:: VALUED_2 semantic presentation

REAL is non empty complex-membered ext-real-membered real-membered V59() V60() set
K235() is set
{} is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V37() complex-valued ext-real-valued real-valued natural-valued real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V59() V60() FinSequence-like FinSubsequence-like FinSequence-membered set
NAT is non empty epsilon-transitive epsilon-connected ordinal complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V59() Element of K19(REAL)
K19(REAL) is set
RAT is non empty complex-membered ext-real-membered real-membered rational-membered V59() V60() set
K226() is set
{{}} is functional non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
K20({{}},K226()) is Relation-like set
K226() \/ K20({{}},K226()) is set
[{},{}] is set
{{},{}} is functional non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
{{{},{}},{{}}} is non empty set
{[{},{}]} is Relation-like Function-like non empty set
(K226() \/ K20({{}},K226())) \ {[{},{}]} is Element of K19((K226() \/ K20({{}},K226())))
K19((K226() \/ K20({{}},K226()))) is set
K20({{}},K235()) is Relation-like set
K235() \/ K20({{}},K235()) is set
(K235() \/ K20({{}},K235())) \ {[{},{}]} is Element of K19((K235() \/ K20({{}},K235())))
K19((K235() \/ K20({{}},K235()))) is set
COMPLEX is non empty complex-membered V59() V60() set
1 is non empty complex epsilon-transitive epsilon-connected ordinal natural V37() V38() real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
{{},1} is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
Funcs ({{},1},REAL) is non empty FUNCTION_DOMAIN of {{},1}, REAL
{ b₁ where b₁ is Relation-like {{},1} -defined REAL -valued Function-like quasi_total complex-valued ext-real-valued real-valued Element of Funcs ({{},1},REAL) : b₁ . 1 = {} } is set
(Funcs ({{},1},REAL)) \ { b₁ where b₁ is Relation-like {{},1} -defined REAL -valued Function-like quasi_total complex-valued ext-real-valued real-valued Element of Funcs ({{},1},REAL) : b₁ . 1 = {} } is Element of K19((Funcs ({{},1},REAL)))
K19((Funcs ({{},1},REAL))) is set
((Funcs ({{},1},REAL)) \ { b₁ where b₁ is Relation-like {{},1} -defined REAL -valued Function-like quasi_total complex-valued ext-real-valued real-valued Element of Funcs ({{},1},REAL) : b₁ . 1 = {} } ) \/ REAL is non empty set
INT is non empty complex-membered ext-real-membered real-membered rational-membered integer-membered V59() V60() set
omega is non empty epsilon-transitive epsilon-connected ordinal complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V59() set
K20({{}},omega) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
omega \/ K20({{}},omega) is non empty set
(omega \/ K20({{}},omega)) \ {[{},{}]} is Element of K19((omega \/ K20({{}},omega)))
K19((omega \/ K20({{}},omega))) is set
K19(omega) is set
K19(NAT) is set
K19(K226()) is set
K19(K19(K226())) is set
K234() is Element of K19(K19(K226()))
2 is non empty complex epsilon-transitive epsilon-connected ordinal natural V37() V38() real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
3 is non empty complex epsilon-transitive epsilon-connected ordinal natural V37() V38() real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of NAT
K100() is Relation-like non-empty empty-yielding NAT -defined RAT -valued Function-like one-to-one constant functional empty complex epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V37() complex-valued ext-real-valued real-valued natural-valued real integer rational complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V59() V60() FinSequence-like FinSubsequence-like FinSequence-membered Element of NAT
ff is set
X is set
X1 is set
X /\ X1 is set
ff /\ (X /\ X1) is set
ff /\ ff is set
(ff /\ ff) /\ X is set
((ff /\ ff) /\ X) /\ X1 is set
ff /\ X is set
ff /\ (ff /\ X) is set
(ff /\ (ff /\ X)) /\ X1 is set
ff /\ X1 is set
(ff /\ X) /\ (ff /\ X1) is set
ff is functional set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ff : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ff : verum } is set
ff is set
X is set
ff is set
X is set
ff is set
X is set
ff is set
X is set
ff is set
X is set
ff is set
X is set
ff is Relation-like Function-like complex-valued set
{ff} is functional non empty set
X is set
ff is set
X is set
ff is set
X is set
the Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
{ the Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set } is functional non empty () set
X is set
X is functional () set
K19(X) is set
X1 is functional Element of K19(X)
X2 is set
X is functional () set
K19(X) is set
X1 is functional Element of K19(X)
X2 is set
X is functional () () () set
K19(X) is set
X1 is functional () () Element of K19(X)
X2 is set
X is functional () () () () set
K19(X) is set
X1 is functional () () () Element of K19(X)
X2 is set
X is functional () () () () () set
K19(X) is set
X1 is functional () () () () Element of K19(X)
X2 is set
X is functional () () () () () () set
K19(X) is set
X1 is functional () () () () () Element of K19(X)
X2 is set
X1 is set
K20(X1,COMPLEX) is Relation-like complex-valued set
K19(K20(X1,COMPLEX)) is set
PFuncs (X1,COMPLEX) is set
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,COMPLEX) is Relation-like complex-valued set
K19(K20(X1,COMPLEX)) is set
Funcs (X1,COMPLEX) is non empty FUNCTION_DOMAIN of X1, COMPLEX
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
ExtREAL is non empty ext-real-membered set
[K100(),REAL] is set
{K100(),REAL} is non empty set
{K100()} is functional non empty complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered () set
{{K100(),REAL},{K100()}} is non empty set
{REAL,[K100(),REAL]} is non empty set
REAL \/ {REAL,[K100(),REAL]} is non empty set
X1 is set
K20(X1,ExtREAL) is Relation-like ext-real-valued set
K19(K20(X1,ExtREAL)) is set
PFuncs (X1,ExtREAL) is set
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,ExtREAL) is Relation-like ext-real-valued set
K19(K20(X1,ExtREAL)) is set
Funcs (X1,ExtREAL) is non empty FUNCTION_DOMAIN of X1, ExtREAL
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(X1,REAL)) is set
PFuncs (X1,REAL) is set
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(X1,REAL)) is set
Funcs (X1,REAL) is non empty FUNCTION_DOMAIN of X1, REAL
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(X1,RAT)) is set
PFuncs (X1,RAT) is set
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(X1,RAT)) is set
Funcs (X1,RAT) is non empty FUNCTION_DOMAIN of X1, RAT
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(X1,INT)) is set
PFuncs (X1,INT) is set
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(X1,INT)) is set
Funcs (X1,INT) is non empty FUNCTION_DOMAIN of X1, INT
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20(X1,NAT)) is set
PFuncs (X1,NAT) is set
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X1 is set
K20(X1,NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20(X1,NAT)) is set
Funcs (X1,NAT) is non empty FUNCTION_DOMAIN of X1, NAT
X2 is set
Y is set
X2 is set
Y is set
Y1 is set
Y2 is set
Y1 is set
Y2 is set
X is set
(X) is set
(X) is set
K19((X)) is set
X1 is set
K20(X,COMPLEX) is Relation-like complex-valued set
K19(K20(X,COMPLEX)) is set
X is set
(X) is set
(X) is set
K19((X)) is set
X1 is set
K20(X,ExtREAL) is Relation-like ext-real-valued set
K19(K20(X,ExtREAL)) is set
X is set
(X) is set
(X) is set
K19((X)) is set
X1 is set
K20(X,REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(X,REAL)) is set
X is set
(X) is set
(X) is set
K19((X)) is set
X1 is set
K20(X,RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(X,RAT)) is set
X is set
(X) is set
(X) is set
K19((X)) is set
X1 is set
K20(X,INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(X,INT)) is set
X is set
(X) is set
(X) is set
K19((X)) is set
X1 is set
K20(X,NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20(X,NAT)) is set
X is set
(X) is set
X1 is set
(X) is set
K19((X)) is set
X1 is functional () Element of K19((X))
(X) is set
X1 is set
(X) is set
K19((X)) is set
X1 is functional () Element of K19((X))
(X) is set
X1 is set
(X) is set
K19((X)) is set
X1 is functional () () () Element of K19((X))
(X) is set
X1 is set
(X) is set
K19((X)) is set
X1 is functional () () () () Element of K19((X))
(X) is set
X1 is set
(X) is set
K19((X)) is set
X1 is functional () () () () () Element of K19((X))
(X) is set
X1 is set
(X) is set
K19((X)) is set
X1 is functional () () () () () () Element of K19((X))
X is functional () set
X1 is Relation-like Function-like Element of X
X is functional () set
X1 is Relation-like Function-like Element of X
X is functional () () () set
X1 is Relation-like Function-like complex-valued ext-real-valued Element of X
X is functional () () () () set
X1 is Relation-like Function-like complex-valued ext-real-valued real-valued Element of X
X is functional () () () () () set
X1 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued Element of X
X is functional () () () () () () set
X1 is Relation-like INT -valued Function-like complex-valued ext-real-valued real-valued Element of X
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like Function-like set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like Function-like set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like Function-like set
dom Y is Element of K19(X)
K19(X) is set
rng Y is functional () Element of K19(X2)
K19(X2) is set
dom Y is Element of K19(X)
K19(X) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like Function-like set
dom Y is Element of K19(X)
K19(X) is set
rng Y is functional () Element of K19(X2)
K19(X2) is set
dom Y is Element of K19(X)
K19(X) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X2 is functional () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like Function-like complex-valued ext-real-valued set
dom Y is Element of K19(X)
K19(X) is set
rng Y is functional () () () Element of K19(X2)
K19(X2) is set
dom Y is Element of K19(X)
K19(X) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X2 is functional () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like Function-like complex-valued ext-real-valued real-valued set
dom Y is Element of K19(X)
K19(X) is set
rng Y is functional () () () () Element of K19(X2)
K19(X2) is set
dom Y is Element of K19(X)
K19(X) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X2 is functional () () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
dom Y is Element of K19(X)
K19(X) is set
rng Y is functional () () () () () Element of K19(X2)
K19(X2) is set
dom Y is Element of K19(X)
K19(X) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X2 is functional () () () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like Element of K19(K20(X,X2))
X1 is set
Y . X1 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
dom Y is Element of K19(X)
K19(X) is set
rng Y is functional () () () () () () Element of K19(X2)
K19(X2) is set
dom Y is Element of K19(X)
K19(X) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X1 is complex-membered set
PFuncs (X,X1) is set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like complex-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued Element of K19(K20(X,X1))
X is set
X1 is ext-real-membered set
PFuncs (X,X1) is set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like ext-real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like ext-real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered set
PFuncs (X,X1) is functional () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered rational-membered set
PFuncs (X,X1) is functional () () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered rational-membered integer-membered set
PFuncs (X,X1) is functional () () () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
PFuncs (X,X1) is functional () () () () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered set
Funcs (X,X1) is set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like complex-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued Element of K19(K20(X,X1))
X is set
X1 is ext-real-membered set
Funcs (X,X1) is set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like ext-real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like ext-real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered set
Funcs (X,X1) is functional () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered rational-membered set
Funcs (X,X1) is functional () () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered rational-membered integer-membered set
Funcs (X,X1) is functional () () () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued Element of K19(K20(X,X1))
X is set
X1 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered set
Funcs (X,X1) is functional () () () () () set
X2 is set
Y is Relation-like Function-like set
dom Y is set
rng Y is set
K20(X,X1) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20(X,X1)) is set
Y1 is Relation-like X -defined X1 -valued Function-like complex-valued ext-real-valued real-valued natural-valued Element of K19(K20(X,X1))
X is functional () set
X1 is Relation-like X -valued Function-like set
rng X1 is functional () Element of K19(X)
K19(X) is set
X is Relation-like Function-like set
dom X is set
rng X is set
X1 is set
X . X1 is set
X1 is set
rng X is set
X2 is set
X . X2 is set
rng X is set
X1 is set
X . X1 is set
X1 is set
rng X is set
X2 is set
X . X2 is set
rng X is set
X1 is set
X . X1 is set
X1 is set
rng X is set
X2 is set
X . X2 is set
rng X is set
X1 is set
X . X1 is set
X1 is set
rng X is set
X2 is set
X . X2 is set
rng X is set
X1 is set
X . X1 is set
X1 is set
rng X is set
X2 is set
X . X2 is set
rng X is set
X1 is set
X . X1 is set
X1 is set
rng X is set
X2 is set
X . X2 is set
X is Relation-like set
rng X is set
X1 is set
X is Relation-like set
rng X is set
X1 is set
X is Relation-like set
rng X is set
X1 is set
X is Relation-like set
rng X is set
X1 is set
X is Relation-like set
rng X is set
X1 is set
X is Relation-like set
X1 is set
rng X is set
X is Relation-like () set
rng X is set
X is Relation-like () set
rng X is set
X is Relation-like () () () set
rng X is functional () () set
X is Relation-like () () () () set
rng X is functional () () () set
X is Relation-like () () () () () set
rng X is functional () () () () set
X is Relation-like () () () () () () set
rng X is functional () () () () () set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like Element of K19(K20(X,X1))
Y is set
dom X2 is set
X2 . Y is Relation-like Function-like ext-real-valued set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () Element of K19(K20(X,X1))
Y is set
dom X2 is set
X2 . Y is Relation-like Function-like complex-valued ext-real-valued real-valued set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is set
dom X2 is set
X2 . Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is set
dom X2 is set
X2 . Y is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
X is set
X1 is functional () () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
Y is set
dom X2 is set
X2 . Y is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
X is Relation-like Function-like () set
X1 is set
X . X1 is set
dom X is set
rng X is functional () set
dom X is set
dom X is set
X is Relation-like Function-like () set
X1 is set
X . X1 is set
dom X is set
rng X is functional () set
dom X is set
dom X is set
X is Relation-like Function-like () set
X1 is set
X . X1 is Relation-like Function-like set
dom X is set
rng X is functional () set
dom X is set
dom X is set
X is Relation-like Function-like () set
X1 is set
X . X1 is Relation-like Function-like set
dom X is set
rng X is functional () set
dom X is set
dom X is set
X is Relation-like Function-like () () () set
X1 is set
X . X1 is Relation-like Function-like complex-valued ext-real-valued set
dom X is set
rng X is functional () () () set
dom X is set
dom X is set
X is Relation-like Function-like () () () () set
X1 is set
X . X1 is Relation-like Function-like complex-valued ext-real-valued real-valued set
dom X is set
rng X is functional () () () () set
dom X is set
dom X is set
X is Relation-like Function-like () () () () () set
X1 is set
X . X1 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
dom X is set
rng X is functional () () () () () set
dom X is set
dom X is set
X is Relation-like Function-like () () () () () () set
X1 is set
X . X1 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
dom X is set
rng X is functional () () () () () () set
dom X is set
dom X is set
X is complex set
X1 is complex set
X2 is Relation-like Function-like complex-valued set
X + X2 is Relation-like Function-like complex-valued set
X1 + X2 is Relation-like Function-like complex-valued set
dom X2 is set
Y is set
dom (X1 + X2) is set
(X1 + X2) . Y is complex set
X2 . Y is complex set
(X2 . Y) + X1 is complex set
dom (X + X2) is set
(X + X2) . Y is complex set
(X2 . Y) + X is complex set
X is complex set
X1 is complex set
X2 is Relation-like Function-like complex-valued set
X2 - X is Relation-like Function-like complex-valued set
- X is complex set
(- X) + X2 is Relation-like Function-like complex-valued set
X2 - X1 is Relation-like Function-like complex-valued set
- X1 is complex set
(- X1) + X2 is Relation-like Function-like complex-valued set
dom X2 is set
Y is set
dom (X2 - X1) is set
(X2 - X1) . Y is complex set
X2 . Y is complex set
(X2 . Y) - X1 is complex set
(X2 . Y) + (- X1) is complex set
dom (X2 - X) is set
(X2 - X) . Y is complex set
(X2 . Y) - X is complex set
(X2 . Y) + (- X) is complex set
X is complex set
X1 is complex set
X2 is Relation-like Function-like complex-valued set
X (#) X2 is Relation-like Function-like complex-valued set
X1 (#) X2 is Relation-like Function-like complex-valued set
dom X2 is set
Y is set
X2 . Y is complex set
rng X2 is complex-membered set
(X (#) X2) . Y is complex set
(X2 . Y) * X is complex set
(X1 (#) X2) . Y is complex set
(X2 . Y) * X1 is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
X + X1 is Relation-like Function-like complex-valued set
- (X + X1) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X + X1) is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
(- X1) - X is Relation-like Function-like complex-valued set
- X is complex set
(- X) + (- X1) is Relation-like Function-like complex-valued set
dom (- (X + X1)) is set
dom (X + X1) is set
dom X1 is set
dom ((- X1) - X) is set
dom (- X1) is set
X2 is set
(- (X + X1)) . X2 is complex set
((- X1) - X) . X2 is complex set
(X + X1) . X2 is complex set
- ((X + X1) . X2) is complex set
X1 . X2 is complex set
(X1 . X2) + X is complex set
- ((X1 . X2) + X) is complex set
- (X1 . X2) is complex set
(- (X1 . X2)) - X is complex set
