p
[seq,(m . v1)] is set
{seq,(m . v1)} is non empty set
{{seq,(m . v1)},{seq}} is non empty set
the Mult of p . [seq,(m . v1)] is set
seq * (v . v1) is right_complementable Element of the carrier of p
[seq,(v . v1)] is set
{seq,(v . v1)} is non empty set
{{seq,(v . v1)},{seq}} is non empty set
the Mult of p . [seq,(v . v1)] is set
(seq * (m . v1)) + (seq * (v . v1)) is right_complementable Element of the carrier of p
the addF of p . ((seq * (m . v1)),(seq * (v . v1))) is right_complementable Element of the carrier of p
[(seq * (m . v1)),(seq * (v . v1))] is set
{(seq * (m . v1)),(seq * (v . v1))} is non empty set
{(seq * (m . v1))} is non empty set
{{(seq * (m . v1)),(seq * (v . v1))},{(seq * (m . v1))}} is non empty set
the addF of p . [(seq * (m . v1)),(seq * (v . v1))] is set
(seq * m) . v1 is right_complementable Element of the carrier of p
((seq * m) . v1) + (seq * (v . v1)) is right_complementable Element of the carrier of p
the addF of p . (((seq * m) . v1),(seq * (v . v1))) is right_complementable Element of the carrier of p
[((seq * m) . v1),(seq * (v . v1))] is set
{((seq * m) . v1),(seq * (v . v1))} is non empty set
{((seq * m) . v1)} is non empty set
{{((seq * m) . v1),(seq * (v . v1))},{((seq * m) . v1)}} is non empty set
the addF of p . [((seq * m) . v1),(seq * (v . v1))] is set
(seq * v) . v1 is right_complementable Element of the carrier of p
((seq * m) . v1) + ((seq * v) . v1) is right_complementable Element of the carrier of p
the addF of p . (((seq * m) . v1),((seq * v) . v1)) is right_complementable Element of the carrier of p
[((seq * m) . v1),((seq * v) . v1)] is set
{((seq * m) . v1),((seq * v) . v1)} is non empty set
{{((seq * m) . v1),((seq * v) . v1)},{((seq * m) . v1)}} is non empty set
the addF of p . [((seq * m) . v1),((seq * v) . v1)] is set
(p,(seq * m),(seq * v)) . v1 is right_complementable Element of the carrier of p
seq is complex set
p is complex set
seq + p is complex set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of m is non empty set
[:NAT, the carrier of m:] is non empty set
bool [:NAT, the carrier of m:] is non empty set
v is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
(seq + p) * v is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
seq * v is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
p * v is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
(m,(seq * v),(p * v)) is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
((seq + p) * v) . v1 is right_complementable Element of the carrier of m
v . v1 is right_complementable Element of the carrier of m
(seq + p) * (v . v1) is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[(seq + p),(v . v1)] is set
{(seq + p),(v . v1)} is non empty set
{(seq + p)} is non empty V64() set
{{(seq + p),(v . v1)},{(seq + p)}} is non empty set
the Mult of m . [(seq + p),(v . v1)] is set
seq * (v . v1) is right_complementable Element of the carrier of m
[seq,(v . v1)] is set
{seq,(v . v1)} is non empty set
{seq} is non empty V64() set
{{seq,(v . v1)},{seq}} is non empty set
the Mult of m . [seq,(v . v1)] is set
p * (v . v1) is right_complementable Element of the carrier of m
[p,(v . v1)] is set
{p,(v . v1)} is non empty set
{p} is non empty V64() set
{{p,(v . v1)},{p}} is non empty set
the Mult of m . [p,(v . v1)] is set
(seq * (v . v1)) + (p * (v . v1)) is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . ((seq * (v . v1)),(p * (v . v1))) is right_complementable Element of the carrier of m
[(seq * (v . v1)),(p * (v . v1))] is set
{(seq * (v . v1)),(p * (v . v1))} is non empty set
{(seq * (v . v1))} is non empty set
{{(seq * (v . v1)),(p * (v . v1))},{(seq * (v . v1))}} is non empty set
the addF of m . [(seq * (v . v1)),(p * (v . v1))] is set
(seq * v) . v1 is right_complementable Element of the carrier of m
((seq * v) . v1) + (p * (v . v1)) is right_complementable Element of the carrier of m
the addF of m . (((seq * v) . v1),(p * (v . v1))) is right_complementable Element of the carrier of m
[((seq * v) . v1),(p * (v . v1))] is set
{((seq * v) . v1),(p * (v . v1))} is non empty set
{((seq * v) . v1)} is non empty set
{{((seq * v) . v1),(p * (v . v1))},{((seq * v) . v1)}} is non empty set
the addF of m . [((seq * v) . v1),(p * (v . v1))] is set
(p * v) . v1 is right_complementable Element of the carrier of m
((seq * v) . v1) + ((p * v) . v1) is right_complementable Element of the carrier of m
the addF of m . (((seq * v) . v1),((p * v) . v1)) is right_complementable Element of the carrier of m
[((seq * v) . v1),((p * v) . v1)] is set
{((seq * v) . v1),((p * v) . v1)} is non empty set
{{((seq * v) . v1),((p * v) . v1)},{((seq * v) . v1)}} is non empty set
the addF of m . [((seq * v) . v1),((p * v) . v1)] is set
(m,(seq * v),(p * v)) . v1 is right_complementable Element of the carrier of m
seq is complex set
p is complex set
seq * p is complex set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of m is non empty set
[:NAT, the carrier of m:] is non empty set
bool [:NAT, the carrier of m:] is non empty set
v is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
(seq * p) * v is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
p * v is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
seq * (p * v) is Relation-like NAT -defined the carrier of m -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of m:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
((seq * p) * v) . v1 is right_complementable Element of the carrier of m
v . v1 is right_complementable Element of the carrier of m
(seq * p) * (v . v1) is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[(seq * p),(v . v1)] is set
{(seq * p),(v . v1)} is non empty set