(- (X1 . X2)) + (- X) is complex set
(- X1) . X2 is complex set
((- X1) . X2) - X is complex set
((- X1) . X2) + (- X) is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
X1 - X is Relation-like Function-like complex-valued set
- X is complex set
(- X) + X1 is Relation-like Function-like complex-valued set
- (X1 - X) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X1 - X) is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
X + (- X1) is Relation-like Function-like complex-valued set
dom (- (X1 - X)) is set
dom (X1 - X) is set
dom X1 is set
dom (X + (- X1)) is set
dom (- X1) is set
X2 is set
(- (X1 - X)) . X2 is complex set
(X + (- X1)) . X2 is complex set
(X1 - X) . X2 is complex set
- ((X1 - X) . X2) is complex set
X1 . X2 is complex set
(X1 . X2) - X is complex set
(X1 . X2) + (- X) is complex set
- ((X1 . X2) - X) is complex set
- (X1 . X2) is complex set
(- (X1 . X2)) + X is complex set
(- X1) . X2 is complex set
((- X1) . X2) + X is complex set
X is complex set
X1 is complex set
X + X1 is complex set
X2 is Relation-like Function-like complex-valued set
X + X2 is Relation-like Function-like complex-valued set
X1 + (X + X2) is Relation-like Function-like complex-valued set
(X + X1) + X2 is Relation-like Function-like complex-valued set
dom (X1 + (X + X2)) is set
dom (X + X2) is set
dom X2 is set
dom ((X + X1) + X2) is set
Y is set
(X1 + (X + X2)) . Y is complex set
((X + X1) + X2) . Y is complex set
(X + X2) . Y is complex set
((X + X2) . Y) + X1 is complex set
X2 . Y is complex set
(X2 . Y) + X is complex set
((X2 . Y) + X) + X1 is complex set
(X2 . Y) + (X + X1) is complex set
X is complex set
X1 is complex set
X - X1 is complex set
- X1 is complex set
X + (- X1) is complex set
X2 is Relation-like Function-like complex-valued set
X + X2 is Relation-like Function-like complex-valued set
(X + X2) - X1 is Relation-like Function-like complex-valued set
(- X1) + (X + X2) is Relation-like Function-like complex-valued set
(X - X1) + X2 is Relation-like Function-like complex-valued set
dom ((X + X2) - X1) is set
dom (X + X2) is set
dom X2 is set
dom ((X - X1) + X2) is set
Y is set
((X + X2) - X1) . Y is complex set
((X - X1) + X2) . Y is complex set
(X + X2) . Y is complex set
((X + X2) . Y) - X1 is complex set
((X + X2) . Y) + (- X1) is complex set
X2 . Y is complex set
(X2 . Y) + X is complex set
((X2 . Y) + X) - X1 is complex set
((X2 . Y) + X) + (- X1) is complex set
(X2 . Y) + (X - X1) is complex set
X is complex set
X1 is complex set
X - X1 is complex set
- X1 is complex set
X + (- X1) is complex set
X2 is Relation-like Function-like complex-valued set
X2 - X is Relation-like Function-like complex-valued set
- X is complex set
(- X) + X2 is Relation-like Function-like complex-valued set
X1 + (X2 - X) is Relation-like Function-like complex-valued set
X2 - (X - X1) is Relation-like Function-like complex-valued set
- (X - X1) is complex set
(- (X - X1)) + X2 is Relation-like Function-like complex-valued set
dom (X1 + (X2 - X)) is set
dom (X2 - X) is set
dom X2 is set
dom (X2 - (X - X1)) is set
Y is set
(X1 + (X2 - X)) . Y is complex set
(X2 - (X - X1)) . Y is complex set
(X2 - X) . Y is complex set
((X2 - X) . Y) + X1 is complex set
X2 . Y is complex set
(X2 . Y) - X is complex set
(X2 . Y) + (- X) is complex set
((X2 . Y) - X) + X1 is complex set
(X2 . Y) - (X - X1) is complex set
(X2 . Y) + (- (X - X1)) is complex set
X is complex set
X1 is complex set
X + X1 is complex set
X2 is Relation-like Function-like complex-valued set
X2 - X is Relation-like Function-like complex-valued set
- X is complex set
(- X) + X2 is Relation-like Function-like complex-valued set
(X2 - X) - X1 is Relation-like Function-like complex-valued set
- X1 is complex set
(- X1) + (X2 - X) is Relation-like Function-like complex-valued set
X2 - (X + X1) is Relation-like Function-like complex-valued set
- (X + X1) is complex set
(- (X + X1)) + X2 is Relation-like Function-like complex-valued set
dom ((X2 - X) - X1) is set
dom (X2 - X) is set
dom X2 is set
dom (X2 - (X + X1)) is set
Y is set
((X2 - X) - X1) . Y is complex set
(X2 - (X + X1)) . Y is complex set
(X2 - X) . Y is complex set
((X2 - X) . Y) - X1 is complex set
((X2 - X) . Y) + (- X1) is complex set
X2 . Y is complex set
(X2 . Y) - X is complex set
(X2 . Y) + (- X) is complex set
((X2 . Y) - X) - X1 is complex set
((X2 . Y) - X) + (- X1) is complex set
(X2 . Y) - (X + X1) is complex set
(X2 . Y) + (- (X + X1)) is complex set
X is complex set
X1 is complex set
X * X1 is complex set
X2 is Relation-like Function-like complex-valued set
X (#) X2 is Relation-like Function-like complex-valued set
X1 (#) (X (#) X2) is Relation-like Function-like complex-valued set
(X * X1) (#) X2 is Relation-like Function-like complex-valued set
dom (X1 (#) (X (#) X2)) is set
dom (X (#) X2) is set
dom X2 is set
dom ((X * X1) (#) X2) is set
Y is set
(X1 (#) (X (#) X2)) . Y is complex set
((X * X1) (#) X2) . Y is complex set
(X (#) X2) . Y is complex set
((X (#) X2) . Y) * X1 is complex set
X2 . Y is complex set
(X2 . Y) * X is complex set
((X2 . Y) * X) * X1 is complex set
(X2 . Y) * (X * X1) is complex set
X is Relation-like Function-like complex-valued set
- X is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X + X1 is Relation-like Function-like complex-valued set
- (X + X1) is Relation-like Function-like complex-valued set
(- 1) (#) (X + X1) is Relation-like Function-like complex-valued set
(- X) - X1 is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
(- X) + (- X1) is Relation-like Function-like complex-valued set
dom (- (X + X1)) is set
dom (X + X1) is set
dom X is set
dom X1 is set
(dom X) /\ (dom X1) is set
dom ((- X) - X1) is set
dom (- X) is set
(dom (- X)) /\ (dom X1) is set
X2 is set
(- (X + X1)) . X2 is complex set
((- X) - X1) . X2 is complex set
(X + X1) . X2 is complex set
- ((X + X1) . X2) is complex set
X . X2 is complex set
X1 . X2 is complex set
(X . X2) + (X1 . X2) is complex set
- ((X . X2) + (X1 . X2)) is complex set
- (X . X2) is complex set
(- (X . X2)) - (X1 . X2) is complex set
- (X1 . X2) is complex set
(- (X . X2)) + (- (X1 . X2)) is complex set
(- X) . X2 is complex set
((- X) . X2) - (X1 . X2) is complex set
((- X) . X2) + (- (X1 . X2)) is complex set
X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X - X1 is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
X + (- X1) is Relation-like Function-like complex-valued set
X1 - X is Relation-like Function-like complex-valued set
- X is Relation-like Function-like complex-valued set
(- 1) (#) X is Relation-like Function-like complex-valued set
X1 + (- X) is Relation-like Function-like complex-valued set
- (X1 - X) is Relation-like Function-like complex-valued set
(- 1) (#) (X1 - X) is Relation-like Function-like complex-valued set
dom (- (X1 - X)) is set
dom (X1 - X) is set
dom (X - X1) is set
dom X is set
dom X1 is set
(dom X) /\ (dom X1) is set
X2 is set
(X - X1) . X2 is complex set
(- (X1 - X)) . X2 is complex set
X . X2 is complex set
X1 . X2 is complex set
(X . X2) - (X1 . X2) is complex set
- (X1 . X2) is complex set
(X . X2) + (- (X1 . X2)) is complex set
(X1 . X2) - (X . X2) is complex set
- (X . X2) is complex set
(X1 . X2) + (- (X . X2)) is complex set
- ((X1 . X2) - (X . X2)) is complex set
(X1 - X) . X2 is complex set
- ((X1 - X) . X2) is complex set
X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X (#) X1 is Relation-like Function-like complex-valued set
X2 is Relation-like Function-like complex-valued set
(X (#) X1) /" X2 is Relation-like Function-like complex-valued set
X2 " is Relation-like Function-like complex-valued set
(X (#) X1) (#) (X2 ") is Relation-like Function-like complex-valued set
X1 /" X2 is Relation-like Function-like complex-valued set
X1 (#) (X2 ") is Relation-like Function-like complex-valued set
X (#) (X1 /" X2) is Relation-like Function-like complex-valued set
dom (X (#) (X1 /" X2)) is set
dom X is set
dom (X1 /" X2) is set
(dom X) /\ (dom (X1 /" X2)) is set
dom ((X (#) X1) /" X2) is set
dom (X (#) X1) is set
dom X2 is set
(dom (X (#) X1)) /\ (dom X2) is set
dom X1 is set
(dom X) /\ (dom X1) is set
(dom X1) /\ (dom X2) is set
Y is set
((X (#) X1) /" X2) . Y is complex set
(X (#) (X1 /" X2)) . Y is complex set
(X (#) X1) . Y is complex set
X2 . Y is complex set
((X (#) X1) . Y) / (X2 . Y) is complex set
(X2 . Y) " is complex set
((X (#) X1) . Y) * ((X2 . Y) ") is complex set
X . Y is complex set
X1 . Y is complex set
(X . Y) * (X1 . Y) is complex set
((X . Y) * (X1 . Y)) / (X2 . Y) is complex set
((X . Y) * (X1 . Y)) * ((X2 . Y) ") is complex set
(X1 . Y) / (X2 . Y) is complex set
(X1 . Y) * ((X2 . Y) ") is complex set
(X . Y) * ((X1 . Y) / (X2 . Y)) is complex set
(X1 /" X2) . Y is complex set
(X . Y) * ((X1 /" X2) . Y) is complex set
X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X /" X1 is Relation-like Function-like complex-valued set
X1 " is Relation-like Function-like complex-valued set
X (#) (X1 ") is Relation-like Function-like complex-valued set
X2 is Relation-like Function-like complex-valued set
(X /" X1) (#) X2 is Relation-like Function-like complex-valued set
X (#) X2 is Relation-like Function-like complex-valued set
(X (#) X2) /" X1 is Relation-like Function-like complex-valued set
(X (#) X2) (#) (X1 ") is Relation-like Function-like complex-valued set
dom ((X /" X1) (#) X2) is set
dom (X /" X1) is set
dom X2 is set
(dom (X /" X1)) /\ (dom X2) is set
dom ((X (#) X2) /" X1) is set
dom (X (#) X2) is set
dom X1 is set
(dom (X (#) X2)) /\ (dom X1) is set
dom X is set
(dom X) /\ (dom X1) is set
(dom X) /\ (dom X2) is set
Y is set
((X /" X1) (#) X2) . Y is complex set
((X (#) X2) /" X1) . Y is complex set
(X /" X1) . Y is complex set
X2 . Y is complex set
((X /" X1) . Y) * (X2 . Y) is complex set
X . Y is complex set
X1 . Y is complex set
(X . Y) / (X1 . Y) is complex set
(X1 . Y) " is complex set
(X . Y) * ((X1 . Y) ") is complex set
((X . Y) / (X1 . Y)) * (X2 . Y) is complex set
(X . Y) * (X2 . Y) is complex set
((X . Y) * (X2 . Y)) / (X1 . Y) is complex set
((X . Y) * (X2 . Y)) * ((X1 . Y) ") is complex set
(X (#) X2) . Y is complex set
((X (#) X2) . Y) / (X1 . Y) is complex set
((X (#) X2) . Y) * ((X1 . Y) ") is complex set
X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X /" X1 is Relation-like Function-like complex-valued set
X1 " is Relation-like Function-like complex-valued set
X (#) (X1 ") is Relation-like Function-like complex-valued set
X2 is Relation-like Function-like complex-valued set
(X /" X1) /" X2 is Relation-like Function-like complex-valued set
X2 " is Relation-like Function-like complex-valued set
(X /" X1) (#) (X2 ") is Relation-like Function-like complex-valued set
X1 (#) X2 is Relation-like Function-like complex-valued set
X /" (X1 (#) X2) is Relation-like Function-like complex-valued set
(X1 (#) X2) " is Relation-like Function-like complex-valued set
X (#) ((X1 (#) X2) ") is Relation-like Function-like complex-valued set
dom ((X /" X1) /" X2) is set
dom (X /" X1) is set
dom X2 is set
(dom (X /" X1)) /\ (dom X2) is set
dom (X /" (X1 (#) X2)) is set
dom X is set
dom (X1 (#) X2) is set
(dom X) /\ (dom (X1 (#) X2)) is set
dom X1 is set
(dom X) /\ (dom X1) is set
(dom X1) /\ (dom X2) is set
Y is set
((X /" X1) /" X2) . Y is complex set
(X /" (X1 (#) X2)) . Y is complex set
(X /" X1) . Y is complex set
X2 . Y is complex set
((X /" X1) . Y) / (X2 . Y) is complex set
(X2 . Y) " is complex set
((X /" X1) . Y) * ((X2 . Y) ") is complex set
X . Y is complex set
X1 . Y is complex set
(X . Y) / (X1 . Y) is complex set
(X1 . Y) " is complex set
(X . Y) * ((X1 . Y) ") is complex set
((X . Y) / (X1 . Y)) / (X2 . Y) is complex set
((X . Y) / (X1 . Y)) * ((X2 . Y) ") is complex set
(X1 . Y) * (X2 . Y) is complex set
(X . Y) / ((X1 . Y) * (X2 . Y)) is complex set
((X1 . Y) * (X2 . Y)) " is complex set
(X . Y) * (((X1 . Y) * (X2 . Y)) ") is complex set
(X1 (#) X2) . Y is complex set
(X . Y) / ((X1 (#) X2) . Y) is complex set
((X1 (#) X2) . Y) " is complex set
(X . Y) * (((X1 (#) X2) . Y) ") is complex set
X is complex set
- X is complex set
X1 is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
X (#) (- X1) is Relation-like Function-like complex-valued set
(- X) (#) X1 is Relation-like Function-like complex-valued set
dom (X (#) (- X1)) is set
dom (- X1) is set
dom X1 is set
dom ((- X) (#) X1) is set
X2 is set
(X (#) (- X1)) . X2 is complex set
((- X) (#) X1) . X2 is complex set
(- X1) . X2 is complex set
X * ((- X1) . X2) is complex set
X1 . X2 is complex set
- (X1 . X2) is complex set
X * (- (X1 . X2)) is complex set
(- X) * (X1 . X2) is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
X (#) (- X1) is Relation-like Function-like complex-valued set
X (#) X1 is Relation-like Function-like complex-valued set
- (X (#) X1) is Relation-like Function-like complex-valued set
(- 1) (#) (X (#) X1) is Relation-like Function-like complex-valued set
dom (- (X (#) X1)) is set
dom (X (#) X1) is set
dom X1 is set
dom (X (#) (- X1)) is set
dom (- X1) is set
X2 is set
(X (#) (- X1)) . X2 is complex set
(- (X (#) X1)) . X2 is complex set
(- X1) . X2 is complex set
X * ((- X1) . X2) is complex set
X1 . X2 is complex set
- (X1 . X2) is complex set
X * (- (X1 . X2)) is complex set
X * (X1 . X2) is complex set
- (X * (X1 . X2)) is complex set
(X (#) X1) . X2 is complex set
- ((X (#) X1) . X2) is complex set
X is complex set
- X is complex set
X1 is Relation-like Function-like complex-valued set
(- X) (#) X1 is Relation-like Function-like complex-valued set
X (#) X1 is Relation-like Function-like complex-valued set
- (X (#) X1) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X (#) X1) is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
X (#) (- X1) is Relation-like Function-like complex-valued set
X is Relation-like Function-like complex-valued set
- X is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X (#) X1 is Relation-like Function-like complex-valued set
- (X (#) X1) is Relation-like Function-like complex-valued set
(- 1) (#) (X (#) X1) is Relation-like Function-like complex-valued set
(- X) (#) X1 is Relation-like Function-like complex-valued set
dom (- (X (#) X1)) is set
dom (X (#) X1) is set
dom X is set
dom X1 is set
(dom X) /\ (dom X1) is set
dom ((- X) (#) X1) is set
dom (- X) is set
(dom (- X)) /\ (dom X1) is set
X2 is set
(- (X (#) X1)) . X2 is complex set
((- X) (#) X1) . X2 is complex set
(X (#) X1) . X2 is complex set
- ((X (#) X1) . X2) is complex set
X . X2 is complex set
X1 . X2 is complex set
(X . X2) * (X1 . X2) is complex set
- ((X . X2) * (X1 . X2)) is complex set
- (X . X2) is complex set
(- (X . X2)) * (X1 . X2) is complex set
(- X) . X2 is complex set
((- X) . X2) * (X1 . X2) is complex set
X is Relation-like Function-like complex-valued set
- X is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X /" X1 is Relation-like Function-like complex-valued set
X1 " is Relation-like Function-like complex-valued set
X (#) (X1 ") is Relation-like Function-like complex-valued set
- (X /" X1) is Relation-like Function-like complex-valued set
(- 1) (#) (X /" X1) is Relation-like Function-like complex-valued set
(- X) /" X1 is Relation-like Function-like complex-valued set
(- X) (#) (X1 ") is Relation-like Function-like complex-valued set
dom (- (X /" X1)) is set
dom (X /" X1) is set
dom X is set
dom X1 is set
(dom X) /\ (dom X1) is set
dom ((- X) /" X1) is set
dom (- X) is set
(dom (- X)) /\ (dom X1) is set
X2 is set
(- (X /" X1)) . X2 is complex set
((- X) /" X1) . X2 is complex set
(X /" X1) . X2 is complex set
- ((X /" X1) . X2) is complex set
X . X2 is complex set
X1 . X2 is complex set
(X . X2) / (X1 . X2) is complex set
(X1 . X2) " is complex set
(X . X2) * ((X1 . X2) ") is complex set
- ((X . X2) / (X1 . X2)) is complex set
- (X . X2) is complex set
(- (X . X2)) / (X1 . X2) is complex set
(- (X . X2)) * ((X1 . X2) ") is complex set
(- X) . X2 is complex set
((- X) . X2) / (X1 . X2) is complex set
((- X) . X2) * ((X1 . X2) ") is complex set
X is Relation-like Function-like complex-valued set
X1 is Relation-like Function-like complex-valued set
X /" X1 is Relation-like Function-like complex-valued set
X1 " is Relation-like Function-like complex-valued set
X (#) (X1 ") is Relation-like Function-like complex-valued set
- (X /" X1) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X /" X1) is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
X /" (- X1) is Relation-like Function-like complex-valued set
(- X1) " is Relation-like Function-like complex-valued set
X (#) ((- X1) ") is Relation-like Function-like complex-valued set
dom (- X1) is set
dom X1 is set
dom (X /" X1) is set
dom X is set
(dom X) /\ (dom X1) is set
dom (X /" (- X1)) is set
(dom X) /\ (dom (- X1)) is set
dom (- (X /" X1)) is set
X2 is set
(- (X /" X1)) . X2 is complex set
(X /" (- X1)) . X2 is complex set
(X /" X1) . X2 is complex set
- ((X /" X1) . X2) is complex set
X . X2 is complex set
X1 . X2 is complex set
(X . X2) / (X1 . X2) is complex set
(X1 . X2) " is complex set
(X . X2) * ((X1 . X2) ") is complex set
- ((X . X2) / (X1 . X2)) is complex set
- (X1 . X2) is complex set
(X . X2) / (- (X1 . X2)) is complex set
(- (X1 . X2)) " is complex set
(X . X2) * ((- (X1 . X2)) ") is complex set
(- X1) . X2 is complex set
(X . X2) / ((- X1) . X2) is complex set
((- X1) . X2) " is complex set
(X . X2) * (((- X1) . X2) ") is complex set
X is Relation-like Function-like complex-valued set
X1 is complex set
1 / X1 is complex set
X1 " is complex set
1 * (X1 ") is complex set
(1 / X1) (#) X is Relation-like Function-like complex-valued set
X is Relation-like Function-like complex-valued set
X1 is complex set
(X,X1) is Relation-like Function-like set
1 / X1 is complex set
X1 " is complex set
1 * (X1 ") is complex set
(1 / X1) (#) X is Relation-like Function-like complex-valued set
X is Relation-like Function-like complex-valued ext-real-valued real-valued set
X1 is complex V37() real set
(X,X1) is Relation-like Function-like complex-valued set
1 / X1 is complex V37() real set
X1 " is complex V37() real set
1 * (X1 ") is complex V37() real set
(1 / X1) (#) X is Relation-like Function-like complex-valued ext-real-valued real-valued set
X is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X1 is complex V37() real rational set
(X,X1) is Relation-like Function-like complex-valued ext-real-valued real-valued set
1 / X1 is complex V37() real rational set
X1 " is complex V37() real rational set
1 * (X1 ") is complex V37() real rational set
(1 / X1) (#) X is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
X1 is complex set
(X,X1) is Relation-like Function-like complex-valued set
1 / X1 is complex set
X1 " is complex set
1 * (X1 ") is complex set
(1 / X1) (#) X is Relation-like NAT -defined Function-like complex-valued V60() FinSequence-like FinSubsequence-like set
X1 is Relation-like Function-like complex-valued set
X is complex set
(X1,X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) X1 is Relation-like Function-like complex-valued set
dom (X1,X) is set
dom X1 is set
X2 is Relation-like Function-like complex-valued set
X1 is complex set
(X2,X1) is Relation-like Function-like complex-valued set
1 / X1 is complex set
X1 " is complex set
1 * (X1 ") is complex set
(1 / X1) (#) X2 is Relation-like Function-like complex-valued set
X is set
(X2,X1) . X is complex set
X2 . X is complex set
(X2 . X) / X1 is complex set
(X2 . X) * (X1 ") is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
((- X1),X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) (- X1) is Relation-like Function-like complex-valued set
(X1,X) is Relation-like Function-like complex-valued set
(1 / X) (#) X1 is Relation-like Function-like complex-valued set
- (X1,X) is Relation-like Function-like complex-valued set
(- 1) (#) (X1,X) is Relation-like Function-like complex-valued set
- (1 / X) is complex set
(- (1 / X)) (#) X1 is Relation-like Function-like complex-valued set
X is complex set
- X is complex set
X1 is Relation-like Function-like complex-valued set
(X1,(- X)) is Relation-like Function-like complex-valued set
1 / (- X) is complex set
(- X) " is complex set
1 * ((- X) ") is complex set
(1 / (- X)) (#) X1 is Relation-like Function-like complex-valued set
(X1,X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) X1 is Relation-like Function-like complex-valued set
- (X1,X) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X1,X) is Relation-like Function-like complex-valued set
- (1 / X) is complex set
(- (1 / X)) (#) X1 is Relation-like Function-like complex-valued set
X is complex set
- X is complex set
X1 is Relation-like Function-like complex-valued set
(X1,(- X)) is Relation-like Function-like complex-valued set
1 / (- X) is complex set
(- X) " is complex set
1 * ((- X) ") is complex set
(1 / (- X)) (#) X1 is Relation-like Function-like complex-valued set
- X1 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X1 is Relation-like Function-like complex-valued set
((- X1),X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) (- X1) is Relation-like Function-like complex-valued set
(X1,X) is Relation-like Function-like complex-valued set
(1 / X) (#) X1 is Relation-like Function-like complex-valued set
- (X1,X) is Relation-like Function-like complex-valued set
(- 1) (#) (X1,X) is Relation-like Function-like complex-valued set
X is complex set
X1 is complex set
X2 is Relation-like Function-like complex-valued set
(X2,X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) X2 is Relation-like Function-like complex-valued set
(X2,X1) is Relation-like Function-like complex-valued set
1 / X1 is complex set
X1 " is complex set
1 * (X1 ") is complex set
(1 / X1) (#) X2 is Relation-like Function-like complex-valued set
dom X2 is set
Y is set
X2 . Y is complex set
rng X2 is complex-membered set
(X2,X) . Y is complex set
(X2 . Y) / X is complex set
(X2 . Y) * (X ") is complex set
(X2,X1) . Y is complex set
(X2 . Y) / X1 is complex set
(X2 . Y) * (X1 ") is complex set
X is complex set
X1 is complex set
X / X1 is complex set
X1 " is complex set
X * (X1 ") is complex set
X2 is Relation-like Function-like complex-valued set
X (#) X2 is Relation-like Function-like complex-valued set
((X (#) X2),X1) is Relation-like Function-like complex-valued set
1 / X1 is complex set
1 * (X1 ") is complex set
(1 / X1) (#) (X (#) X2) is Relation-like Function-like complex-valued set
(X / X1) (#) X2 is Relation-like Function-like complex-valued set
dom (X (#) X2) is set
dom X2 is set
dom ((X (#) X2),X1) is set
dom ((X / X1) (#) X2) is set
Y is set
((X (#) X2),X1) . Y is complex set
((X / X1) (#) X2) . Y is complex set
(X (#) X2) . Y is complex set
((X (#) X2) . Y) * (X1 ") is complex set
X2 . Y is complex set
(X2 . Y) * X is complex set
((X2 . Y) * X) * (X1 ") is complex set
(X2 . Y) * (X / X1) is complex set
X is complex set
X1 is complex set
X2 is Relation-like Function-like complex-valued set
(X2,X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) X2 is Relation-like Function-like complex-valued set
X1 (#) (X2,X) is Relation-like Function-like complex-valued set
X1 (#) X2 is Relation-like Function-like complex-valued set
((X1 (#) X2),X) is Relation-like Function-like complex-valued set
(1 / X) (#) (X1 (#) X2) is Relation-like Function-like complex-valued set
dom (X1 (#) (X2,X)) is set
dom (X2,X) is set
dom X2 is set
dom (X1 (#) X2) is set
dom ((X1 (#) X2),X) is set
Y is set
(X1 (#) (X2,X)) . Y is complex set
((X1 (#) X2),X) . Y is complex set
(X2,X) . Y is complex set
((X2,X) . Y) * X1 is complex set
X2 . Y is complex set
(X2 . Y) * (X ") is complex set
((X2 . Y) * (X ")) * X1 is complex set
(X2 . Y) * X1 is complex set
((X2 . Y) * X1) * (X ") is complex set
(X1 (#) X2) . Y is complex set
((X1 (#) X2) . Y) * (X ") is complex set
X is complex set
X1 is complex set
X * X1 is complex set
X2 is Relation-like Function-like complex-valued set
(X2,X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) X2 is Relation-like Function-like complex-valued set
((X2,X),X1) is Relation-like Function-like complex-valued set
1 / X1 is complex set
X1 " is complex set
1 * (X1 ") is complex set
(1 / X1) (#) (X2,X) is Relation-like Function-like complex-valued set
(X2,(X * X1)) is Relation-like Function-like complex-valued set
1 / (X * X1) is complex set
(X * X1) " is complex set
1 * ((X * X1) ") is complex set
(1 / (X * X1)) (#) X2 is Relation-like Function-like complex-valued set
dom (X2,X) is set
dom X2 is set
dom (X2,(X * X1)) is set
dom ((X2,X),X1) is set
Y is set
((X2,X),X1) . Y is complex set
(X2,(X * X1)) . Y is complex set
(X2,X) . Y is complex set
((X2,X) . Y) * (X1 ") is complex set
X2 . Y is complex set
(X2 . Y) * (X ") is complex set
((X2 . Y) * (X ")) * (X1 ") is complex set
(X ") * (X1 ") is complex set
(X2 . Y) * ((X ") * (X1 ")) is complex set
(X2 . Y) * ((X * X1) ") is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
(X1,X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) X1 is Relation-like Function-like complex-valued set
X2 is Relation-like Function-like complex-valued set
X1 + X2 is Relation-like Function-like complex-valued set
((X1 + X2),X) is Relation-like Function-like complex-valued set
(1 / X) (#) (X1 + X2) is Relation-like Function-like complex-valued set
(X2,X) is Relation-like Function-like complex-valued set
(1 / X) (#) X2 is Relation-like Function-like complex-valued set
(X1,X) + (X2,X) is Relation-like Function-like complex-valued set
dom ((X1 + X2),X) is set
dom (X1 + X2) is set
dom X1 is set
dom X2 is set
(dom X1) /\ (dom X2) is set
dom (X1,X) is set
dom (X2,X) is set
dom ((X1,X) + (X2,X)) is set
Y is set
((X1 + X2),X) . Y is complex set
((X1,X) + (X2,X)) . Y is complex set
(X1 + X2) . Y is complex set
((X1 + X2) . Y) * (X ") is complex set
X1 . Y is complex set
X2 . Y is complex set
(X1 . Y) + (X2 . Y) is complex set
((X1 . Y) + (X2 . Y)) * (X ") is complex set
(X1 . Y) * (X ") is complex set
(X2 . Y) * (X ") is complex set
((X1 . Y) * (X ")) + ((X2 . Y) * (X ")) is complex set
(X1,X) . Y is complex set
((X1,X) . Y) + ((X2 . Y) * (X ")) is complex set
(X2,X) . Y is complex set
((X1,X) . Y) + ((X2,X) . Y) is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
(X1,X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) X1 is Relation-like Function-like complex-valued set
X2 is Relation-like Function-like complex-valued set
X1 - X2 is Relation-like Function-like complex-valued set
- X2 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X2 is Relation-like Function-like complex-valued set
X1 + (- X2) is Relation-like Function-like complex-valued set
((X1 - X2),X) is Relation-like Function-like complex-valued set
(1 / X) (#) (X1 - X2) is Relation-like Function-like complex-valued set
(X2,X) is Relation-like Function-like complex-valued set
(1 / X) (#) X2 is Relation-like Function-like complex-valued set
(X1,X) - (X2,X) is Relation-like Function-like complex-valued set
- (X2,X) is Relation-like Function-like complex-valued set
(- 1) (#) (X2,X) is Relation-like Function-like complex-valued set
(X1,X) + (- (X2,X)) is Relation-like Function-like complex-valued set
dom ((X1 - X2),X) is set
dom (X1 - X2) is set
dom X1 is set
dom X2 is set
(dom X1) /\ (dom X2) is set
dom (X1,X) is set
dom (X2,X) is set
dom ((X1,X) - (X2,X)) is set
Y is set
((X1 - X2),X) . Y is complex set
((X1,X) - (X2,X)) . Y is complex set
(X1 - X2) . Y is complex set
((X1 - X2) . Y) * (X ") is complex set
X1 . Y is complex set
X2 . Y is complex set
(X1 . Y) - (X2 . Y) is complex set
- (X2 . Y) is complex set
(X1 . Y) + (- (X2 . Y)) is complex set
((X1 . Y) - (X2 . Y)) * (X ") is complex set
(X1 . Y) * (X ") is complex set
(X2 . Y) * (X ") is complex set
((X1 . Y) * (X ")) - ((X2 . Y) * (X ")) is complex set
- ((X2 . Y) * (X ")) is complex set
((X1 . Y) * (X ")) + (- ((X2 . Y) * (X "))) is complex set
(X1,X) . Y is complex set
((X1,X) . Y) - ((X2 . Y) * (X ")) is complex set
((X1,X) . Y) + (- ((X2 . Y) * (X "))) is complex set
(X2,X) . Y is complex set
((X1,X) . Y) - ((X2,X) . Y) is complex set
- ((X2,X) . Y) is complex set
((X1,X) . Y) + (- ((X2,X) . Y)) is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
X2 is Relation-like Function-like complex-valued set
X1 (#) X2 is Relation-like Function-like complex-valued set
((X1 (#) X2),X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) (X1 (#) X2) is Relation-like Function-like complex-valued set
(X2,X) is Relation-like Function-like complex-valued set
(1 / X) (#) X2 is Relation-like Function-like complex-valued set
X1 (#) (X2,X) is Relation-like Function-like complex-valued set
dom ((X1 (#) X2),X) is set
dom (X1 (#) X2) is set
dom X1 is set
dom X2 is set
(dom X1) /\ (dom X2) is set
dom (X2,X) is set
dom (X1 (#) (X2,X)) is set
Y is set
((X1 (#) X2),X) . Y is complex set
(X1 (#) (X2,X)) . Y is complex set
(X1 (#) X2) . Y is complex set
((X1 (#) X2) . Y) * (X ") is complex set
X1 . Y is complex set
X2 . Y is complex set
(X1 . Y) * (X2 . Y) is complex set
((X1 . Y) * (X2 . Y)) * (X ") is complex set
(X2 . Y) * (X ") is complex set
(X1 . Y) * ((X2 . Y) * (X ")) is complex set
(X2,X) . Y is complex set
(X1 . Y) * ((X2,X) . Y) is complex set
X is complex set
X1 is Relation-like Function-like complex-valued set
X2 is Relation-like Function-like complex-valued set
X1 /" X2 is Relation-like Function-like complex-valued set
X2 " is Relation-like Function-like complex-valued set
X1 (#) (X2 ") is Relation-like Function-like complex-valued set
((X1 /" X2),X) is Relation-like Function-like complex-valued set
1 / X is complex set
X " is complex set
1 * (X ") is complex set
(1 / X) (#) (X1 /" X2) is Relation-like Function-like complex-valued set
X (#) X2 is Relation-like Function-like complex-valued set
X1 /" (X (#) X2) is Relation-like Function-like complex-valued set
(X (#) X2) " is Relation-like Function-like complex-valued set
X1 (#) ((X (#) X2) ") is Relation-like Function-like complex-valued set
dom ((X1 /" X2),X) is set
dom (X1 /" X2) is set
dom X1 is set
dom X2 is set
(dom X1) /\ (dom X2) is set
dom (X (#) X2) is set
dom (X1 /" (X (#) X2)) is set
Y is set
((X1 /" X2),X) . Y is complex set
(X1 /" (X (#) X2)) . Y is complex set
(X1 /" X2) . Y is complex set
((X1 /" X2) . Y) * (X ") is complex set
X1 . Y is complex set
X2 . Y is complex set
(X1 . Y) / (X2 . Y) is complex set
(X2 . Y) " is complex set
(X1 . Y) * ((X2 . Y) ") is complex set
((X1 . Y) / (X2 . Y)) / X is complex set
((X1 . Y) / (X2 . Y)) * (X ") is complex set
(X2 . Y) * X is complex set
(X1 . Y) / ((X2 . Y) * X) is complex set
((X2 . Y) * X) " is complex set
(X1 . Y) * (((X2 . Y) * X) ") is complex set
(X (#) X2) . Y is complex set
(X1 . Y) / ((X (#) X2) . Y) is complex set
((X (#) X2) . Y) " is complex set
(X1 . Y) * (((X (#) X2) . Y) ") is complex set
X is Relation-like Function-like () set
dom X is set
X1 is Relation-like Function-like set
dom X1 is set
X1 is Relation-like Function-like set
dom X1 is set
X2 is Relation-like Function-like set
dom X2 is set
Y is set
X1 . Y is set
X2 . Y is set
X . Y is Relation-like Function-like complex-valued set
- (X . Y) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X . Y) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X2) is set
dom X2 is Element of K19(X)
K19(X) is set
rng (X2) is set
Y1 is set
Y2 is set
(X2) . Y2 is set
X2 . Y2 is Relation-like Function-like complex-valued set
- (X2 . Y2) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X2 . Y2) is Relation-like Function-like complex-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like Function-like complex-valued set
X2 . Y2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
- (X2 . Y2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X2 . Y2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . Y2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
- (X2 . Y2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X2 . Y2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () () () () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . Y2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
- (X2 . Y2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (X2 . Y2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),INT)) is set
X is functional () set
X1 is Relation-like NAT -defined X -valued Function-like V60() FinSequence-like FinSubsequence-like () FinSequence of X
(NAT,X,X1) is Relation-like NAT -defined ((X)) -valued Function-like () Element of K19(K20(NAT,((X))))
(X) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X : verum } is set
((X)) is functional () set
K20(NAT,((X))) is Relation-like set
K19(K20(NAT,((X)))) is set
dom (NAT,X,X1) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of K19(NAT)
dom X1 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of K19(NAT)
X2 is complex epsilon-transitive epsilon-connected ordinal natural V37() real integer rational set
Seg X2 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V60() V71(X2) Element of K19(NAT)
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,((X1)),(X,X1,X2)) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
dom (X,((X1)),(X,X1,X2)) is Element of K19(X)
dom (X,((X1)),(X,X1,X2)) is set
Y1 is set
(X,((X1)),(X,X1,X2)) . Y1 is Relation-like Function-like complex-valued set
X2 . Y1 is Relation-like Function-like complex-valued set
(X,X1,X2) . Y1 is Relation-like Function-like complex-valued set
- ((X,X1,X2) . Y1) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) ((X,X1,X2) . Y1) is Relation-like Function-like complex-valued set
- (X2 . Y1) is Relation-like Function-like complex-valued set
(- 1) (#) (X2 . Y1) is Relation-like Function-like complex-valued set
- (- (X2 . Y1)) is Relation-like Function-like complex-valued set
(- 1) (#) (- (X2 . Y1)) is Relation-like Function-like complex-valued set
X is set
X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
(X,X2,Y1) is Relation-like X -defined ((X2)) -valued Function-like () Element of K19(K20(X,((X2))))
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
((X2)) is functional () set
K20(X,((X2))) is Relation-like set
K19(K20(X,((X2)))) is set
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X1,Y,Y2) is Relation-like X1 -defined ((Y)) -valued Function-like () Element of K19(K20(X1,((Y))))
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
((Y)) is functional () set
K20(X1,((Y))) is Relation-like set
K19(K20(X1,((Y)))) is set
dom (X,X2,Y1) is Element of K19(X)
K19(X) is set
dom Y1 is Element of K19(X)
dom Y2 is Element of K19(X1)
K19(X1) is set
dom Y1 is set
f is set
Y1 . f is Relation-like Function-like complex-valued set
Y2 . f is Relation-like Function-like complex-valued set
- (Y1 . f) is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) (Y1 . f) is Relation-like Function-like complex-valued set
- (- (Y1 . f)) is Relation-like Function-like complex-valued set
(- 1) (#) (- (Y1 . f)) is Relation-like Function-like complex-valued set
(X,X2,Y1) . f is Relation-like Function-like complex-valued set
- ((X,X2,Y1) . f) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X2,Y1) . f) is Relation-like Function-like complex-valued set
- (Y2 . f) is Relation-like Function-like complex-valued set
(- 1) (#) (Y2 . f) is Relation-like Function-like complex-valued set
- (- (Y2 . f)) is Relation-like Function-like complex-valued set
(- 1) (#) (- (Y2 . f)) is Relation-like Function-like complex-valued set
X is functional () set
X1 is set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like Element of K19(K20(X,X1))
dom X2 is functional () Element of K19(X)
K19(X) is set
Y is set
Y1 is Relation-like Function-like complex-valued set
- Y1 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) Y1 is Relation-like Function-like complex-valued set
X2 . (- Y1) is set
Y is Relation-like Function-like set
dom Y is set
Y1 is Relation-like Function-like complex-valued set
Y . Y1 is set
- Y1 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) Y1 is Relation-like Function-like complex-valued set
X2 . (- Y1) is set
Y2 is Relation-like Function-like complex-valued set
- Y2 is Relation-like Function-like complex-valued set
(- 1) (#) Y2 is Relation-like Function-like complex-valued set
X2 . (- Y2) is set
Y is Relation-like Function-like set
dom Y is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is set
Y . Y2 is set
Y1 . Y2 is set
f is Relation-like Function-like complex-valued set
- f is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) f is Relation-like Function-like complex-valued set
X2 . (- f) is set
X is Relation-like Function-like () set
dom X is set
X1 is Relation-like Function-like set
dom X1 is set
X1 is Relation-like Function-like set
dom X1 is set
X2 is Relation-like Function-like set
dom X2 is set
Y is set
X1 . Y is set
X2 . Y is set
X . Y is Relation-like Function-like complex-valued set
(X . Y) " is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X2) is set
dom X2 is Element of K19(X)
K19(X) is set
rng (X2) is set
Y1 is set
Y2 is set
(X2) . Y2 is set
X2 . Y2 is Relation-like Function-like complex-valued set
(X2 . Y2) " is Relation-like Function-like complex-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like Function-like complex-valued set
X2 . Y2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
(X2 . Y2) " is Relation-like Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . Y2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(X2 . Y2) " is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is functional () set
X1 is Relation-like NAT -defined X -valued Function-like V60() FinSequence-like FinSubsequence-like () FinSequence of X