{(seq * p)} is non empty V64() set
{{(seq * p),(v . v1)},{(seq * p)}} is non empty set
the Mult of m . [(seq * p),(v . v1)] is set
p * (v . v1) is right_complementable Element of the carrier of m
[p,(v . v1)] is set
{p,(v . v1)} is non empty set
{p} is non empty V64() set
{{p,(v . v1)},{p}} is non empty set
the Mult of m . [p,(v . v1)] is set
seq * (p * (v . v1)) is right_complementable Element of the carrier of m
[seq,(p * (v . v1))] is set
{seq,(p * (v . v1))} is non empty set
{seq} is non empty V64() set
{{seq,(p * (v . v1))},{seq}} is non empty set
the Mult of m . [seq,(p * (v . v1))] is set
(p * v) . v1 is right_complementable Element of the carrier of m
seq * ((p * v) . v1) is right_complementable Element of the carrier of m
[seq,((p * v) . v1)] is set
{seq,((p * v) . v1)} is non empty set
{{seq,((p * v) . v1)},{seq}} is non empty set
the Mult of m . [seq,((p * v) . v1)] is set
(seq * (p * v)) . v1 is right_complementable Element of the carrier of m
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
1r * p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(1r * p) . m is right_complementable Element of the carrier of seq
p . m is right_complementable Element of the carrier of seq
1r * (p . m) is right_complementable Element of the carrier of seq
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([:COMPLEX, the carrier of seq:]) quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is non empty set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
[1r,(p . m)] is set
{1r,(p . m)} is non empty set
{1r} is non empty V64() set
{{1r,(p . m)},{1r}} is non empty set
the Mult of seq . [1r,(p . m)] is set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(- 1r) * p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
- p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
((- 1r) * p) . m is right_complementable Element of the carrier of seq
p . m is right_complementable Element of the carrier of seq
(- 1r) * (p . m) is right_complementable Element of the carrier of seq
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([:COMPLEX, the carrier of seq:]) quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is non empty set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
[(- 1r),(p . m)] is set
{(- 1r),(p . m)} is non empty set
{(- 1r)} is non empty V64() set
{{(- 1r),(p . m)},{(- 1r)}} is non empty set
the Mult of seq . [(- 1r),(p . m)] is set
- (p . m) is right_complementable Element of the carrier of seq
(- p) . m is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is right_complementable Element of the carrier of seq
- p is right_complementable Element of the carrier of seq
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m - p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m + (- p) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(m - p) . v is right_complementable Element of the carrier of seq
m . v is right_complementable Element of the carrier of seq
(m . v) - p is right_complementable Element of the carrier of seq
(m . v) + (- p) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((m . v),(- p)) is right_complementable Element of the carrier of seq
[(m . v),(- p)] is set
{(m . v),(- p)} is non empty set
{(m . v)} is non empty set
{{(m . v),(- p)},{(m . v)}} is non empty set
the addF of seq . [(m . v),(- p)] is set
(m + (- p)) . v is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m - p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
- (m - p) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(p - m) . v is right_complementable Element of the carrier of seq
p . v is right_complementable Element of the carrier of seq
m . v is right_complementable Element of the carrier of seq
(p . v) - (m . v) is right_complementable Element of the carrier of seq
- (m . v) is right_complementable Element of the carrier of seq
(p . v) + (- (m . v)) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p . v),(- (m . v))) is right_complementable Element of the carrier of seq
[(p . v),(- (m . v))] is set
{(p . v),(- (m . v))} is non empty set
{(p . v)} is non empty set
{{(p . v),(- (m . v))},{(p . v)}} is non empty set
the addF of seq . [(p . v),(- (m . v))] is set
(m . v) - (p . v) is right_complementable Element of the carrier of seq
- (p . v) is right_complementable Element of the carrier of seq
(m . v) + (- (p . v)) is right_complementable Element of the carrier of seq
the addF of seq . ((m . v),(- (p . v))) is right_complementable Element of the carrier of seq
[(m . v),(- (p . v))] is set
{(m . v),(- (p . v))} is non empty set
{(m . v)} is non empty set
{{(m . v),(- (p . v))},{(m . v)}} is non empty set
the addF of seq . [(m . v),(- (p . v))] is set
- ((m . v) - (p . v)) is right_complementable Element of the carrier of seq
(m - p) . v is right_complementable Element of the carrier of seq
- ((m - p) . v) is right_complementable Element of the carrier of seq
(- (m - p)) . v is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
0. seq is zero right_complementable Element of the carrier of seq
the ZeroF of seq is right_complementable Element of the carrier of seq
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - (0. seq) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - H₁(seq) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(p - H₁(seq)) . m is right_complementable Element of the carrier of seq
p . m is right_complementable Element of the carrier of seq
(p . m) - H₁(seq) is right_complementable Element of the carrier of seq
- (0. seq) is right_complementable Element of the carrier of seq
(p . m) + (- (0. seq)) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p . m),(- (0. seq))) is right_complementable Element of the carrier of seq
[(p . m),(- (0. seq))] is set
{(p . m),(- (0. seq))} is non empty set
{(p . m)} is non empty set
{{(p . m),(- (0. seq))},{(p . m)}} is non empty set
the addF of seq . [(p . m),(- (0. seq))] is set
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
- p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
- (- p) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(- (- p)) . m is right_complementable Element of the carrier of seq
(- p) . m is right_complementable Element of the carrier of seq
- ((- p) . m) is right_complementable Element of the carrier of seq
p . m is right_complementable Element of the carrier of seq
- (p . m) is right_complementable Element of the carrier of seq
- (- (p . m)) is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,m,v) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - (seq,m,v) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(p - m) - v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(p - (seq,m,v)) . v1 is right_complementable Element of the carrier of seq
p . v1 is right_complementable Element of the carrier of seq
(seq,m,v) . v1 is right_complementable Element of the carrier of seq
(p . v1) - ((seq,m,v) . v1) is right_complementable Element of the carrier of seq
- ((seq,m,v) . v1) is right_complementable Element of the carrier of seq
(p . v1) + (- ((seq,m,v) . v1)) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p . v1),(- ((seq,m,v) . v1))) is right_complementable Element of the carrier of seq
[(p . v1),(- ((seq,m,v) . v1))] is set
{(p . v1),(- ((seq,m,v) . v1))} is non empty set
{(p . v1)} is non empty set
{{(p . v1),(- ((seq,m,v) . v1))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(- ((seq,m,v) . v1))] is set
m . v1 is right_complementable Element of the carrier of seq
v . v1 is right_complementable Element of the carrier of seq
(m . v1) + (v . v1) is right_complementable Element of the carrier of seq
the addF of seq . ((m . v1),(v . v1)) is right_complementable Element of the carrier of seq
[(m . v1),(v . v1)] is set
{(m . v1),(v . v1)} is non empty set
{(m . v1)} is non empty set
{{(m . v1),(v . v1)},{(m . v1)}} is non empty set
the addF of seq . [(m . v1),(v . v1)] is set
(p . v1) - ((m . v1) + (v . v1)) is right_complementable Element of the carrier of seq
- ((m . v1) + (v . v1)) is right_complementable Element of the carrier of seq
(p . v1) + (- ((m . v1) + (v . v1))) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),(- ((m . v1) + (v . v1)))) is right_complementable Element of the carrier of seq
[(p . v1),(- ((m . v1) + (v . v1)))] is set
{(p . v1),(- ((m . v1) + (v . v1)))} is non empty set
{{(p . v1),(- ((m . v1) + (v . v1)))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(- ((m . v1) + (v . v1)))] is set
(p . v1) - (m . v1) is right_complementable Element of the carrier of seq
- (m . v1) is right_complementable Element of the carrier of seq
(p . v1) + (- (m . v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),(- (m . v1))) is right_complementable Element of the carrier of seq
[(p . v1),(- (m . v1))] is set
{(p . v1),(- (m . v1))} is non empty set
{{(p . v1),(- (m . v1))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(- (m . v1))] is set
((p . v1) - (m . v1)) - (v . v1) is right_complementable Element of the carrier of seq
- (v . v1) is right_complementable Element of the carrier of seq
((p . v1) - (m . v1)) + (- (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq . (((p . v1) - (m . v1)),(- (v . v1))) is right_complementable Element of the carrier of seq
[((p . v1) - (m . v1)),(- (v . v1))] is set
{((p . v1) - (m . v1)),(- (v . v1))} is non empty set
{((p . v1) - (m . v1))} is non empty set
{{((p . v1) - (m . v1)),(- (v . v1))},{((p . v1) - (m . v1))}} is non empty set
the addF of seq . [((p . v1) - (m . v1)),(- (v . v1))] is set
(p - m) . v1 is right_complementable Element of the carrier of seq
((p - m) . v1) - (v . v1) is right_complementable Element of the carrier of seq
((p - m) . v1) + (- (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq . (((p - m) . v1),(- (v . v1))) is right_complementable Element of the carrier of seq
[((p - m) . v1),(- (v . v1))] is set
{((p - m) . v1),(- (v . v1))} is non empty set
{((p - m) . v1)} is non empty set
{{((p - m) . v1),(- (v . v1))},{((p - m) . v1)}} is non empty set
the addF of seq . [((p - m) . v1),(- (v . v1))] is set
((p - m) - v) . v1 is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,p,m) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,p,m) - v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m - v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,p,(m - v)) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
((seq,p,m) - v) . v1 is right_complementable Element of the carrier of seq
(seq,p,m) . v1 is right_complementable Element of the carrier of seq
v . v1 is right_complementable Element of the carrier of seq
((seq,p,m) . v1) - (v . v1) is right_complementable Element of the carrier of seq
- (v . v1) is right_complementable Element of the carrier of seq
((seq,p,m) . v1) + (- (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . (((seq,p,m) . v1),(- (v . v1))) is right_complementable Element of the carrier of seq
[((seq,p,m) . v1),(- (v . v1))] is set
{((seq,p,m) . v1),(- (v . v1))} is non empty set
{((seq,p,m) . v1)} is non empty set
{{((seq,p,m) . v1),(- (v . v1))},{((seq,p,m) . v1)}} is non empty set
the addF of seq . [((seq,p,m) . v1),(- (v . v1))] is set
p . v1 is right_complementable Element of the carrier of seq
m . v1 is right_complementable Element of the carrier of seq