(NAT,X,X1) is Relation-like NAT -defined ((X)) -valued Function-like () Element of K19(K20(NAT,((X))))
(X) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X : verum } is set
((X)) is functional () set
K20(NAT,((X))) is Relation-like set
K19(K20(NAT,((X)))) is set
dom (NAT,X,X1) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of K19(NAT)
dom X1 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of K19(NAT)
X2 is complex epsilon-transitive epsilon-connected ordinal natural V37() real integer rational set
Seg X2 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V60() V71(X2) Element of K19(NAT)
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,((X1)),(X,X1,X2)) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
dom (X,((X1)),(X,X1,X2)) is Element of K19(X)
dom (X,((X1)),(X,X1,X2)) is set
Y1 is set
(X,((X1)),(X,X1,X2)) . Y1 is Relation-like Function-like complex-valued set
X2 . Y1 is Relation-like Function-like complex-valued set
(X,X1,X2) . Y1 is Relation-like Function-like complex-valued set
((X,X1,X2) . Y1) " is Relation-like Function-like complex-valued set
(X2 . Y1) " is Relation-like Function-like complex-valued set
((X2 . Y1) ") " is Relation-like Function-like complex-valued set
X is Relation-like Function-like () set
dom X is set
X1 is Relation-like Function-like set
dom X1 is set
X1 is Relation-like Function-like set
dom X1 is set
X2 is Relation-like Function-like set
dom X2 is set
Y is set
X1 . Y is set
X2 . Y is set
X . Y is Relation-like Function-like complex-valued set
|.(X . Y).| is Relation-like Function-like complex-valued ext-real-valued real-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X2) is set
dom X2 is Element of K19(X)
K19(X) is set
rng (X2) is set
Y1 is set
Y2 is set
(X2) . Y2 is set
X2 . Y2 is Relation-like Function-like complex-valued set
|.(X2 . Y2).| is Relation-like Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like Function-like complex-valued set
X2 . Y2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
|.(X2 . Y2).| is Relation-like Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . Y2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
|.(X2 . Y2).| is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
(X2) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2) is functional () () () () Element of K19(((X1)))
K19(((X1))) is set
Y1 is set
Y2 is set
(X,X1,X2) . Y2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . Y2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
|.(X2 . Y2).| is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
f is Relation-like Function-like set
rng f is set
f1 is set
dom (X2 . Y2) is set
dom f is set
K20((X1),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20((X1),NAT)) is set
X is functional () set
X1 is Relation-like NAT -defined X -valued Function-like V60() FinSequence-like FinSubsequence-like () FinSequence of X
(NAT,X,X1) is Relation-like NAT -defined ((X)) -valued Function-like () Element of K19(K20(NAT,((X))))
(X) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X : verum } is set
((X)) is functional () set
K20(NAT,((X))) is Relation-like set
K19(K20(NAT,((X)))) is set
dom (NAT,X,X1) is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of K19(NAT)
dom X1 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered Element of K19(NAT)
X2 is complex epsilon-transitive epsilon-connected ordinal natural V37() real integer rational set
Seg X2 is complex-membered ext-real-membered real-membered rational-membered integer-membered natural-membered V60() V71(X2) Element of K19(NAT)
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,((X1)),(X,X1,X2)) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
dom (X,((X1)),(X,X1,X2)) is Element of K19(X)
K19(X) is set
dom (X,X1,X2) is Element of K19(X)
dom (X,((X1)),(X,X1,X2)) is set
Y1 is set
(X,((X1)),(X,X1,X2)) . Y1 is Relation-like Function-like complex-valued set
(X,X1,X2) . Y1 is Relation-like Function-like complex-valued set
|.((X,X1,X2) . Y1).| is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . Y1 is Relation-like Function-like complex-valued set
|.(X2 . Y1).| is Relation-like Function-like complex-valued ext-real-valued real-valued set
|.|.(X2 . Y1).|.| is Relation-like Function-like complex-valued ext-real-valued real-valued set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is complex set
dom X1 is set
Y is Relation-like Function-like set
dom Y is set
Y is Relation-like Function-like set
dom Y is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is set
Y . Y2 is set
Y1 . Y2 is set
X1 . Y2 is Relation-like Function-like complex-valued set
X2 + (X1 . Y2) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is complex set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X1,X2,Y) is set
dom X2 is Element of K19(X)
K19(X) is set
rng (X1,X2,Y) is set
Y2 is set
f is set
(X1,X2,Y) . f is set
X2 . f is Relation-like Function-like complex-valued set
Y + (X2 . f) is Relation-like Function-like complex-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is complex V37() real set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y + (X2 . f) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is complex V37() real rational set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y + (X2 . f) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
Y is complex V37() real integer rational set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y + (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),INT)) is set
X is set
X1 is functional () () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () () Element of K19(K20(X,X1))
Y is complex epsilon-transitive epsilon-connected ordinal natural V37() real integer rational set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
Y + (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20((X1),NAT)) is set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
X2 + Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,((X1)),(X,X1,Y1,X2),Y) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
(X,X1,Y1,(X2 + Y)) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
dom (X,((X1)),(X,X1,Y1,X2),Y) is Element of K19(X)
K19(X) is set
dom (X,X1,Y1,X2) is Element of K19(X)
dom Y1 is Element of K19(X)
dom (X,X1,Y1,(X2 + Y)) is Element of K19(X)
dom (X,((X1)),(X,X1,Y1,X2),Y) is set
f is set
(X,((X1)),(X,X1,Y1,X2),Y) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,(X2 + Y)) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,X2) . f is Relation-like Function-like complex-valued set
Y + ((X,X1,Y1,X2) . f) is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
X2 + (Y1 . f) is Relation-like Function-like complex-valued set
Y + (X2 + (Y1 . f)) is Relation-like Function-like complex-valued set
(X2 + Y) + (Y1 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,Y1,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
dom Y1 is Element of K19(X)
K19(X) is set
Y2 is set
Y1 . Y2 is Relation-like Function-like complex-valued set
rng Y1 is functional () Element of K19(X1)
K19(X1) is set
dom (X,X1,Y1,Y) is Element of K19(X)
(X,X1,Y1,Y) . Y2 is Relation-like Function-like complex-valued set
Y + (Y1 . Y2) is Relation-like Function-like complex-valued set
dom (X,X1,Y1,X2) is Element of K19(X)
(X,X1,Y1,X2) . Y2 is Relation-like Function-like complex-valued set
X2 + (Y1 . Y2) is Relation-like Function-like complex-valued set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is complex set
- X2 is complex set
(X,X1,(- X2)) is Relation-like Function-like set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
Y is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
X2 is complex set
(X1,Y,X2) is Relation-like Function-like set
- X2 is complex set
(X1,Y,(- X2)) is Relation-like Function-like set
dom (X1,Y,X2) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y is complex set
(X2,Y1,Y) is Relation-like Function-like set
- Y is complex set
(X2,Y1,(- Y)) is Relation-like Function-like set
dom (X2,Y1,Y) is set
(X2,Y1,Y) . X1 is set
Y1 . X1 is Relation-like Function-like complex-valued set
(Y1 . X1) - Y is Relation-like Function-like complex-valued set
(- Y) + (Y1 . X1) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is complex set
(X1,X2,Y) is Relation-like Function-like set
- Y is complex set
(X1,X2,(- Y)) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,(- Y)) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is complex V37() real set
(X1,X2,Y) is Relation-like Function-like set
- Y is complex V37() real set
(X1,X2,(- Y)) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,(- Y)) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is complex V37() real rational set
(X1,X2,Y) is Relation-like Function-like set
- Y is complex V37() real rational set
(X1,X2,(- Y)) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,(- Y)) is Relation-like X -defined ((X1)) -valued Function-like () () () () Element of K19(K20(X,((X1))))
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
Y is complex V37() real integer rational set
(X1,X2,Y) is Relation-like Function-like set
- Y is complex V37() real integer rational set
(X1,X2,(- Y)) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,(- Y)) is Relation-like X -defined ((X1)) -valued Function-like () () () () () Element of K19(K20(X,((X1))))
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
- X2 is complex set
(X1,Y1,(- X2)) is Relation-like Function-like set
(X,X1,Y1,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
- Y is complex set
(X1,Y1,(- Y)) is Relation-like Function-like set
dom Y1 is Element of K19(X)
K19(X) is set
Y2 is set
Y1 . Y2 is Relation-like Function-like complex-valued set
rng Y1 is functional () Element of K19(X1)
K19(X1) is set
dom (X,X1,Y1,Y) is Element of K19(X)
(X,X1,Y1,Y) . Y2 is Relation-like Function-like complex-valued set
(Y1 . Y2) - Y is Relation-like Function-like complex-valued set
(- Y) + (Y1 . Y2) is Relation-like Function-like complex-valued set
dom (X,X1,Y1,X2) is Element of K19(X)
(X,X1,Y1,X2) . Y2 is Relation-like Function-like complex-valued set
(Y1 . Y2) - X2 is Relation-like Function-like complex-valued set
(- X2) + (Y1 . Y2) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
X2 - Y is complex set
- Y is complex set
X2 + (- Y) is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,((X1)),(X,X1,Y1,X2),Y) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
(((X1)),(X,X1,Y1,X2),(- Y)) is Relation-like Function-like set
(X,X1,Y1,(X2 - Y)) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
dom (X,((X1)),(X,X1,Y1,X2),Y) is Element of K19(X)
K19(X) is set
dom (X,X1,Y1,X2) is Element of K19(X)
dom Y1 is Element of K19(X)
dom (X,X1,Y1,(X2 - Y)) is Element of K19(X)
dom (X,((X1)),(X,X1,Y1,X2),Y) is set
f is set
(X,((X1)),(X,X1,Y1,X2),Y) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,(X2 - Y)) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,X2) . f is Relation-like Function-like complex-valued set
((X,X1,Y1,X2) . f) - Y is Relation-like Function-like complex-valued set
(- Y) + ((X,X1,Y1,X2) . f) is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
X2 + (Y1 . f) is Relation-like Function-like complex-valued set
(X2 + (Y1 . f)) - Y is Relation-like Function-like complex-valued set
(- Y) + (X2 + (Y1 . f)) is Relation-like Function-like complex-valued set
(X2 - Y) + (Y1 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
X2 - Y is complex set
- Y is complex set
X2 + (- Y) is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
- X2 is complex set
(X1,Y1,(- X2)) is Relation-like Function-like set
(X,((X1)),(X,X1,Y1,X2),Y) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
(X,X1,Y1,(X2 - Y)) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
- (X2 - Y) is complex set
(X1,Y1,(- (X2 - Y))) is Relation-like Function-like set
dom (X,((X1)),(X,X1,Y1,X2),Y) is Element of K19(X)
K19(X) is set
dom (X,X1,Y1,X2) is Element of K19(X)
dom Y1 is Element of K19(X)
dom (X,X1,Y1,(X2 - Y)) is Element of K19(X)
dom (X,((X1)),(X,X1,Y1,X2),Y) is set
f is set
(X,((X1)),(X,X1,Y1,X2),Y) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,(X2 - Y)) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,X2) . f is Relation-like Function-like complex-valued set
Y + ((X,X1,Y1,X2) . f) is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
(Y1 . f) - X2 is Relation-like Function-like complex-valued set
(- X2) + (Y1 . f) is Relation-like Function-like complex-valued set
Y + ((Y1 . f) - X2) is Relation-like Function-like complex-valued set
(Y1 . f) - (X2 - Y) is Relation-like Function-like complex-valued set
(- (X2 - Y)) + (Y1 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
X2 + Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
- X2 is complex set
(X1,Y1,(- X2)) is Relation-like Function-like set
(X,((X1)),(X,X1,Y1,X2),Y) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
- Y is complex set
(((X1)),(X,X1,Y1,X2),(- Y)) is Relation-like Function-like set
(X,X1,Y1,(X2 + Y)) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
- (X2 + Y) is complex set
(X1,Y1,(- (X2 + Y))) is Relation-like Function-like set
dom (X,((X1)),(X,X1,Y1,X2),Y) is Element of K19(X)
K19(X) is set
dom (X,X1,Y1,X2) is Element of K19(X)
dom Y1 is Element of K19(X)
dom (X,X1,Y1,(X2 + Y)) is Element of K19(X)
dom (X,((X1)),(X,X1,Y1,X2),Y) is set
f is set
(X,((X1)),(X,X1,Y1,X2),Y) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,(X2 + Y)) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,X2) . f is Relation-like Function-like complex-valued set
((X,X1,Y1,X2) . f) - Y is Relation-like Function-like complex-valued set
(- Y) + ((X,X1,Y1,X2) . f) is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
(Y1 . f) - X2 is Relation-like Function-like complex-valued set
(- X2) + (Y1 . f) is Relation-like Function-like complex-valued set
((Y1 . f) - X2) - Y is Relation-like Function-like complex-valued set
(- Y) + ((Y1 . f) - X2) is Relation-like Function-like complex-valued set
(Y1 . f) - (X2 + Y) is Relation-like Function-like complex-valued set
(- (X2 + Y)) + (Y1 . f) is Relation-like Function-like complex-valued set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is complex set
dom X1 is set
Y is Relation-like Function-like set
dom Y is set
Y is Relation-like Function-like set
dom Y is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is set
Y . Y2 is set
Y1 . Y2 is set
X1 . Y2 is Relation-like Function-like complex-valued set
X2 (#) (X1 . Y2) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is complex set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X1,X2,Y) is set
dom X2 is Element of K19(X)
K19(X) is set
rng (X1,X2,Y) is set
Y2 is set
f is set
(X1,X2,Y) . f is set
X2 . f is Relation-like Function-like complex-valued set
Y (#) (X2 . f) is Relation-like Function-like complex-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is complex V37() real set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y (#) (X2 . f) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is complex V37() real rational set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y (#) (X2 . f) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
Y is complex V37() real integer rational set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y (#) (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),INT)) is set
X is set
X1 is functional () () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () () Element of K19(K20(X,X1))
Y is complex epsilon-transitive epsilon-connected ordinal natural V37() real integer rational set
(X1,X2,Y) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
dom (X,X1,X2,Y) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
Y (#) (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20((X1),NAT)) is set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
X2 * Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,((X1)),(X,X1,Y1,X2),Y) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
(X,X1,Y1,(X2 * Y)) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
dom (X,((X1)),(X,X1,Y1,X2),Y) is Element of K19(X)
K19(X) is set
dom (X,X1,Y1,X2) is Element of K19(X)
dom Y1 is Element of K19(X)
dom (X,X1,Y1,(X2 * Y)) is Element of K19(X)
dom (X,((X1)),(X,X1,Y1,X2),Y) is set
f is set
(X,((X1)),(X,X1,Y1,X2),Y) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,(X2 * Y)) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,X2) . f is Relation-like Function-like complex-valued set
Y (#) ((X,X1,Y1,X2) . f) is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
X2 (#) (Y1 . f) is Relation-like Function-like complex-valued set
Y (#) (X2 (#) (Y1 . f)) is Relation-like Function-like complex-valued set
(X2 * Y) (#) (Y1 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
dom Y1 is Element of K19(X)
K19(X) is set
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,Y1,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
Y2 is set
dom (X,X1,Y1,Y) is Element of K19(X)
(X,X1,Y1,Y) . Y2 is Relation-like Function-like complex-valued set
Y1 . Y2 is Relation-like Function-like complex-valued set
Y (#) (Y1 . Y2) is Relation-like Function-like complex-valued set
dom (X,X1,Y1,X2) is Element of K19(X)
(X,X1,Y1,X2) . Y2 is Relation-like Function-like complex-valued set
X2 (#) (Y1 . Y2) is Relation-like Function-like complex-valued set
rng Y1 is functional () Element of K19(X1)
K19(X1) is set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is complex set
X2 " is complex set
(X,X1,(X2 ")) is Relation-like Function-like set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
Y is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
X2 is complex set
(X1,Y,X2) is Relation-like Function-like set
X2 " is complex set
(X1,Y,(X2 ")) is Relation-like Function-like set
dom (X1,Y,X2) is set
dom Y is Element of K19(X)
K19(X) is set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y is complex set
(X2,Y1,Y) is Relation-like Function-like set
Y " is complex set
(X2,Y1,(Y ")) is Relation-like Function-like set
dom (X2,Y1,Y) is set
(X2,Y1,Y) . X1 is set
Y1 . X1 is Relation-like Function-like complex-valued set
(Y ") (#) (Y1 . X1) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is complex set
(X1,X2,Y) is Relation-like Function-like set
Y " is complex set
(X1,X2,(Y ")) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,(Y ")) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is complex V37() real set
(X1,X2,Y) is Relation-like Function-like set
Y " is complex V37() real set
(X1,X2,(Y ")) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
((X1)) is functional () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,(Y ")) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is complex V37() real rational set
(X1,X2,Y) is Relation-like Function-like set
Y " is complex V37() real rational set
(X1,X2,(Y ")) is Relation-like Function-like set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,Y) is Relation-like X -defined ((X1)) -valued Function-like () () () Element of K19(K20(X,((X1))))
((X1)) is functional () () () set
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
(X,X1,X2,(Y ")) is Relation-like X -defined ((X1)) -valued Function-like () () () () Element of K19(K20(X,((X1))))
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
X2 * Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
X2 " is complex set
(X1,Y1,(X2 ")) is Relation-like Function-like set
(X,((X1)),(X,X1,Y1,X2),Y) is Relation-like X -defined ((((X1)))) -valued Function-like () Element of K19(K20(X,((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(X,((((X1))))) is Relation-like set
K19(K20(X,((((X1)))))) is set
Y " is complex set
(((X1)),(X,X1,Y1,X2),(Y ")) is Relation-like Function-like set
(X,X1,Y1,(X2 * Y)) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
(X2 * Y) " is complex set
(X1,Y1,((X2 * Y) ")) is Relation-like Function-like set
dom (X,((X1)),(X,X1,Y1,X2),Y) is Element of K19(X)
K19(X) is set
dom (X,X1,Y1,X2) is Element of K19(X)
dom Y1 is Element of K19(X)
dom (X,X1,Y1,(X2 * Y)) is Element of K19(X)
dom (X,((X1)),(X,X1,Y1,X2),Y) is set
f is set
(X,((X1)),(X,X1,Y1,X2),Y) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,(X2 * Y)) . f is Relation-like Function-like complex-valued set
(X,X1,Y1,X2) . f is Relation-like Function-like complex-valued set
(Y ") (#) ((X,X1,Y1,X2) . f) is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
(X2 ") (#) (Y1 . f) is Relation-like Function-like complex-valued set
(Y ") (#) ((X2 ") (#) (Y1 . f)) is Relation-like Function-like complex-valued set
(X2 ") * (Y ") is complex set
((X2 ") * (Y ")) (#) (Y1 . f) is Relation-like Function-like complex-valued set
((X2 * Y) ") (#) (Y1 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is complex set
Y is complex set
Y1 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
dom Y1 is Element of K19(X)
K19(X) is set
(X,X1,Y1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
X2 " is complex set
(X1,Y1,(X2 ")) is Relation-like Function-like set
(X,X1,Y1,Y) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
Y " is complex set
(X1,Y1,(Y ")) is Relation-like Function-like set
Y2 is set
dom (X,X1,Y1,Y) is Element of K19(X)
(X,X1,Y1,Y) . Y2 is Relation-like Function-like complex-valued set
Y1 . Y2 is Relation-like Function-like complex-valued set
((Y1 . Y2),Y) is Relation-like Function-like complex-valued set
1 / Y is complex set
1 * (Y ") is complex set
(1 / Y) (#) (Y1 . Y2) is Relation-like Function-like complex-valued set
dom (X,X1,Y1,X2) is Element of K19(X)
(X,X1,Y1,X2) . Y2 is Relation-like Function-like complex-valued set
((Y1 . Y2),X2) is Relation-like Function-like complex-valued set
1 / X2 is complex set
1 * (X2 ") is complex set
(1 / X2) (#) (Y1 . Y2) is Relation-like Function-like complex-valued set
rng Y1 is functional () Element of K19(X1)
K19(X1) is set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is Relation-like Function-like complex-valued set
dom X1 is set
dom X2 is set
(dom X1) /\ (dom X2) is set
Y is Relation-like Function-like set
dom Y is set
Y is Relation-like Function-like set
dom Y is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is set
Y . Y2 is set
Y1 . Y2 is set
X1 . Y2 is Relation-like Function-like complex-valued set
X2 . Y2 is complex set
(X2 . Y2) + (X1 . Y2) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X1,X2,Y) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X1,X2,Y) is set
Y2 is set
f is set
(X1,X2,Y) . f is set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(Y . f) + (X2 . f) is Relation-like Function-like complex-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real set
(Y . f) + (X2 . f) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real rational set
(Y . f) + (X2 . f) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
Y is Relation-like INT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real integer rational set
(Y . f) + (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),INT)) is set
X is set
X1 is functional () () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () () Element of K19(K20(X,X1))
Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
Y . f is complex epsilon-transitive epsilon-connected ordinal natural V37() real integer rational set
(Y . f) + (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20((X1),NAT)) is set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
Y1 is Relation-like Function-like complex-valued set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Relation-like (X /\ (dom Y)) /\ (dom Y1) -defined ((((X1)))) -valued Function-like () Element of K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))))
dom Y1 is set
(X /\ (dom Y)) /\ (dom Y1) is set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))) is Relation-like set
K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1)))))) is set
Y + Y1 is Relation-like Function-like complex-valued set
(X,X1,X2,(Y + Y1)) is Relation-like X /\ (dom (Y + Y1)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (Y + Y1))),((X1))))
dom (Y + Y1) is set
X /\ (dom (Y + Y1)) is set
K20((X /\ (dom (Y + Y1))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y + Y1))),((X1)))) is set
(dom Y) /\ (dom Y1) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Element of K19(((X /\ (dom Y)) /\ (dom Y1)))
K19(((X /\ (dom Y)) /\ (dom Y1))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
(dom (X,X1,X2,Y)) /\ (dom Y1) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(Y + Y1)) is Element of K19((X /\ (dom (Y + Y1))))
K19((X /\ (dom (Y + Y1)))) is set
(dom X2) /\ (dom (Y + Y1)) is Element of K19(X)
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) . f is Relation-like Function-like complex-valued set
(X,X1,X2,(Y + Y1)) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
Y1 . f is complex set
(Y1 . f) + ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(Y . f) + (X2 . f) is Relation-like Function-like complex-valued set
(Y1 . f) + ((Y . f) + (X2 . f)) is Relation-like Function-like complex-valued set
(Y . f) + (Y1 . f) is complex set
((Y . f) + (Y1 . f)) + (X2 . f) is Relation-like Function-like complex-valued set
(Y + Y1) . f is complex set
((Y + Y1) . f) + (X2 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is Relation-like X /\ (dom Y) -defined ((((X1)))) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20((X /\ (dom Y)),((((X1))))) is Relation-like set
K19(K20((X /\ (dom Y)),((((X1)))))) is set
- Y is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X,((X1)),(X,X1,X2),(- Y)) is Relation-like X /\ (dom (- Y)) -defined ((((X1)))) -valued Function-like () Element of K19(K20((X /\ (dom (- Y))),((((X1))))))
dom (- Y) is set
X /\ (dom (- Y)) is set
K20((X /\ (dom (- Y))),((((X1))))) is Relation-like set
K19(K20((X /\ (dom (- Y))),((((X1)))))) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2) is Element of K19(X)
dom (X,((X1)),(X,X1,X2),(- Y)) is Element of K19((X /\ (dom (- Y))))
K19((X /\ (dom (- Y)))) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) . f is Relation-like Function-like complex-valued set
(X,((X1)),(X,X1,X2),(- Y)) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(Y . f) + (X2 . f) is Relation-like Function-like complex-valued set
- ((Y . f) + (X2 . f)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y . f) + (X2 . f)) is Relation-like Function-like complex-valued set
- (X2 . f) is Relation-like Function-like complex-valued set
(- 1) (#) (X2 . f) is Relation-like Function-like complex-valued set
(- (X2 . f)) - (Y . f) is Relation-like Function-like complex-valued set
- (Y . f) is complex set
(- (Y . f)) + (- (X2 . f)) is Relation-like Function-like complex-valued set
(- Y) . f is complex set
((- Y) . f) + (- (X2 . f)) is Relation-like Function-like complex-valued set
(X,X1,X2) . f is Relation-like Function-like complex-valued set
((- Y) . f) + ((X,X1,X2) . f) is Relation-like Function-like complex-valued set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is Relation-like Function-like complex-valued set
- X2 is Relation-like Function-like complex-valued set
- 1 is non empty complex V37() real integer rational set
(- 1) (#) X2 is Relation-like Function-like complex-valued set
(X,X1,(- X2)) is Relation-like Function-like set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
dom X2 is Element of K19(X)
K19(X) is set
Y is Relation-like Function-like complex-valued set
(X1,X2,Y) is Relation-like Function-like set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
dom (X1,X2,Y) is set
dom Y is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (- Y) is set
(dom X2) /\ (dom (- Y)) is Element of K19(X)
X is set
X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y . X1 is Relation-like Function-like complex-valued set
Y1 is Relation-like Function-like complex-valued set
(X2,Y,Y1) is Relation-like Function-like set
- Y1 is Relation-like Function-like complex-valued set
(- 1) (#) Y1 is Relation-like Function-like complex-valued set
(X2,Y,(- Y1)) is Relation-like Function-like set
dom (X2,Y,Y1) is set
(X2,Y,Y1) . X1 is set
Y1 . X1 is complex set
(Y . X1) - (Y1 . X1) is Relation-like Function-like complex-valued set
- (Y1 . X1) is complex set
(- (Y1 . X1)) + (Y . X1) is Relation-like Function-like complex-valued set
(- Y1) . X1 is complex set
((- Y1) . X1) + (Y . X1) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
(X1,X2,Y) is Relation-like Function-like set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X1,X2,Y) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X1,X2,Y) is set
Y2 is set
f is set
(X1,X2,Y) . f is set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(X2 . f) - (Y . f) is Relation-like Function-like complex-valued set
- (Y . f) is complex set
(- (Y . f)) + (X2 . f) is Relation-like Function-like complex-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
- Y is Relation-like Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued ext-real-valued real-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real set
(X2 . f) - (Y . f) is Relation-like Function-like complex-valued ext-real-valued real-valued set
- (Y . f) is complex V37() real set
(- (Y . f)) + (X2 . f) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
- Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real rational set
(X2 . f) - (Y . f) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
- (Y . f) is complex V37() real rational set
(- (Y . f)) + (X2 . f) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
Y is Relation-like INT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
- Y is Relation-like INT -valued Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) Y is Relation-like INT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real integer rational set
(X2 . f) - (Y . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
- (Y . f) is complex V37() real integer rational set
(- (Y . f)) + (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),INT)) is set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X,X1,X2,(- Y)) is Relation-like X /\ (dom (- Y)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (- Y))),((X1))))
dom (- Y) is set
X /\ (dom (- Y)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20((X /\ (dom (- Y))),((X1))) is Relation-like set
K19(K20((X /\ (dom (- Y))),((X1)))) is set
- (- Y) is Relation-like Function-like complex-valued set
(- 1) (#) (- Y) is Relation-like Function-like complex-valued set
(X1,X2,(- (- Y))) is Relation-like Function-like set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
dom Y is set
X /\ (dom Y) is set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is Relation-like X /\ (dom Y) -defined ((((X1)))) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((((X1))))))
K20((X /\ (dom Y)),((((X1))))) is Relation-like set
K19(K20((X /\ (dom Y)),((((X1)))))) is set
(X,((X1)),(X,X1,X2),Y) is Relation-like X /\ (dom Y) -defined ((((X1)))) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((((X1))))))
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2) is Element of K19(X)
dom (X,((X1)),(X,X1,X2),Y) is Element of K19((X /\ (dom Y)))
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) . f is Relation-like Function-like complex-valued set
(X,((X1)),(X,X1,X2),Y) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(X2 . f) - (Y . f) is Relation-like Function-like complex-valued set
- (Y . f) is complex set
(- (Y . f)) + (X2 . f) is Relation-like Function-like complex-valued set
- ((X2 . f) - (Y . f)) is Relation-like Function-like complex-valued set
(- 1) (#) ((X2 . f) - (Y . f)) is Relation-like Function-like complex-valued set
- (X2 . f) is Relation-like Function-like complex-valued set
(- 1) (#) (X2 . f) is Relation-like Function-like complex-valued set
(Y . f) + (- (X2 . f)) is Relation-like Function-like complex-valued set
(X,X1,X2) . f is Relation-like Function-like complex-valued set
(Y . f) + ((X,X1,X2) . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
Y1 is Relation-like Function-like complex-valued set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Relation-like (X /\ (dom Y)) /\ (dom Y1) -defined ((((X1)))) -valued Function-like () Element of K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))))
dom Y1 is set
(X /\ (dom Y)) /\ (dom Y1) is set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))) is Relation-like set
K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1)))))) is set
- Y1 is Relation-like Function-like complex-valued set
(- 1) (#) Y1 is Relation-like Function-like complex-valued set
(((X1)),(X,X1,X2,Y),(- Y1)) is Relation-like Function-like set
Y - Y1 is Relation-like Function-like complex-valued set
Y + (- Y1) is Relation-like Function-like complex-valued set
(X,X1,X2,(Y - Y1)) is Relation-like X /\ (dom (Y - Y1)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (Y - Y1))),((X1))))
dom (Y - Y1) is set
X /\ (dom (Y - Y1)) is set
K20((X /\ (dom (Y - Y1))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y - Y1))),((X1)))) is set
(dom Y) /\ (dom Y1) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Element of K19(((X /\ (dom Y)) /\ (dom Y1)))
K19(((X /\ (dom Y)) /\ (dom Y1))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
(dom (X,X1,X2,Y)) /\ (dom Y1) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(Y - Y1)) is Element of K19((X /\ (dom (Y - Y1))))
K19((X /\ (dom (Y - Y1)))) is set
(dom X2) /\ (dom (Y - Y1)) is Element of K19(X)
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) . f is Relation-like Function-like complex-valued set
(X,X1,X2,(Y - Y1)) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
Y1 . f is complex set
((X,X1,X2,Y) . f) - (Y1 . f) is Relation-like Function-like complex-valued set
- (Y1 . f) is complex set
(- (Y1 . f)) + ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(Y . f) + (X2 . f) is Relation-like Function-like complex-valued set
((Y . f) + (X2 . f)) - (Y1 . f) is Relation-like Function-like complex-valued set
(- (Y1 . f)) + ((Y . f) + (X2 . f)) is Relation-like Function-like complex-valued set
(Y . f) - (Y1 . f) is complex set
(Y . f) + (- (Y1 . f)) is complex set
((Y . f) - (Y1 . f)) + (X2 . f) is Relation-like Function-like complex-valued set
(Y - Y1) . f is complex set
((Y - Y1) . f) + (X2 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
Y1 is Relation-like Function-like complex-valued set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Relation-like (X /\ (dom Y)) /\ (dom Y1) -defined ((((X1)))) -valued Function-like () Element of K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))))
dom Y1 is set
(X /\ (dom Y)) /\ (dom Y1) is set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))) is Relation-like set
K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1)))))) is set
Y - Y1 is Relation-like Function-like complex-valued set
- Y1 is Relation-like Function-like complex-valued set
(- 1) (#) Y1 is Relation-like Function-like complex-valued set
Y + (- Y1) is Relation-like Function-like complex-valued set
(X,X1,X2,(Y - Y1)) is Relation-like X /\ (dom (Y - Y1)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (Y - Y1))),((X1))))
dom (Y - Y1) is set
X /\ (dom (Y - Y1)) is set
K20((X /\ (dom (Y - Y1))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y - Y1))),((X1)))) is set
- (Y - Y1) is Relation-like Function-like complex-valued set
(- 1) (#) (Y - Y1) is Relation-like Function-like complex-valued set
(X1,X2,(- (Y - Y1))) is Relation-like Function-like set
(dom Y) /\ (dom Y1) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Element of K19(((X /\ (dom Y)) /\ (dom Y1)))
K19(((X /\ (dom Y)) /\ (dom Y1))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
(dom (X,X1,X2,Y)) /\ (dom Y1) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(Y - Y1)) is Element of K19((X /\ (dom (Y - Y1))))
K19((X /\ (dom (Y - Y1)))) is set
(dom X2) /\ (dom (Y - Y1)) is Element of K19(X)
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) . f is Relation-like Function-like complex-valued set
(X,X1,X2,(Y - Y1)) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
Y1 . f is complex set
(Y1 . f) + ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(X2 . f) - (Y . f) is Relation-like Function-like complex-valued set
- (Y . f) is complex set
(- (Y . f)) + (X2 . f) is Relation-like Function-like complex-valued set
(Y1 . f) + ((X2 . f) - (Y . f)) is Relation-like Function-like complex-valued set
(Y . f) - (Y1 . f) is complex set
- (Y1 . f) is complex set
(Y . f) + (- (Y1 . f)) is complex set
(X2 . f) - ((Y . f) - (Y1 . f)) is Relation-like Function-like complex-valued set
- ((Y . f) - (Y1 . f)) is complex set
(- ((Y . f) - (Y1 . f))) + (X2 . f) is Relation-like Function-like complex-valued set
(Y - Y1) . f is complex set
(X2 . f) - ((Y - Y1) . f) is Relation-like Function-like complex-valued set
- ((Y - Y1) . f) is complex set
(- ((Y - Y1) . f)) + (X2 . f) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X1,X2,(- Y)) is Relation-like Function-like set
Y1 is Relation-like Function-like complex-valued set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Relation-like (X /\ (dom Y)) /\ (dom Y1) -defined ((((X1)))) -valued Function-like () Element of K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))))
dom Y1 is set
(X /\ (dom Y)) /\ (dom Y1) is set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))) is Relation-like set
K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1)))))) is set
- Y1 is Relation-like Function-like complex-valued set
(- 1) (#) Y1 is Relation-like Function-like complex-valued set
(((X1)),(X,X1,X2,Y),(- Y1)) is Relation-like Function-like set