(p . v1) + (m . v1) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),(m . v1)) is right_complementable Element of the carrier of seq
[(p . v1),(m . v1)] is set
{(p . v1),(m . v1)} is non empty set
{(p . v1)} is non empty set
{{(p . v1),(m . v1)},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(m . v1)] is set
((p . v1) + (m . v1)) - (v . v1) is right_complementable Element of the carrier of seq
((p . v1) + (m . v1)) + (- (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq . (((p . v1) + (m . v1)),(- (v . v1))) is right_complementable Element of the carrier of seq
[((p . v1) + (m . v1)),(- (v . v1))] is set
{((p . v1) + (m . v1)),(- (v . v1))} is non empty set
{((p . v1) + (m . v1))} is non empty set
{{((p . v1) + (m . v1)),(- (v . v1))},{((p . v1) + (m . v1))}} is non empty set
the addF of seq . [((p . v1) + (m . v1)),(- (v . v1))] is set
(m . v1) - (v . v1) is right_complementable Element of the carrier of seq
(m . v1) + (- (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((m . v1),(- (v . v1))) is right_complementable Element of the carrier of seq
[(m . v1),(- (v . v1))] is set
{(m . v1),(- (v . v1))} is non empty set
{(m . v1)} is non empty set
{{(m . v1),(- (v . v1))},{(m . v1)}} is non empty set
the addF of seq . [(m . v1),(- (v . v1))] is set
(p . v1) + ((m . v1) - (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),((m . v1) - (v . v1))) is right_complementable Element of the carrier of seq
[(p . v1),((m . v1) - (v . v1))] is set
{(p . v1),((m . v1) - (v . v1))} is non empty set
{{(p . v1),((m . v1) - (v . v1))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),((m . v1) - (v . v1))] is set
(m - v) . v1 is right_complementable Element of the carrier of seq
(p . v1) + ((m - v) . v1) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),((m - v) . v1)) is right_complementable Element of the carrier of seq
[(p . v1),((m - v) . v1)] is set
{(p . v1),((m - v) . v1)} is non empty set
{{(p . v1),((m - v) . v1)},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),((m - v) . v1)] is set
(seq,p,(m - v)) . v1 is right_complementable Element of the carrier of seq
seq is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of seq is non empty set
[:NAT, the carrier of seq:] is non empty set
bool [:NAT, the carrier of seq:] is non empty set
p is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - m is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
m - v is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
p - (m - v) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
(seq,(p - m),v) is Relation-like NAT -defined the carrier of seq -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of seq:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(p - (m - v)) . v1 is right_complementable Element of the carrier of seq
p . v1 is right_complementable Element of the carrier of seq
(m - v) . v1 is right_complementable Element of the carrier of seq
(p . v1) - ((m - v) . v1) is right_complementable Element of the carrier of seq
- ((m - v) . v1) is right_complementable Element of the carrier of seq
(p . v1) + (- ((m - v) . v1)) is right_complementable Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like non empty V14([: the carrier of seq, the carrier of seq:]) quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is non empty set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the addF of seq . ((p . v1),(- ((m - v) . v1))) is right_complementable Element of the carrier of seq
[(p . v1),(- ((m - v) . v1))] is set
{(p . v1),(- ((m - v) . v1))} is non empty set
{(p . v1)} is non empty set
{{(p . v1),(- ((m - v) . v1))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(- ((m - v) . v1))] is set
m . v1 is right_complementable Element of the carrier of seq
v . v1 is right_complementable Element of the carrier of seq
(m . v1) - (v . v1) is right_complementable Element of the carrier of seq
- (v . v1) is right_complementable Element of the carrier of seq
(m . v1) + (- (v . v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((m . v1),(- (v . v1))) is right_complementable Element of the carrier of seq
[(m . v1),(- (v . v1))] is set
{(m . v1),(- (v . v1))} is non empty set
{(m . v1)} is non empty set
{{(m . v1),(- (v . v1))},{(m . v1)}} is non empty set
the addF of seq . [(m . v1),(- (v . v1))] is set
(p . v1) - ((m . v1) - (v . v1)) is right_complementable Element of the carrier of seq
- ((m . v1) - (v . v1)) is right_complementable Element of the carrier of seq
(p . v1) + (- ((m . v1) - (v . v1))) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),(- ((m . v1) - (v . v1)))) is right_complementable Element of the carrier of seq
[(p . v1),(- ((m . v1) - (v . v1)))] is set
{(p . v1),(- ((m . v1) - (v . v1)))} is non empty set
{{(p . v1),(- ((m . v1) - (v . v1)))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(- ((m . v1) - (v . v1)))] is set
(p . v1) - (m . v1) is right_complementable Element of the carrier of seq
- (m . v1) is right_complementable Element of the carrier of seq
(p . v1) + (- (m . v1)) is right_complementable Element of the carrier of seq
the addF of seq . ((p . v1),(- (m . v1))) is right_complementable Element of the carrier of seq
[(p . v1),(- (m . v1))] is set
{(p . v1),(- (m . v1))} is non empty set
{{(p . v1),(- (m . v1))},{(p . v1)}} is non empty set
the addF of seq . [(p . v1),(- (m . v1))] is set
((p . v1) - (m . v1)) + (v . v1) is right_complementable Element of the carrier of seq
the addF of seq . (((p . v1) - (m . v1)),(v . v1)) is right_complementable Element of the carrier of seq
[((p . v1) - (m . v1)),(v . v1)] is set
{((p . v1) - (m . v1)),(v . v1)} is non empty set
{((p . v1) - (m . v1))} is non empty set
{{((p . v1) - (m . v1)),(v . v1)},{((p . v1) - (m . v1))}} is non empty set
the addF of seq . [((p . v1) - (m . v1)),(v . v1)] is set
(p - m) . v1 is right_complementable Element of the carrier of seq
((p - m) . v1) + (v . v1) is right_complementable Element of the carrier of seq
the addF of seq . (((p - m) . v1),(v . v1)) is right_complementable Element of the carrier of seq
[((p - m) . v1),(v . v1)] is set
{((p - m) . v1),(v . v1)} is non empty set
{((p - m) . v1)} is non empty set
{{((p - m) . v1),(v . v1)},{((p - m) . v1)}} is non empty set
the addF of seq . [((p - m) . v1),(v . v1)] is set
(seq,(p - m),v) . v1 is right_complementable Element of the carrier of seq
seq is complex set
p is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital () ()
the carrier of p is non empty set
[:NAT, the carrier of p:] is non empty set
bool [:NAT, the carrier of p:] is non empty set
m is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
seq * m is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
v is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
m - v is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
seq * (m - v) is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
seq * v is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
(seq * m) - (seq * v) is Relation-like NAT -defined the carrier of p -valued Function-like non empty V14( NAT ) quasi_total Element of bool [:NAT, the carrier of p:]
v1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(seq * (m - v)) . v1 is right_complementable Element of the carrier of p
(m - v) . v1 is right_complementable Element of the carrier of p
seq * ((m - v) . v1) is right_complementable Element of the carrier of p
the Mult of p is Relation-like [:COMPLEX, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([:COMPLEX, the carrier of p:]) quasi_total Element of bool [:[:COMPLEX, the carrier of p:], the carrier of p:]
[:COMPLEX, the carrier of p:] is non empty set
[:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
bool [:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
[seq,((m - v) . v1)] is set
{seq,((m - v) . v1)} is non empty set
{seq} is non empty V64() set
{{seq,((m - v) . v1)},{seq}} is non empty set
the Mult of p . [seq,((m - v) . v1)] is set
m . v1 is right_complementable Element of the carrier of p
v . v1 is right_complementable Element of the carrier of p
(m . v1) - (v . v1) is right_complementable Element of the carrier of p
- (v . v1) is right_complementable Element of the carrier of p
(m . v1) + (- (v . v1)) is right_complementable Element of the carrier of p
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([: the carrier of p, the carrier of p:]) quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the addF of p . ((m . v1),(- (v . v1))) is right_complementable Element of the carrier of p
[(m . v1),(- (v . v1))] is set
{(m . v1),(- (v . v1))} is non empty set
{(m . v1)} is non empty set
{{(m . v1),(- (v . v1))},{(m . v1)}} is non empty set
the addF of p . [(m . v1),(- (v . v1))] is set
seq * ((m . v1) - (v . v1)) is right_complementable Element of the carrier of p
[seq,((m . v1) - (v . v1))] is set
{seq,((m . v1) - (v . v1))} is non empty set
{{seq,((m . v1) - (v . v1))},{seq}} is non empty set
the Mult of p . [seq,((m . v1) - (v . v1))] is set
seq * (m . v1) is right_complementable Element of the carrier of p
[seq,(m . v1)] is set
{seq,(m . v1)} is non empty set
{{seq,(m . v1)},{seq}} is non empty set
the Mult of p . [seq,(m . v1)] is set
seq * (v . v1) is right_complementable Element of the carrier of p
[seq,(v . v1)] is set
{seq,(v . v1)} is non empty set
{{seq,(v . v1)},{seq}} is non empty set
the Mult of p . [seq,(v . v1)] is set
(seq * (m . v1)) - (seq * (v . v1)) is right_complementable Element of the carrier of p
- (seq * (v . v1)) is right_complementable Element of the carrier of p
(seq * (m . v1)) + (- (seq * (v . v1))) is right_complementable Element of the carrier of p
the addF of p . ((seq * (m . v1)),(- (seq * (v . v1)))) is right_complementable Element of the carrier of p
[(seq * (m . v1)),(- (seq * (v . v1)))] is set
{(seq * (m . v1)),(- (seq * (v . v1)))} is non empty set
{(seq * (m . v1))} is non empty set
{{(seq * (m . v1)),(- (seq * (v . v1)))},{(seq * (m . v1))}} is non empty set
the addF of p . [(seq * (m . v1)),(- (seq * (v . v1)))] is set
(seq * m) . v1 is right_complementable Element of the carrier of p
((seq * m) . v1) - (seq * (v . v1)) is right_complementable Element of the carrier of p
((seq * m) . v1) + (- (seq * (v . v1))) is right_complementable Element of the carrier of p
the addF of p . (((seq * m) . v1),(- (seq * (v . v1)))) is right_complementable Element of the carrier of p
[((seq * m) . v1),(- (seq * (v . v1)))] is set
{((seq * m) . v1),(- (seq * (v . v1)))} is non empty set
{((seq * m) . v1)} is non empty set
{{((seq * m) . v1),(- (seq * (v . v1)))},{((seq * m) . v1)}} is non empty set
the addF of p . [((seq * m) . v1),(- (seq * (v . v1)))] is set
(seq * v) . v1 is right_complementable Element of the carrier of p
((seq * m) . v1) - ((seq * v) . v1) is right_complementable Element of the carrier of p
- ((seq * v) . v1) is right_complementable Element of the carrier of p
((seq * m) . v1) + (- ((seq * v) . v1)) is right_complementable Element of the carrier of p
the addF of p . (((seq * m) . v1),(- ((seq * v) . v1))) is right_complementable Element of the carrier of p
[((seq * m) . v1),(- ((seq * v) . v1))] is set
{((seq * m) . v1),(- ((seq * v) . v1))} is non empty set
{{((seq * m) . v1),(- ((seq * v) . v1))},{((seq * m) . v1)}} is non empty set
the addF of p . [((seq * m) . v1),(- ((seq * v) . v1))] is set
((seq * m) - (seq * v)) . v1 is right_complementable Element of the carrier of p