Y + Y1 is Relation-like Function-like complex-valued set
(X,X1,X2,(Y + Y1)) is Relation-like X /\ (dom (Y + Y1)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (Y + Y1))),((X1))))
dom (Y + Y1) is set
X /\ (dom (Y + Y1)) is set
K20((X /\ (dom (Y + Y1))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y + Y1))),((X1)))) is set
- (Y + Y1) is Relation-like Function-like complex-valued set
(- 1) (#) (Y + Y1) is Relation-like Function-like complex-valued set
(X1,X2,(- (Y + Y1))) is Relation-like Function-like set
(dom Y) /\ (dom Y1) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Element of K19(((X /\ (dom Y)) /\ (dom Y1)))
K19(((X /\ (dom Y)) /\ (dom Y1))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
(dom (X,X1,X2,Y)) /\ (dom Y1) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(Y + Y1)) is Element of K19((X /\ (dom (Y + Y1))))
K19((X /\ (dom (Y + Y1)))) is set
(dom X2) /\ (dom (Y + Y1)) is Element of K19(X)
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) . f is Relation-like Function-like complex-valued set
(X,X1,X2,(Y + Y1)) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
Y1 . f is complex set
((X,X1,X2,Y) . f) - (Y1 . f) is Relation-like Function-like complex-valued set
- (Y1 . f) is complex set
(- (Y1 . f)) + ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(X2 . f) - (Y . f) is Relation-like Function-like complex-valued set
- (Y . f) is complex set
(- (Y . f)) + (X2 . f) is Relation-like Function-like complex-valued set
((X2 . f) - (Y . f)) - (Y1 . f) is Relation-like Function-like complex-valued set
(- (Y1 . f)) + ((X2 . f) - (Y . f)) is Relation-like Function-like complex-valued set
(Y . f) + (Y1 . f) is complex set
(X2 . f) - ((Y . f) + (Y1 . f)) is Relation-like Function-like complex-valued set
- ((Y . f) + (Y1 . f)) is complex set
(- ((Y . f) + (Y1 . f))) + (X2 . f) is Relation-like Function-like complex-valued set
(Y + Y1) . f is complex set
(X2 . f) - ((Y + Y1) . f) is Relation-like Function-like complex-valued set
- ((Y + Y1) . f) is complex set
(- ((Y + Y1) . f)) + (X2 . f) is Relation-like Function-like complex-valued set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is Relation-like Function-like complex-valued set
dom X1 is set
dom X2 is set
(dom X1) /\ (dom X2) is set
Y is Relation-like Function-like set
dom Y is set
Y is Relation-like Function-like set
dom Y is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is set
Y . Y2 is set
Y1 . Y2 is set
X1 . Y2 is Relation-like Function-like complex-valued set
X2 . Y2 is complex set
(X2 . Y2) (#) (X1 . Y2) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X1,X2,Y) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X1,X2,Y) is set
Y2 is set
f is set
(X1,X2,Y) . f is set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(Y . f) (#) (X2 . f) is Relation-like Function-like complex-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),COMPLEX) is Relation-like complex-valued set
K19(K20((X1),COMPLEX)) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real set
(Y . f) (#) (X2 . f) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20((X1),REAL)) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real rational set
(Y . f) (#) (X2 . f) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),RAT)) is set
X is set
X1 is functional () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () Element of K19(K20(X,X1))
Y is Relation-like INT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y . f is complex V37() real integer rational set
(Y . f) (#) (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20((X1),INT)) is set
X is set
X1 is functional () () () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () () () Element of K19(K20(X,X1))
Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(X1,X2,Y) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
rng (X,X1,X2,Y) is functional () () () () Element of K19(((X1)))
K19(((X1))) is set
Y2 is set
f is set
(X,X1,X2,Y) . f is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
X2 . f is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
Y . f is complex epsilon-transitive epsilon-connected ordinal natural V37() real integer rational set
(Y . f) (#) (X2 . f) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
f1 is Relation-like Function-like set
rng f1 is set
f2 is set
dom (X2 . f) is set
dom f1 is set
K20((X1),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20((X1),NAT)) is set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
(X,X1,X2) is Relation-like X -defined ((X1)) -valued Function-like () Element of K19(K20(X,((X1))))
K20(X,((X1))) is Relation-like set
K19(K20(X,((X1)))) is set
Y is Relation-like Function-like complex-valued set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X,X1,X2,(- Y)) is Relation-like X /\ (dom (- Y)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (- Y))),((X1))))
dom (- Y) is set
X /\ (dom (- Y)) is set
K20((X /\ (dom (- Y))),((X1))) is Relation-like set
K19(K20((X /\ (dom (- Y))),((X1)))) is set
(X,((X1)),(X,X1,X2),Y) is Relation-like X /\ (dom Y) -defined ((((X1)))) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((((X1))))))
dom Y is set
X /\ (dom Y) is set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20((X /\ (dom Y)),((((X1))))) is Relation-like set
K19(K20((X /\ (dom Y)),((((X1)))))) is set
dom (X,X1,X2) is Element of K19(X)
K19(X) is set
dom X2 is Element of K19(X)
dom (X,X1,X2,(- Y)) is Element of K19((X /\ (dom (- Y))))
K19((X /\ (dom (- Y)))) is set
(dom X2) /\ (dom (- Y)) is Element of K19(X)
dom (X,((X1)),(X,X1,X2),Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
(dom (X,X1,X2)) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(- Y)) is set
Y2 is set
(X,X1,X2,(- Y)) . Y2 is Relation-like Function-like complex-valued set
(X,((X1)),(X,X1,X2),Y) . Y2 is Relation-like Function-like complex-valued set
X2 . Y2 is Relation-like Function-like complex-valued set
(- Y) . Y2 is complex set
((- Y) . Y2) (#) (X2 . Y2) is Relation-like Function-like complex-valued set
Y . Y2 is complex set
- (Y . Y2) is complex set
(- (Y . Y2)) (#) (X2 . Y2) is Relation-like Function-like complex-valued set
- (X2 . Y2) is Relation-like Function-like complex-valued set
(- 1) (#) (X2 . Y2) is Relation-like Function-like complex-valued set
(Y . Y2) (#) (- (X2 . Y2)) is Relation-like Function-like complex-valued set
(X,X1,X2) . Y2 is Relation-like Function-like complex-valued set
(Y . Y2) (#) ((X,X1,X2) . Y2) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
- Y is Relation-like Function-like complex-valued set
(- 1) (#) Y is Relation-like Function-like complex-valued set
(X,X1,X2,(- Y)) is Relation-like X /\ (dom (- Y)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (- Y))),((X1))))
dom (- Y) is set
X /\ (dom (- Y)) is set
K20((X /\ (dom (- Y))),((X1))) is Relation-like set
K19(K20((X /\ (dom (- Y))),((X1)))) is set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is Relation-like X /\ (dom Y) -defined ((((X1)))) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((((X1))))))
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20((X /\ (dom Y)),((((X1))))) is Relation-like set
K19(K20((X /\ (dom Y)),((((X1)))))) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(- Y)) is Element of K19((X /\ (dom (- Y))))
K19((X /\ (dom (- Y)))) is set
(dom X2) /\ (dom (- Y)) is Element of K19(X)
dom (X,X1,X2,(- Y)) is set
Y2 is set
(X,X1,X2,(- Y)) . Y2 is Relation-like Function-like complex-valued set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y)) . Y2 is Relation-like Function-like complex-valued set
X2 . Y2 is Relation-like Function-like complex-valued set
(- Y) . Y2 is complex set
((- Y) . Y2) (#) (X2 . Y2) is Relation-like Function-like complex-valued set
Y . Y2 is complex set
- (Y . Y2) is complex set
(- (Y . Y2)) (#) (X2 . Y2) is Relation-like Function-like complex-valued set
(Y . Y2) (#) (X2 . Y2) is Relation-like Function-like complex-valued set
- ((Y . Y2) (#) (X2 . Y2)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y . Y2) (#) (X2 . Y2)) is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . Y2 is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y) . Y2) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y) . Y2) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
Y1 is Relation-like Function-like complex-valued set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Relation-like (X /\ (dom Y)) /\ (dom Y1) -defined ((((X1)))) -valued Function-like () Element of K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))))
dom Y1 is set
(X /\ (dom Y)) /\ (dom Y1) is set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))) is Relation-like set
K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1)))))) is set
Y (#) Y1 is Relation-like Function-like complex-valued set
(X,X1,X2,(Y (#) Y1)) is Relation-like X /\ (dom (Y (#) Y1)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (Y (#) Y1))),((X1))))
dom (Y (#) Y1) is set
X /\ (dom (Y (#) Y1)) is set
K20((X /\ (dom (Y (#) Y1))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y (#) Y1))),((X1)))) is set
(dom Y) /\ (dom Y1) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Element of K19(((X /\ (dom Y)) /\ (dom Y1)))
K19(((X /\ (dom Y)) /\ (dom Y1))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
(dom (X,X1,X2,Y)) /\ (dom Y1) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(Y (#) Y1)) is Element of K19((X /\ (dom (Y (#) Y1))))
K19((X /\ (dom (Y (#) Y1)))) is set
(dom X2) /\ (dom (Y (#) Y1)) is Element of K19(X)
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) . f is Relation-like Function-like complex-valued set
(X,X1,X2,(Y (#) Y1)) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
Y1 . f is complex set
(Y1 . f) (#) ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(Y . f) (#) (X2 . f) is Relation-like Function-like complex-valued set
(Y1 . f) (#) ((Y . f) (#) (X2 . f)) is Relation-like Function-like complex-valued set
(Y . f) * (Y1 . f) is complex set
((Y . f) * (Y1 . f)) (#) (X2 . f) is Relation-like Function-like complex-valued set
(Y (#) Y1) . f is complex set
((Y (#) Y1) . f) (#) (X2 . f) is Relation-like Function-like complex-valued set
X is functional () set
X1 is Relation-like X -valued Function-like () set
X2 is Relation-like Function-like complex-valued set
X2 " is Relation-like Function-like complex-valued set
(X,X1,(X2 ")) is Relation-like Function-like set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
dom X2 is Element of K19(X)
K19(X) is set
Y is Relation-like Function-like complex-valued set
(X1,X2,Y) is Relation-like Function-like set
Y " is Relation-like Function-like complex-valued set
(X1,X2,(Y ")) is Relation-like Function-like set
dom (X1,X2,Y) is set
dom Y is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (Y ") is set
(dom X2) /\ (dom (Y ")) is Element of K19(X)
X is set
X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y . X1 is Relation-like Function-like complex-valued set
Y1 is Relation-like Function-like complex-valued set
(X2,Y,Y1) is Relation-like Function-like set
Y1 " is Relation-like Function-like complex-valued set
(X2,Y,(Y1 ")) is Relation-like Function-like set
dom (X2,Y,Y1) is set
(X2,Y,Y1) . X1 is set
Y1 . X1 is complex set
((Y . X1),(Y1 . X1)) is Relation-like Function-like complex-valued set
1 / (Y1 . X1) is complex set
(Y1 . X1) " is complex set
1 * ((Y1 . X1) ") is complex set
(1 / (Y1 . X1)) (#) (Y . X1) is Relation-like Function-like complex-valued set
(Y1 ") . X1 is complex set
((Y1 ") . X1) (#) (Y . X1) is Relation-like Function-like complex-valued set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
(X1,X2,Y) is Relation-like Function-like set
Y " is Relation-like Function-like complex-valued set
(X1,X2,(Y ")) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,(Y ")) is Relation-like X /\ (dom (Y ")) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (Y "))),((X1))))
dom (Y ") is set
X /\ (dom (Y ")) is set
K20((X /\ (dom (Y "))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y "))),((X1)))) is set
X is set
X1 is functional () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
Y " is Relation-like Function-like complex-valued ext-real-valued real-valued set
(X1,X2,(Y ")) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,(Y ")) is Relation-like X /\ (dom (Y ")) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom (Y "))),((X1))))
dom (Y ") is set
X /\ (dom (Y ")) is set
K20((X /\ (dom (Y "))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y "))),((X1)))) is set
X is set
X1 is functional () () () () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
X2 is Relation-like X -defined X1 -valued Function-like () () () () Element of K19(K20(X,X1))
Y is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,Y) is Relation-like Function-like set
Y " is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(X1,X2,(Y ")) is Relation-like Function-like set
dom Y is set
X /\ (dom Y) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () () () Element of K19(K20((X /\ (dom Y)),((X1))))
((X1)) is functional () () () set
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
(X,X1,X2,(Y ")) is Relation-like X /\ (dom (Y ")) -defined ((X1)) -valued Function-like () () () () Element of K19(K20((X /\ (dom (Y "))),((X1))))
dom (Y ") is set
X /\ (dom (Y ")) is set
K20((X /\ (dom (Y "))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y "))),((X1)))) is set
X is set
X1 is functional () set
K20(X,X1) is Relation-like set
K19(K20(X,X1)) is set
(X1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X1 : verum } is set
((X1)) is functional () set
X2 is Relation-like X -defined X1 -valued Function-like () Element of K19(K20(X,X1))
Y is Relation-like Function-like complex-valued set
dom Y is set
X /\ (dom Y) is set
(X,X1,X2,Y) is Relation-like X /\ (dom Y) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom Y)),((X1))))
K20((X /\ (dom Y)),((X1))) is Relation-like set
K19(K20((X /\ (dom Y)),((X1)))) is set
Y1 is Relation-like Function-like complex-valued set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Relation-like (X /\ (dom Y)) /\ (dom Y1) -defined ((((X1)))) -valued Function-like () Element of K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))))
dom Y1 is set
(X /\ (dom Y)) /\ (dom Y1) is set
(((X1))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X1)) : verum } is set
((((X1)))) is functional () set
K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1))))) is Relation-like set
K19(K20(((X /\ (dom Y)) /\ (dom Y1)),((((X1)))))) is set
Y1 " is Relation-like Function-like complex-valued set
(((X1)),(X,X1,X2,Y),(Y1 ")) is Relation-like Function-like set
Y /" Y1 is Relation-like Function-like complex-valued set
Y (#) (Y1 ") is Relation-like Function-like complex-valued set
(X,X1,X2,(Y /" Y1)) is Relation-like X /\ (dom (Y /" Y1)) -defined ((X1)) -valued Function-like () Element of K19(K20((X /\ (dom (Y /" Y1))),((X1))))
dom (Y /" Y1) is set
X /\ (dom (Y /" Y1)) is set
K20((X /\ (dom (Y /" Y1))),((X1))) is Relation-like set
K19(K20((X /\ (dom (Y /" Y1))),((X1)))) is set
(dom Y) /\ (dom Y1) is set
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is Element of K19(((X /\ (dom Y)) /\ (dom Y1)))
K19(((X /\ (dom Y)) /\ (dom Y1))) is set
dom (X,X1,X2,Y) is Element of K19((X /\ (dom Y)))
K19((X /\ (dom Y))) is set
(dom (X,X1,X2,Y)) /\ (dom Y1) is Element of K19((X /\ (dom Y)))
dom X2 is Element of K19(X)
K19(X) is set
(dom X2) /\ (dom Y) is Element of K19(X)
dom (X,X1,X2,(Y /" Y1)) is Element of K19((X /\ (dom (Y /" Y1))))
K19((X /\ (dom (Y /" Y1)))) is set
(dom X2) /\ (dom (Y /" Y1)) is Element of K19(X)
dom ((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) is set
f is set
((X /\ (dom Y)),((X1)),(X,X1,X2,Y),Y1) . f is Relation-like Function-like complex-valued set
(X,X1,X2,(Y /" Y1)) . f is Relation-like Function-like complex-valued set
(X,X1,X2,Y) . f is Relation-like Function-like complex-valued set
Y1 . f is complex set
(((X,X1,X2,Y) . f),(Y1 . f)) is Relation-like Function-like complex-valued set
1 / (Y1 . f) is complex set
(Y1 . f) " is complex set
1 * ((Y1 . f) ") is complex set
(1 / (Y1 . f)) (#) ((X,X1,X2,Y) . f) is Relation-like Function-like complex-valued set
X2 . f is Relation-like Function-like complex-valued set
Y . f is complex set
(Y . f) (#) (X2 . f) is Relation-like Function-like complex-valued set
(((Y . f) (#) (X2 . f)),(Y1 . f)) is Relation-like Function-like complex-valued set
(1 / (Y1 . f)) (#) ((Y . f) (#) (X2 . f)) is Relation-like Function-like complex-valued set
(Y . f) / (Y1 . f) is complex set
(Y . f) * ((Y1 . f) ") is complex set
((Y . f) / (Y1 . f)) (#) (X2 . f) is Relation-like Function-like complex-valued set
(Y /" Y1) . f is complex set
((Y /" Y1) . f) (#) (X2 . f) is Relation-like Function-like complex-valued set
X is functional () set
X1 is functional () set
X2 is Relation-like X -valued Function-like () set
Y is Relation-like X1 -valued Function-like () set
dom X2 is set
dom Y is set
(dom X2) /\ (dom Y) is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is Relation-like Function-like set
dom Y2 is set
f is set
Y1 . f is set
Y2 . f is set
X2 . f is Relation-like Function-like complex-valued set
Y . f is Relation-like Function-like complex-valued set
(X2 . f) + (Y . f) is Relation-like Function-like complex-valued set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X2,Y,Y1,Y2) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X2,Y,Y1,Y2) is set
f1 is set
f2 is set
(X2,Y,Y1,Y2) . f2 is set
Y1 . f2 is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
(Y1 . f2) + (Y2 . f2) is Relation-like Function-like complex-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),COMPLEX) is Relation-like complex-valued set
K19(K20(((X2) /\ (Y)),COMPLEX)) is set
X is set
X2 is functional () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) + (Y2 . f2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),REAL)) is set
X is set
X2 is functional () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) + (Y2 . f2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),RAT)) is set
X is set
X2 is functional () () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) + (Y2 . f2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),INT)) is set
X is set
X2 is functional () () () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
Y2 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(Y1 . f2) + (Y2 . f2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20(((X2) /\ (Y)),NAT)) is set
X is set
X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X1,X,Y,X2,Y2,Y1) is Relation-like X1 /\ X -defined (((Y) /\ (X2))) -valued Function-like () Element of K19(K20((X1 /\ X),(((Y) /\ (X2)))))
X1 /\ X is set
(Y) /\ (X2) is set
(((Y) /\ (X2))) is functional () set
K20((X1 /\ X),(((Y) /\ (X2)))) is Relation-like set
K19(K20((X1 /\ X),(((Y) /\ (X2))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X1,X,Y,X2,Y2,Y1) is Element of K19((X1 /\ X))
K19((X1 /\ X)) is set
dom (X,X1,X2,Y,Y1,Y2) is set
f is set
(X,X1,X2,Y,Y1,Y2) . f is Relation-like Function-like complex-valued set
(X1,X,Y,X2,Y2,Y1) . f is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
Y2 . f is Relation-like Function-like complex-valued set
(Y1 . f) + (Y2 . f) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) + (f2 . f5) is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) + (f1 . f5) is Relation-like Function-like complex-valued set
((f . f5) + (f1 . f5)) + (f2 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) + (f2 . f5) is Relation-like Function-like complex-valued set
(f . f5) + ((f1 . f5) + (f2 . f5)) is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . f5 is Relation-like Function-like complex-valued set
(f . f5) + ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
((X2)) is functional () set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
((Y)) is functional () set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
(X,X2,Y1) is Relation-like X -defined ((X2)) -valued Function-like () Element of K19(K20(X,((X2))))
K20(X,((X2))) is Relation-like set
K19(K20(X,((X2)))) is set
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Relation-like X /\ X1 -defined (((((X2) /\ (Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2) /\ (Y)))))))
((((X2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
(((((X2) /\ (Y))))) is functional () set
K20((X /\ X1),(((((X2) /\ (Y)))))) is Relation-like set
K19(K20((X /\ X1),(((((X2) /\ (Y))))))) is set
(X1,Y,Y2) is Relation-like X1 -defined ((Y)) -valued Function-like () Element of K19(K20(X1,((Y))))
K20(X1,((Y))) is Relation-like set
K19(K20(X1,((Y)))) is set
(X,X1,((X2)),((Y)),(X,X2,Y1),(X1,Y,Y2)) is Relation-like X /\ X1 -defined (((((X2))) /\ (((Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2))) /\ (((Y)))))))
(((X2))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
(((Y))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((Y)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((Y)) : verum } is set
(((X2))) /\ (((Y))) is set
(((((X2))) /\ (((Y))))) is functional () set
K20((X /\ X1),(((((X2))) /\ (((Y)))))) is Relation-like set
K19(K20((X /\ X1),(((((X2))) /\ (((Y))))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X1,Y,Y2) is Element of K19(X1)
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Element of K19((X /\ X1))
dom (X,X2,Y1) is Element of K19(X)
dom (X,X1,((X2)),((Y)),(X,X2,Y1),(X1,Y,Y2)) is Element of K19((X /\ X1))
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is set
f3 is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) . f3 is Relation-like Function-like complex-valued set
(X,X1,((X2)),((Y)),(X,X2,Y1),(X1,Y,Y2)) . f3 is Relation-like Function-like complex-valued set
(X,X1,X2,Y,Y1,Y2) . f3 is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y,Y1,Y2) . f3) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y,Y1,Y2) . f3) is Relation-like Function-like complex-valued set
Y1 . f3 is Relation-like Function-like complex-valued set
Y2 . f3 is Relation-like Function-like complex-valued set
(Y1 . f3) + (Y2 . f3) is Relation-like Function-like complex-valued set
- ((Y1 . f3) + (Y2 . f3)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y1 . f3) + (Y2 . f3)) is Relation-like Function-like complex-valued set
- (Y1 . f3) is Relation-like Function-like complex-valued set
(- 1) (#) (Y1 . f3) is Relation-like Function-like complex-valued set
(- (Y1 . f3)) - (Y2 . f3) is Relation-like Function-like complex-valued set
- (Y2 . f3) is Relation-like Function-like complex-valued set
(- 1) (#) (Y2 . f3) is Relation-like Function-like complex-valued set
(- (Y1 . f3)) + (- (Y2 . f3)) is Relation-like Function-like complex-valued set
(X,X2,Y1) . f3 is Relation-like Function-like complex-valued set
((X,X2,Y1) . f3) + (- (Y2 . f3)) is Relation-like Function-like complex-valued set
(X1,Y,Y2) . f3 is Relation-like Function-like complex-valued set
((X,X2,Y1) . f3) + ((X1,Y,Y2) . f3) is Relation-like Function-like complex-valued set
X is functional () set
X1 is functional () set
X2 is Relation-like X -valued Function-like () set
Y is Relation-like X1 -valued Function-like () set
dom X2 is set
dom Y is set
(dom X2) /\ (dom Y) is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is Relation-like Function-like set
dom Y2 is set
f is set
Y1 . f is set
Y2 . f is set
X2 . f is Relation-like Function-like complex-valued set
Y . f is Relation-like Function-like complex-valued set
(X2 . f) - (Y . f) is Relation-like Function-like complex-valued set
- (Y . f) is Relation-like Function-like complex-valued set
(- 1) (#) (Y . f) is Relation-like Function-like complex-valued set
(X2 . f) + (- (Y . f)) is Relation-like Function-like complex-valued set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X2,Y,Y1,Y2) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X2,Y,Y1,Y2) is set
f1 is set
f2 is set
(X2,Y,Y1,Y2) . f2 is set
Y1 . f2 is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
(Y1 . f2) - (Y2 . f2) is Relation-like Function-like complex-valued set
- (Y2 . f2) is Relation-like Function-like complex-valued set
(- 1) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
(Y1 . f2) + (- (Y2 . f2)) is Relation-like Function-like complex-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),COMPLEX) is Relation-like complex-valued set
K19(K20(((X2) /\ (Y)),COMPLEX)) is set
X is set
X2 is functional () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) - (Y2 . f2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
- (Y2 . f2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (Y2 . f2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) + (- (Y2 . f2)) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),REAL)) is set
X is set
X2 is functional () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) - (Y2 . f2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
- (Y2 . f2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (Y2 . f2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) + (- (Y2 . f2)) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),RAT)) is set
X is set
X2 is functional () () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) - (Y2 . f2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
- (Y2 . f2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (Y2 . f2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) + (- (Y2 . f2)) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),INT)) is set
X is set
X1 is set
X1 /\ X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(Y) /\ (X2) is set
(((Y) /\ (X2))) is functional () set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
X /\ X1 is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X1,X,Y,X2,Y2,Y1) is Relation-like X1 /\ X -defined (((Y) /\ (X2))) -valued Function-like () Element of K19(K20((X1 /\ X),(((Y) /\ (X2)))))
K20((X1 /\ X),(((Y) /\ (X2)))) is Relation-like set
K19(K20((X1 /\ X),(((Y) /\ (X2))))) is set
((X1 /\ X),(((Y) /\ (X2))),(X1,X,Y,X2,Y2,Y1)) is Relation-like X1 /\ X -defined (((((Y) /\ (X2))))) -valued Function-like () Element of K19(K20((X1 /\ X),(((((Y) /\ (X2)))))))
((((Y) /\ (X2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (X2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (X2))) : verum } is set
(((((Y) /\ (X2))))) is functional () set
K20((X1 /\ X),(((((Y) /\ (X2)))))) is Relation-like set
K19(K20((X1 /\ X),(((((Y) /\ (X2))))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X1,X,Y,X2,Y2,Y1) is Element of K19((X1 /\ X))
K19((X1 /\ X)) is set
(dom Y2) /\ (dom Y1) is Element of K19(X)
dom ((X1 /\ X),(((Y) /\ (X2))),(X1,X,Y,X2,Y2,Y1)) is Element of K19((X1 /\ X))
dom (X,X1,X2,Y,Y1,Y2) is set
f1 is set
(X,X1,X2,Y,Y1,Y2) . f1 is Relation-like Function-like complex-valued set
((X1 /\ X),(((Y) /\ (X2))),(X1,X,Y,X2,Y2,Y1)) . f1 is Relation-like Function-like complex-valued set
Y1 . f1 is Relation-like Function-like complex-valued set
Y2 . f1 is Relation-like Function-like complex-valued set
(Y1 . f1) - (Y2 . f1) is Relation-like Function-like complex-valued set
- (Y2 . f1) is Relation-like Function-like complex-valued set
(- 1) (#) (Y2 . f1) is Relation-like Function-like complex-valued set
(Y1 . f1) + (- (Y2 . f1)) is Relation-like Function-like complex-valued set
(Y2 . f1) - (Y1 . f1) is Relation-like Function-like complex-valued set
- (Y1 . f1) is Relation-like Function-like complex-valued set
(- 1) (#) (Y1 . f1) is Relation-like Function-like complex-valued set
(Y2 . f1) + (- (Y1 . f1)) is Relation-like Function-like complex-valued set
- ((Y2 . f1) - (Y1 . f1)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y2 . f1) - (Y1 . f1)) is Relation-like Function-like complex-valued set
(X1,X,Y,X2,Y2,Y1) . f1 is Relation-like Function-like complex-valued set
- ((X1,X,Y,X2,Y2,Y1) . f1) is Relation-like Function-like complex-valued set
(- 1) (#) ((X1,X,Y,X2,Y2,Y1) . f1) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
((X2)) is functional () set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
(X,X2,Y1) is Relation-like X -defined ((X2)) -valued Function-like () Element of K19(K20(X,((X2))))
K20(X,((X2))) is Relation-like set
K19(K20(X,((X2)))) is set
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Relation-like X /\ X1 -defined (((((X2) /\ (Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2) /\ (Y)))))))
((((X2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
(((((X2) /\ (Y))))) is functional () set
K20((X /\ X1),(((((X2) /\ (Y)))))) is Relation-like set
K19(K20((X /\ X1),(((((X2) /\ (Y))))))) is set
(X,X1,((X2)),Y,(X,X2,Y1),Y2) is Relation-like X /\ X1 -defined (((((X2))) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2))) /\ (Y)))))
(((X2))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
(((X2))) /\ (Y) is set
(((((X2))) /\ (Y))) is functional () set
K20((X /\ X1),(((((X2))) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((((X2))) /\ (Y))))) is set
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X,X2,Y1) is Element of K19(X)
dom (X,X1,((X2)),Y,(X,X2,Y1),Y2) is Element of K19((X /\ X1))
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is set
f2 is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) . f2 is Relation-like Function-like complex-valued set
(X,X1,((X2)),Y,(X,X2,Y1),Y2) . f2 is Relation-like Function-like complex-valued set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
(Y1 . f2) - (Y2 . f2) is Relation-like Function-like complex-valued set
- (Y2 . f2) is Relation-like Function-like complex-valued set
(- 1) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
(Y1 . f2) + (- (Y2 . f2)) is Relation-like Function-like complex-valued set
- ((Y1 . f2) - (Y2 . f2)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y1 . f2) - (Y2 . f2)) is Relation-like Function-like complex-valued set
- (Y1 . f2) is Relation-like Function-like complex-valued set
(- 1) (#) (Y1 . f2) is Relation-like Function-like complex-valued set
(- (Y1 . f2)) - (- (Y2 . f2)) is Relation-like Function-like complex-valued set
- (- (Y2 . f2)) is Relation-like Function-like complex-valued set
(- 1) (#) (- (Y2 . f2)) is Relation-like Function-like complex-valued set
(- (Y1 . f2)) + (- (- (Y2 . f2))) is Relation-like Function-like complex-valued set
(X,X2,Y1) . f2 is Relation-like Function-like complex-valued set
((X,X2,Y1) . f2) + (Y2 . f2) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) - (f2 . f5) is Relation-like Function-like complex-valued set
- (f2 . f5) is Relation-like Function-like complex-valued set
(- 1) (#) (f2 . f5) is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) + (f1 . f5) is Relation-like Function-like complex-valued set
((f . f5) + (f1 . f5)) - (f2 . f5) is Relation-like Function-like complex-valued set
((f . f5) + (f1 . f5)) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
(f1 . f5) - (f2 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
(f . f5) + ((f1 . f5) - (f2 . f5)) is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . f5 is Relation-like Function-like complex-valued set
(f . f5) + ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) + (f2 . f5) is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) - (f1 . f5) is Relation-like Function-like complex-valued set
- (f1 . f5) is Relation-like Function-like complex-valued set
(- 1) (#) (f1 . f5) is Relation-like Function-like complex-valued set
(f . f5) + (- (f1 . f5)) is Relation-like Function-like complex-valued set
((f . f5) - (f1 . f5)) + (f2 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) - (f2 . f5) is Relation-like Function-like complex-valued set
- (f2 . f5) is Relation-like Function-like complex-valued set
(- 1) (#) (f2 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
(f . f5) - ((f1 . f5) - (f2 . f5)) is Relation-like Function-like complex-valued set
- ((f1 . f5) - (f2 . f5)) is Relation-like Function-like complex-valued set
(- 1) (#) ((f1 . f5) - (f2 . f5)) is Relation-like Function-like complex-valued set
(f . f5) + (- ((f1 . f5) - (f2 . f5))) is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . f5 is Relation-like Function-like complex-valued set
(f . f5) - ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
- ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
(- 1) (#) ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
(f . f5) + (- ((X1,X2,Y1,Y2,f1,f2) . f5)) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) - (f2 . f5) is Relation-like Function-like complex-valued set
- (f2 . f5) is Relation-like Function-like complex-valued set
(- 1) (#) (f2 . f5) is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) - (f1 . f5) is Relation-like Function-like complex-valued set
- (f1 . f5) is Relation-like Function-like complex-valued set
(- 1) (#) (f1 . f5) is Relation-like Function-like complex-valued set
(f . f5) + (- (f1 . f5)) is Relation-like Function-like complex-valued set
((f . f5) - (f1 . f5)) - (f2 . f5) is Relation-like Function-like complex-valued set
((f . f5) - (f1 . f5)) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
(f1 . f5) + (f2 . f5) is Relation-like Function-like complex-valued set
(f . f5) - ((f1 . f5) + (f2 . f5)) is Relation-like Function-like complex-valued set
- ((f1 . f5) + (f2 . f5)) is Relation-like Function-like complex-valued set
(- 1) (#) ((f1 . f5) + (f2 . f5)) is Relation-like Function-like complex-valued set
(f . f5) + (- ((f1 . f5) + (f2 . f5))) is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . f5 is Relation-like Function-like complex-valued set
(f . f5) - ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
- ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
(- 1) (#) ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
(f . f5) + (- ((X1,X2,Y1,Y2,f1,f2) . f5)) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y) /\ (Y2) is set
(((Y) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X,X2,Y,Y2,f,f2) is Relation-like X /\ X2 -defined (((Y) /\ (Y2))) -valued Function-like () Element of K19(K20((X /\ X2),(((Y) /\ (Y2)))))
K20((X /\ X2),(((Y) /\ (Y2)))) is Relation-like set
K19(K20((X /\ X2),(((Y) /\ (Y2))))) is set
((X /\ X2),X1,(((Y) /\ (Y2))),Y1,(X,X2,Y,Y2,f,f2),f1) is Relation-like (X /\ X2) /\ X1 -defined ((((((Y) /\ (Y2)))) /\ (Y1))) -valued Function-like () Element of K19(K20(((X /\ X2) /\ X1),((((((Y) /\ (Y2)))) /\ (Y1)))))
(X /\ X2) /\ X1 is set
((((Y) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
((((Y) /\ (Y2)))) /\ (Y1) is set
((((((Y) /\ (Y2)))) /\ (Y1))) is functional () set
K20(((X /\ X2) /\ X1),((((((Y) /\ (Y2)))) /\ (Y1)))) is Relation-like set
K19(K20(((X /\ X2) /\ X1),((((((Y) /\ (Y2)))) /\ (Y1))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X2),X1,(((Y) /\ (Y2))),Y1,(X,X2,Y,Y2,f,f2),f1) is Element of K19(((X /\ X2) /\ X1))
K19(((X /\ X2) /\ X1)) is set
dom (X,X2,Y,Y2,f,f2) is Element of K19((X /\ X2))
K19((X /\ X2)) is set
dom f1 is Element of K19(X1)
K19(X1) is set
(dom (X,X2,Y,Y2,f,f2)) /\ (dom f1) is Element of K19(X1)
dom f is Element of K19(X)
K19(X) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
((X /\ X2),X1,(((Y) /\ (Y2))),Y1,(X,X2,Y,Y2,f,f2),f1) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) - (f2 . f5) is Relation-like Function-like complex-valued set
- (f2 . f5) is Relation-like Function-like complex-valued set
(- 1) (#) (f2 . f5) is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) - (f1 . f5) is Relation-like Function-like complex-valued set
- (f1 . f5) is Relation-like Function-like complex-valued set
(- 1) (#) (f1 . f5) is Relation-like Function-like complex-valued set
(f . f5) + (- (f1 . f5)) is Relation-like Function-like complex-valued set
((f . f5) - (f1 . f5)) - (f2 . f5) is Relation-like Function-like complex-valued set
((f . f5) - (f1 . f5)) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
(f . f5) - (f2 . f5) is Relation-like Function-like complex-valued set
(f . f5) + (- (f2 . f5)) is Relation-like Function-like complex-valued set
((f . f5) - (f2 . f5)) - (f1 . f5) is Relation-like Function-like complex-valued set
((f . f5) - (f2 . f5)) + (- (f1 . f5)) is Relation-like Function-like complex-valued set
(X,X2,Y,Y2,f,f2) . f5 is Relation-like Function-like complex-valued set
((X,X2,Y,Y2,f,f2) . f5) - (f1 . f5) is Relation-like Function-like complex-valued set
((X,X2,Y,Y2,f,f2) . f5) + (- (f1 . f5)) is Relation-like Function-like complex-valued set
X is functional () set
X1 is functional () set
X2 is Relation-like X -valued Function-like () set
Y is Relation-like X1 -valued Function-like () set
dom X2 is set
dom Y is set
(dom X2) /\ (dom Y) is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is Relation-like Function-like set
dom Y2 is set
f is set
Y1 . f is set
Y2 . f is set
X2 . f is Relation-like Function-like complex-valued set
Y . f is Relation-like Function-like complex-valued set
(X2 . f) (#) (Y . f) is Relation-like Function-like complex-valued set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X2,Y,Y1,Y2) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X2,Y,Y1,Y2) is set
f1 is set
f2 is set
(X2,Y,Y1,Y2) . f2 is set
Y1 . f2 is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
(Y1 . f2) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),COMPLEX) is Relation-like complex-valued set
K19(K20(((X2) /\ (Y)),COMPLEX)) is set
X is set
X2 is functional () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) (#) (Y2 . f2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),REAL)) is set
X is set
X2 is functional () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) (#) (Y2 . f2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),RAT)) is set