[:[:(),():],COMPLEX:] is V38() set
bool [:[:(),():],COMPLEX:] is non empty set
p is set
m is set
(p) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(m) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(m) *' is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(p) (#) ((m) *') is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
Sum ((p) (#) ((m) *')) is complex Element of COMPLEX
p is Relation-like [:(),():] -defined COMPLEX -valued Function-like V14([:(),():]) quasi_total V38() Element of bool [:[:(),():],COMPLEX:]
p is Relation-like [:(),():] -defined COMPLEX -valued Function-like V14([:(),():]) quasi_total V38() Element of bool [:[:(),():],COMPLEX:]
m is Relation-like [:(),():] -defined COMPLEX -valued Function-like V14([:(),():]) quasi_total V38() Element of bool [:[:(),():],COMPLEX:]
v is set
v1 is set
p . (v,v1) is set
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
p . [v,v1] is complex set
m . (v,v1) is set
m . [v,v1] is complex set
(v) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(v1) is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(v1) *' is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
(v) (#) ((v1) *') is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
Sum ((v) (#) ((v1) *')) is complex Element of COMPLEX
() is Relation-like [:(),():] -defined COMPLEX -valued Function-like V14([:(),():]) quasi_total V38() Element of bool [:[:(),():],COMPLEX:]
((),((),()),((),()),((),()),()) is () ()
() is non empty ()
seq is CLSStruct
the carrier of seq is set
the ZeroF of seq is Element of the carrier of seq
the addF of seq is Relation-like [: the carrier of seq, the carrier of seq:] -defined the carrier of seq -valued Function-like quasi_total Element of bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:]
[: the carrier of seq, the carrier of seq:] is set
[:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is set
bool [:[: the carrier of seq, the carrier of seq:], the carrier of seq:] is non empty set
the Mult of seq is Relation-like [:COMPLEX, the carrier of seq:] -defined the carrier of seq -valued Function-like quasi_total Element of bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:]
[:COMPLEX, the carrier of seq:] is set
[:[:COMPLEX, the carrier of seq:], the carrier of seq:] is set
bool [:[:COMPLEX, the carrier of seq:], the carrier of seq:] is non empty set
CLSStruct(# the carrier of seq, the ZeroF of seq, the addF of seq, the Mult of seq #) is strict CLSStruct
p is non empty CLSStruct
the carrier of p is non empty set
0. p is zero Element of the carrier of p
the ZeroF of p is Element of the carrier of p
the addF of p is Relation-like [: the carrier of p, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([: the carrier of p, the carrier of p:]) quasi_total Element of bool [:[: the carrier of p, the carrier of p:], the carrier of p:]
[: the carrier of p, the carrier of p:] is non empty set
[:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
bool [:[: the carrier of p, the carrier of p:], the carrier of p:] is non empty set
the Mult of p is Relation-like [:COMPLEX, the carrier of p:] -defined the carrier of p -valued Function-like non empty V14([:COMPLEX, the carrier of p:]) quasi_total Element of bool [:[:COMPLEX, the carrier of p:], the carrier of p:]
[:COMPLEX, the carrier of p:] is non empty set
[:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
bool [:[:COMPLEX, the carrier of p:], the carrier of p:] is non empty set
CLSStruct(# the carrier of p,(0. p), the addF of p, the Mult of p #) is non empty strict CLSStruct
v is Element of the carrier of p
v1 is Element of the carrier of p
v + v1 is Element of the carrier of p
the addF of p . (v,v1) is Element of the carrier of p
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
the addF of p . [v,v1] is set
v1 + v is Element of the carrier of p
the addF of p . (v1,v) is Element of the carrier of p
[v1,v] is set
{v1,v} is non empty set
{v1} is non empty set
{{v1,v},{v1}} is non empty set
the addF of p . [v1,v] is set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
w1 is right_complementable Element of the carrier of m
w is right_complementable Element of the carrier of m
w1 + w is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . (w1,w) is right_complementable Element of the carrier of m
[w1,w] is set
{w1,w} is non empty set
{w1} is non empty set
{{w1,w},{w1}} is non empty set
the addF of m . [w1,w] is set
w + w1 is right_complementable Element of the carrier of m
the addF of m . (w,w1) is right_complementable Element of the carrier of m
[w,w1] is set
{w,w1} is non empty set
{w} is non empty set
{{w,w1},{w}} is non empty set
the addF of m . [w,w1] is set
v is Element of the carrier of p
v1 is Element of the carrier of p
v + v1 is Element of the carrier of p
the addF of p . (v,v1) is Element of the carrier of p
[v,v1] is set
{v,v1} is non empty set
{v} is non empty set
{{v,v1},{v}} is non empty set
the addF of p . [v,v1] is set
w1 is Element of the carrier of p
(v + v1) + w1 is Element of the carrier of p
the addF of p . ((v + v1),w1) is Element of the carrier of p
[(v + v1),w1] is set
{(v + v1),w1} is non empty set
{(v + v1)} is non empty set
{{(v + v1),w1},{(v + v1)}} is non empty set
the addF of p . [(v + v1),w1] is set
v1 + w1 is Element of the carrier of p
the addF of p . (v1,w1) is Element of the carrier of p
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty set
{{v1,w1},{v1}} is non empty set
the addF of p . [v1,w1] is set
v + (v1 + w1) is Element of the carrier of p
the addF of p . (v,(v1 + w1)) is Element of the carrier of p
[v,(v1 + w1)] is set
{v,(v1 + w1)} is non empty set
{{v,(v1 + w1)},{v}} is non empty set
the addF of p . [v,(v1 + w1)] is set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
w is right_complementable Element of the carrier of m
c₁₁ is right_complementable Element of the carrier of m
w + c₁₁ is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . (w,c₁₁) is right_complementable Element of the carrier of m
[w,c₁₁] is set
{w,c₁₁} is non empty set
{w} is non empty set
{{w,c₁₁},{w}} is non empty set
the addF of m . [w,c₁₁] is set
w1 is right_complementable Element of the carrier of m
(w + c₁₁) + w1 is right_complementable Element of the carrier of m
the addF of m . ((w + c₁₁),w1) is right_complementable Element of the carrier of m
[(w + c₁₁),w1] is set
{(w + c₁₁),w1} is non empty set
{(w + c₁₁)} is non empty set
{{(w + c₁₁),w1},{(w + c₁₁)}} is non empty set
the addF of m . [(w + c₁₁),w1] is set
c₁₁ + w1 is right_complementable Element of the carrier of m
the addF of m . (c₁₁,w1) is right_complementable Element of the carrier of m
[c₁₁,w1] is set
{c₁₁,w1} is non empty set
{c₁₁} is non empty set
{{c₁₁,w1},{c₁₁}} is non empty set
the addF of m . [c₁₁,w1] is set
w + (c₁₁ + w1) is right_complementable Element of the carrier of m
the addF of m . (w,(c₁₁ + w1)) is right_complementable Element of the carrier of m
[w,(c₁₁ + w1)] is set
{w,(c₁₁ + w1)} is non empty set
{{w,(c₁₁ + w1)},{w}} is non empty set
the addF of m . [w,(c₁₁ + w1)] is set
v is complex set
v1 is Element of the carrier of p
w1 is Element of the carrier of p
v1 + w1 is Element of the carrier of p
the addF of p . (v1,w1) is Element of the carrier of p
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty set
{{v1,w1},{v1}} is non empty set
the addF of p . [v1,w1] is set
v * (v1 + w1) is Element of the carrier of p
[v,(v1 + w1)] is set
{v,(v1 + w1)} is non empty set
{v} is non empty V64() set
{{v,(v1 + w1)},{v}} is non empty set
the Mult of p . [v,(v1 + w1)] is set
v * v1 is Element of the carrier of p
[v,v1] is set
{v,v1} is non empty set
{{v,v1},{v}} is non empty set
the Mult of p . [v,v1] is set
v * w1 is Element of the carrier of p
[v,w1] is set
{v,w1} is non empty set
{{v,w1},{v}} is non empty set
the Mult of p . [v,w1] is set
(v * v1) + (v * w1) is Element of the carrier of p
the addF of p . ((v * v1),(v * w1)) is Element of the carrier of p
[(v * v1),(v * w1)] is set
{(v * v1),(v * w1)} is non empty set
{(v * v1)} is non empty set
{{(v * v1),(v * w1)},{(v * v1)}} is non empty set
the addF of p . [(v * v1),(v * w1)] is set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
w is right_complementable Element of the carrier of m
c₁₁ is right_complementable Element of the carrier of m
w + c₁₁ is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . (w,c₁₁) is right_complementable Element of the carrier of m
[w,c₁₁] is set
{w,c₁₁} is non empty set
{w} is non empty set
{{w,c₁₁},{w}} is non empty set
the addF of m . [w,c₁₁] is set
v * (w + c₁₁) is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[v,(w + c₁₁)] is set
{v,(w + c₁₁)} is non empty set
{{v,(w + c₁₁)},{v}} is non empty set
the Mult of m . [v,(w + c₁₁)] is set
v * w is right_complementable Element of the carrier of m
[v,w] is set
{v,w} is non empty set
{{v,w},{v}} is non empty set
the Mult of m . [v,w] is set
v * c₁₁ is right_complementable Element of the carrier of m
[v,c₁₁] is set
{v,c₁₁} is non empty set
{{v,c₁₁},{v}} is non empty set
the Mult of m . [v,c₁₁] is set
(v * w) + (v * c₁₁) is right_complementable Element of the carrier of m
the addF of m . ((v * w),(v * c₁₁)) is right_complementable Element of the carrier of m
[(v * w),(v * c₁₁)] is set
{(v * w),(v * c₁₁)} is non empty set
{(v * w)} is non empty set
{{(v * w),(v * c₁₁)},{(v * w)}} is non empty set
the addF of m . [(v * w),(v * c₁₁)] is set
v is complex set
v1 is complex set
v + v1 is complex set
w1 is Element of the carrier of p
(v + v1) * w1 is Element of the carrier of p
[(v + v1),w1] is set
{(v + v1),w1} is non empty set
{(v + v1)} is non empty V64() set
{{(v + v1),w1},{(v + v1)}} is non empty set
the Mult of p . [(v + v1),w1] is set
v * w1 is Element of the carrier of p
[v,w1] is set
{v,w1} is non empty set
{v} is non empty V64() set
{{v,w1},{v}} is non empty set
the Mult of p . [v,w1] is set
v1 * w1 is Element of the carrier of p
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty V64() set
{{v1,w1},{v1}} is non empty set
the Mult of p . [v1,w1] is set
(v * w1) + (v1 * w1) is Element of the carrier of p
the addF of p . ((v * w1),(v1 * w1)) is Element of the carrier of p
[(v * w1),(v1 * w1)] is set
{(v * w1),(v1 * w1)} is non empty set
{(v * w1)} is non empty set
{{(v * w1),(v1 * w1)},{(v * w1)}} is non empty set
the addF of p . [(v * w1),(v1 * w1)] is set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
w is right_complementable Element of the carrier of m
(v + v1) * w is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[(v + v1),w] is set
{(v + v1),w} is non empty set
{{(v + v1),w},{(v + v1)}} is non empty set
the Mult of m . [(v + v1),w] is set
v * w is right_complementable Element of the carrier of m
[v,w] is set
{v,w} is non empty set
{{v,w},{v}} is non empty set
the Mult of m . [v,w] is set
v1 * w is right_complementable Element of the carrier of m
[v1,w] is set
{v1,w} is non empty set
{{v1,w},{v1}} is non empty set
the Mult of m . [v1,w] is set
(v * w) + (v1 * w) is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . ((v * w),(v1 * w)) is right_complementable Element of the carrier of m
[(v * w),(v1 * w)] is set
{(v * w),(v1 * w)} is non empty set
{(v * w)} is non empty set
{{(v * w),(v1 * w)},{(v * w)}} is non empty set
the addF of m . [(v * w),(v1 * w)] is set
v is complex set
v1 is complex set
v * v1 is complex set
w1 is Element of the carrier of p
(v * v1) * w1 is Element of the carrier of p
[(v * v1),w1] is set
{(v * v1),w1} is non empty set
{(v * v1)} is non empty V64() set
{{(v * v1),w1},{(v * v1)}} is non empty set
the Mult of p . [(v * v1),w1] is set
v1 * w1 is Element of the carrier of p
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty V64() set
{{v1,w1},{v1}} is non empty set
the Mult of p . [v1,w1] is set
v * (v1 * w1) is Element of the carrier of p
[v,(v1 * w1)] is set
{v,(v1 * w1)} is non empty set
{v} is non empty V64() set
{{v,(v1 * w1)},{v}} is non empty set
the Mult of p . [v,(v1 * w1)] is set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
w is right_complementable Element of the carrier of m
(v * v1) * w is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[(v * v1),w] is set
{(v * v1),w} is non empty set
{{(v * v1),w},{(v * v1)}} is non empty set
the Mult of m . [(v * v1),w] is set
v1 * w is right_complementable Element of the carrier of m
[v1,w] is set
{v1,w} is non empty set
{{v1,w},{v1}} is non empty set
the Mult of m . [v1,w] is set
v * (v1 * w) is right_complementable Element of the carrier of m
[v,(v1 * w)] is set
{v,(v1 * w)} is non empty set
{{v,(v1 * w)},{v}} is non empty set
the Mult of m . [v,(v1 * w)] is set
v is Element of the carrier of p
1r * v is Element of the carrier of p
[1r,v] is set
{1r,v} is non empty set
{1r} is non empty V64() set
{{1r,v},{1r}} is non empty set
the Mult of p . [1r,v] is set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
v1 is right_complementable Element of the carrier of m
1r * v1 is right_complementable Element of the carrier of m
the Mult of m is Relation-like [:COMPLEX, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([:COMPLEX, the carrier of m:]) quasi_total Element of bool [:[:COMPLEX, the carrier of m:], the carrier of m:]
[:COMPLEX, the carrier of m:] is non empty set
[:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
bool [:[:COMPLEX, the carrier of m:], the carrier of m:] is non empty set
[1r,v1] is set
{1r,v1} is non empty set
{{1r,v1},{1r}} is non empty set
the Mult of m . [1r,v1] is set
v is Element of the carrier of p
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
v1 is right_complementable Element of the carrier of m
0. m is zero right_complementable Element of the carrier of m
the ZeroF of m is right_complementable Element of the carrier of m
w1 is right_complementable Element of the carrier of m
v1 + w1 is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . (v1,w1) is right_complementable Element of the carrier of m
[v1,w1] is set
{v1,w1} is non empty set
{v1} is non empty set
{{v1,w1},{v1}} is non empty set
the addF of m . [v1,w1] is set
w is Element of the carrier of p
v + w is Element of the carrier of p
the addF of p . (v,w) is Element of the carrier of p
[v,w] is set
{v,w} is non empty set
{v} is non empty set
{{v,w},{v}} is non empty set
the addF of p . [v,w] is set
v is Element of the carrier of p
v + (0. p) is Element of the carrier of p
the addF of p . (v,(0. p)) is Element of the carrier of p
[v,(0. p)] is set
{v,(0. p)} is non empty set
{v} is non empty set
{{v,(0. p)},{v}} is non empty set
the addF of p . [v,(0. p)] is set
m is non empty right_complementable Abelian add-associative right_zeroed vector-distributive scalar-distributive scalar-associative scalar-unital CLSStruct
the carrier of m is non empty set
v1 is right_complementable Element of the carrier of m
0. m is zero right_complementable Element of the carrier of m
the ZeroF of m is right_complementable Element of the carrier of m
v1 + (0. m) is right_complementable Element of the carrier of m
the addF of m is Relation-like [: the carrier of m, the carrier of m:] -defined the carrier of m -valued Function-like non empty V14([: the carrier of m, the carrier of m:]) quasi_total Element of bool [:[: the carrier of m, the carrier of m:], the carrier of m:]
[: the carrier of m, the carrier of m:] is non empty set
[:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
bool [:[: the carrier of m, the carrier of m:], the carrier of m:] is non empty set
the addF of m . (v1,(0. m)) is right_complementable Element of the carrier of m
[v1,(0. m)] is set
{v1,(0. m)} is non empty set
{v1} is non empty set
{{v1,(0. m)},{v1}} is non empty set
the addF of m . [v1,(0. m)] is set
seq is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
Sum seq is complex Element of COMPLEX
Partial_Sums seq is Relation-like NAT -defined COMPLEX -valued Function-like non empty V14( NAT ) quasi_total V38() Element of bool [:NAT,COMPLEX:]
p is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(Partial_Sums seq) . p is complex Element of COMPLEX
m is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
seq . m is complex Element of COMPLEX
(Partial_Sums seq) . m is complex Element of COMPLEX
m + 1 is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
seq . (m + 1) is complex Element of COMPLEX
(Partial_Sums seq) . (m + 1) is complex Element of COMPLEX
0c + (seq . (m + 1)) is complex Element of COMPLEX
(seq . m) + (seq . (m + 1)) is complex Element of COMPLEX
seq . 0 is complex Element of COMPLEX
(Partial_Sums seq) . 0 is complex Element of COMPLEX
seq . p is complex Element of COMPLEX
p is complex V34() ext-real Element of REAL
m is V26() V27() V28() V32() complex V34() ext-real V50() V63() V64() V65() V66() V67() V68() V69() Element of NAT
(Partial_Sums seq) . m is complex Element of COMPLEX
((Partial_Sums seq) . m) - 0c is complex Element of COMPLEX
|.(((Partial_Sums seq) . m) - 0c).| is complex V34() ext-real Element of REAL
lim (Partial_Sums seq) is complex Element of COMPLEX