X is set
X2 is functional () () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) (#) (Y2 . f2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),INT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),INT)) is set
X is set
X2 is functional () () () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
Y2 . f2 is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
(Y1 . f2) (#) (Y2 . f2) is Relation-like RAT -valued INT -valued Function-like complex-valued ext-real-valued real-valued natural-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),NAT) is Relation-like RAT -valued INT -valued complex-valued ext-real-valued real-valued natural-valued set
K19(K20(((X2) /\ (Y)),NAT)) is set
X is set
X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X1,X,Y,X2,Y2,Y1) is Relation-like X1 /\ X -defined (((Y) /\ (X2))) -valued Function-like () Element of K19(K20((X1 /\ X),(((Y) /\ (X2)))))
X1 /\ X is set
(Y) /\ (X2) is set
(((Y) /\ (X2))) is functional () set
K20((X1 /\ X),(((Y) /\ (X2)))) is Relation-like set
K19(K20((X1 /\ X),(((Y) /\ (X2))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X1,X,Y,X2,Y2,Y1) is Element of K19((X1 /\ X))
K19((X1 /\ X)) is set
dom (X,X1,X2,Y,Y1,Y2) is set
f is set
(X,X1,X2,Y,Y1,Y2) . f is Relation-like Function-like complex-valued set
(X1,X,Y,X2,Y2,Y1) . f is Relation-like Function-like complex-valued set
Y1 . f is Relation-like Function-like complex-valued set
Y2 . f is Relation-like Function-like complex-valued set
(Y1 . f) (#) (Y2 . f) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) (#) (f2 . f5) is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) (#) (f1 . f5) is Relation-like Function-like complex-valued set
((f . f5) (#) (f1 . f5)) (#) (f2 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) (#) (f2 . f5) is Relation-like Function-like complex-valued set
(f . f5) (#) ((f1 . f5) (#) (f2 . f5)) is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . f5 is Relation-like Function-like complex-valued set
(f . f5) (#) ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
((X2)) is functional () set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
(X,X2,Y1) is Relation-like X -defined ((X2)) -valued Function-like () Element of K19(K20(X,((X2))))
K20(X,((X2))) is Relation-like set
K19(K20(X,((X2)))) is set
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X,X1,((X2)),Y,(X,X2,Y1),Y2) is Relation-like X /\ X1 -defined (((((X2))) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2))) /\ (Y)))))
(((X2))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
(((X2))) /\ (Y) is set
(((((X2))) /\ (Y))) is functional () set
K20((X /\ X1),(((((X2))) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((((X2))) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Relation-like X /\ X1 -defined (((((X2) /\ (Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2) /\ (Y)))))))
((((X2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
(((((X2) /\ (Y))))) is functional () set
K20((X /\ X1),(((((X2) /\ (Y)))))) is Relation-like set
K19(K20((X /\ X1),(((((X2) /\ (Y))))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X,X2,Y1) is Element of K19(X)
dom (X,X1,((X2)),Y,(X,X2,Y1),Y2) is Element of K19((X /\ X1))
(dom (X,X2,Y1)) /\ (dom Y2) is Element of K19(X1)
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Element of K19((X /\ X1))
dom (X,X1,((X2)),Y,(X,X2,Y1),Y2) is set
f2 is set
(X,X1,((X2)),Y,(X,X2,Y1),Y2) . f2 is Relation-like Function-like complex-valued set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) . f2 is Relation-like Function-like complex-valued set
(X,X2,Y1) . f2 is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
((X,X2,Y1) . f2) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued set
- (Y1 . f2) is Relation-like Function-like complex-valued set
(- 1) (#) (Y1 . f2) is Relation-like Function-like complex-valued set
(- (Y1 . f2)) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
(Y1 . f2) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
- ((Y1 . f2) (#) (Y2 . f2)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y1 . f2) (#) (Y2 . f2)) is Relation-like Function-like complex-valued set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
((Y)) is functional () set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X1,Y,Y2) is Relation-like X1 -defined ((Y)) -valued Function-like () Element of K19(K20(X1,((Y))))
K20(X1,((Y))) is Relation-like set
K19(K20(X1,((Y)))) is set
(X,X1,X2,((Y)),Y1,(X1,Y,Y2)) is Relation-like X /\ X1 -defined (((X2) /\ (((Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (((Y)))))))
(((Y))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((Y)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((Y)) : verum } is set
(X2) /\ (((Y))) is set
(((X2) /\ (((Y))))) is functional () set
K20((X /\ X1),(((X2) /\ (((Y)))))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (((Y))))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Relation-like X /\ X1 -defined (((((X2) /\ (Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2) /\ (Y)))))))
((((X2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
(((((X2) /\ (Y))))) is functional () set
K20((X /\ X1),(((((X2) /\ (Y)))))) is Relation-like set
K19(K20((X /\ X1),(((((X2) /\ (Y))))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X1,Y,Y2) is Element of K19(X1)
dom (X,X1,X2,((Y)),Y1,(X1,Y,Y2)) is Element of K19((X /\ X1))
(dom Y1) /\ (dom (X1,Y,Y2)) is Element of K19(X1)
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Element of K19((X /\ X1))
dom (X,X1,X2,((Y)),Y1,(X1,Y,Y2)) is set
f2 is set
(X,X1,X2,((Y)),Y1,(X1,Y,Y2)) . f2 is Relation-like Function-like complex-valued set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) . f2 is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued set
(X1,Y,Y2) . f2 is Relation-like Function-like complex-valued set
(Y1 . f2) (#) ((X1,Y,Y2) . f2) is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
- (Y2 . f2) is Relation-like Function-like complex-valued set
(- 1) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
(Y1 . f2) (#) (- (Y2 . f2)) is Relation-like Function-like complex-valued set
(Y1 . f2) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
- ((Y1 . f2) (#) (Y2 . f2)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y1 . f2) (#) (Y2 . f2)) is Relation-like Function-like complex-valued set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
X /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
(Y) /\ (Y2) is set
(((Y) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
(X,X2,Y,Y2,f,f2) is Relation-like X /\ X2 -defined (((Y) /\ (Y2))) -valued Function-like () Element of K19(K20((X /\ X2),(((Y) /\ (Y2)))))
K20((X /\ X2),(((Y) /\ (Y2)))) is Relation-like set
K19(K20((X /\ X2),(((Y) /\ (Y2))))) is set
((X /\ X1),(X /\ X2),(((Y) /\ (Y1))),(((Y) /\ (Y2))),(X,X1,Y,Y1,f,f1),(X,X2,Y,Y2,f,f2)) is Relation-like (X /\ X1) /\ (X /\ X2) -defined ((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ (X /\ X2)),((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2))))))))
(X /\ X1) /\ (X /\ X2) is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))) is set
((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))))) is functional () set
K20(((X /\ X1) /\ (X /\ X2)),((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2))))))) is Relation-like set
K19(K20(((X /\ X1) /\ (X /\ X2)),((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))))))) is set
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),(X /\ X2),(((Y) /\ (Y1))),(((Y) /\ (Y2))),(X,X1,Y,Y1,f,f1),(X,X2,Y,Y2,f,f2)) is Element of K19(((X /\ X1) /\ (X /\ X2)))
K19(((X /\ X1) /\ (X /\ X2))) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom (X,X2,Y,Y2,f,f2) is Element of K19((X /\ X2))
K19((X /\ X2)) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom (X,X2,Y,Y2,f,f2)) is Element of K19((X /\ X2))
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is set
x is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . x is Relation-like Function-like complex-valued set
((X /\ X1),(X /\ X2),(((Y) /\ (Y1))),(((Y) /\ (Y2))),(X,X1,Y,Y1,f,f1),(X,X2,Y,Y2,f,f2)) . x is Relation-like Function-like complex-valued set
f . x is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . x is Relation-like Function-like complex-valued set
(f . x) (#) ((X1,X2,Y1,Y2,f1,f2) . x) is Relation-like Function-like complex-valued set
f1 . x is Relation-like Function-like complex-valued set
f2 . x is Relation-like Function-like complex-valued set
(f1 . x) + (f2 . x) is Relation-like Function-like complex-valued set
(f . x) (#) ((f1 . x) + (f2 . x)) is Relation-like Function-like complex-valued set
(f . x) (#) (f1 . x) is Relation-like Function-like complex-valued set
(f . x) (#) (f2 . x) is Relation-like Function-like complex-valued set
((f . x) (#) (f1 . x)) + ((f . x) (#) (f2 . x)) is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . x is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . x) + ((f . x) (#) (f2 . x)) is Relation-like Function-like complex-valued set
(X,X2,Y,Y2,f,f2) . x is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . x) + ((X,X2,Y,Y2,f,f2) . x) is Relation-like Function-like complex-valued set
X is set
X1 is set
X1 /\ X is set
X2 is set
X1 /\ X2 is set
X2 /\ X is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y1) /\ (Y) is set
(((Y1) /\ (Y))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
(Y2) /\ (Y) is set
(((Y2) /\ (Y))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X1,X,Y1,Y,f1,f) is Relation-like X1 /\ X -defined (((Y1) /\ (Y))) -valued Function-like () Element of K19(K20((X1 /\ X),(((Y1) /\ (Y)))))
K20((X1 /\ X),(((Y1) /\ (Y)))) is Relation-like set
K19(K20((X1 /\ X),(((Y1) /\ (Y))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is Relation-like (X1 /\ X2) /\ X -defined ((((((Y1) /\ (Y2)))) /\ (Y))) -valued Function-like () Element of K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))))
(X1 /\ X2) /\ X is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
((((Y1) /\ (Y2)))) /\ (Y) is set
((((((Y1) /\ (Y2)))) /\ (Y))) is functional () set
K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))) is Relation-like set
K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y))))) is set
(X2,X,Y2,Y,f2,f) is Relation-like X2 /\ X -defined (((Y2) /\ (Y))) -valued Function-like () Element of K19(K20((X2 /\ X),(((Y2) /\ (Y)))))
K20((X2 /\ X),(((Y2) /\ (Y)))) is Relation-like set
K19(K20((X2 /\ X),(((Y2) /\ (Y))))) is set
((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) is Relation-like (X1 /\ X) /\ (X2 /\ X) -defined ((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) -valued Function-like () Element of K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))))
(X1 /\ X) /\ (X2 /\ X) is set
((((Y1) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
((((Y2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))) is set
((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) is functional () set
K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))) is Relation-like set
K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))))) is set
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
X /\ X1 is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
(X,X2,Y,Y2,f,f2) is Relation-like X /\ X2 -defined (((Y) /\ (Y2))) -valued Function-like () Element of K19(K20((X /\ X2),(((Y) /\ (Y2)))))
X /\ X2 is set
(Y) /\ (Y2) is set
(((Y) /\ (Y2))) is functional () set
K20((X /\ X2),(((Y) /\ (Y2)))) is Relation-like set
K19(K20((X /\ X2),(((Y) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
X /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
(Y) /\ (Y2) is set
(((Y) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
(X,X2,Y,Y2,f,f2) is Relation-like X /\ X2 -defined (((Y) /\ (Y2))) -valued Function-like () Element of K19(K20((X /\ X2),(((Y) /\ (Y2)))))
K20((X /\ X2),(((Y) /\ (Y2)))) is Relation-like set
K19(K20((X /\ X2),(((Y) /\ (Y2))))) is set
((X /\ X1),(X /\ X2),(((Y) /\ (Y1))),(((Y) /\ (Y2))),(X,X1,Y,Y1,f,f1),(X,X2,Y,Y2,f,f2)) is Relation-like (X /\ X1) /\ (X /\ X2) -defined ((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ (X /\ X2)),((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2))))))))
(X /\ X1) /\ (X /\ X2) is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))) is set
((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))))) is functional () set
K20(((X /\ X1) /\ (X /\ X2)),((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2))))))) is Relation-like set
K19(K20(((X /\ X1) /\ (X /\ X2)),((((((Y) /\ (Y1)))) /\ ((((Y) /\ (Y2)))))))) is set
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),(X /\ X2),(((Y) /\ (Y1))),(((Y) /\ (Y2))),(X,X1,Y,Y1,f,f1),(X,X2,Y,Y2,f,f2)) is Element of K19(((X /\ X1) /\ (X /\ X2)))
K19(((X /\ X1) /\ (X /\ X2))) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom (X,X2,Y,Y2,f,f2) is Element of K19((X /\ X2))
K19((X /\ X2)) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom (X,X2,Y,Y2,f,f2)) is Element of K19((X /\ X2))
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is set
x is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . x is Relation-like Function-like complex-valued set
((X /\ X1),(X /\ X2),(((Y) /\ (Y1))),(((Y) /\ (Y2))),(X,X1,Y,Y1,f,f1),(X,X2,Y,Y2,f,f2)) . x is Relation-like Function-like complex-valued set
f . x is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . x is Relation-like Function-like complex-valued set
(f . x) (#) ((X1,X2,Y1,Y2,f1,f2) . x) is Relation-like Function-like complex-valued set
f1 . x is Relation-like Function-like complex-valued set
f2 . x is Relation-like Function-like complex-valued set
(f1 . x) - (f2 . x) is Relation-like Function-like complex-valued set
- (f2 . x) is Relation-like Function-like complex-valued set
(- 1) (#) (f2 . x) is Relation-like Function-like complex-valued set
(f1 . x) + (- (f2 . x)) is Relation-like Function-like complex-valued set
(f . x) (#) ((f1 . x) - (f2 . x)) is Relation-like Function-like complex-valued set
(f . x) (#) (f1 . x) is Relation-like Function-like complex-valued set
(f . x) (#) (f2 . x) is Relation-like Function-like complex-valued set
((f . x) (#) (f1 . x)) - ((f . x) (#) (f2 . x)) is Relation-like Function-like complex-valued set
- ((f . x) (#) (f2 . x)) is Relation-like Function-like complex-valued set
(- 1) (#) ((f . x) (#) (f2 . x)) is Relation-like Function-like complex-valued set
((f . x) (#) (f1 . x)) + (- ((f . x) (#) (f2 . x))) is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . x is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . x) - ((f . x) (#) (f2 . x)) is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . x) + (- ((f . x) (#) (f2 . x))) is Relation-like Function-like complex-valued set
(X,X2,Y,Y2,f,f2) . x is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . x) - ((X,X2,Y,Y2,f,f2) . x) is Relation-like Function-like complex-valued set
- ((X,X2,Y,Y2,f,f2) . x) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X2,Y,Y2,f,f2) . x) is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . x) + (- ((X,X2,Y,Y2,f,f2) . x)) is Relation-like Function-like complex-valued set
X is set
X1 is set
X1 /\ X is set
X2 is set
X1 /\ X2 is set
X2 /\ X is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y1) /\ (Y) is set
(((Y1) /\ (Y))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
(Y2) /\ (Y) is set
(((Y2) /\ (Y))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X1,X,Y1,Y,f1,f) is Relation-like X1 /\ X -defined (((Y1) /\ (Y))) -valued Function-like () Element of K19(K20((X1 /\ X),(((Y1) /\ (Y)))))
K20((X1 /\ X),(((Y1) /\ (Y)))) is Relation-like set
K19(K20((X1 /\ X),(((Y1) /\ (Y))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is Relation-like (X1 /\ X2) /\ X -defined ((((((Y1) /\ (Y2)))) /\ (Y))) -valued Function-like () Element of K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))))
(X1 /\ X2) /\ X is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
((((Y1) /\ (Y2)))) /\ (Y) is set
((((((Y1) /\ (Y2)))) /\ (Y))) is functional () set
K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))) is Relation-like set
K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y))))) is set
(X2,X,Y2,Y,f2,f) is Relation-like X2 /\ X -defined (((Y2) /\ (Y))) -valued Function-like () Element of K19(K20((X2 /\ X),(((Y2) /\ (Y)))))
K20((X2 /\ X),(((Y2) /\ (Y)))) is Relation-like set
K19(K20((X2 /\ X),(((Y2) /\ (Y))))) is set
((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) is Relation-like (X1 /\ X) /\ (X2 /\ X) -defined ((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) -valued Function-like () Element of K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))))
(X1 /\ X) /\ (X2 /\ X) is set
((((Y1) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
((((Y2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))) is set
((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) is functional () set
K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))) is Relation-like set
K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))))) is set
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
X /\ X1 is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
(X,X2,Y,Y2,f,f2) is Relation-like X /\ X2 -defined (((Y) /\ (Y2))) -valued Function-like () Element of K19(K20((X /\ X2),(((Y) /\ (Y2)))))
X /\ X2 is set
(Y) /\ (Y2) is set
(((Y) /\ (Y2))) is functional () set
K20((X /\ X2),(((Y) /\ (Y2)))) is Relation-like set
K19(K20((X /\ X2),(((Y) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
X is functional () set
X1 is functional () set
X2 is Relation-like X -valued Function-like () set
Y is Relation-like X1 -valued Function-like () set
dom X2 is set
dom Y is set
(dom X2) /\ (dom Y) is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y1 is Relation-like Function-like set
dom Y1 is set
Y2 is Relation-like Function-like set
dom Y2 is set
f is set
Y1 . f is set
Y2 . f is set
X2 . f is Relation-like Function-like complex-valued set
Y . f is Relation-like Function-like complex-valued set
(X2 . f) /" (Y . f) is Relation-like Function-like complex-valued set
(Y . f) " is Relation-like Function-like complex-valued set
(X2 . f) (#) ((Y . f) ") is Relation-like Function-like complex-valued set
X is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X2,Y,Y1,Y2) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X2,Y,Y1,Y2) is set
f1 is set
f2 is set
(X2,Y,Y1,Y2) . f2 is set
Y1 . f2 is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
(Y1 . f2) /" (Y2 . f2) is Relation-like Function-like complex-valued set
(Y2 . f2) " is Relation-like Function-like complex-valued set
(Y1 . f2) (#) ((Y2 . f2) ") is Relation-like Function-like complex-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),COMPLEX) is Relation-like complex-valued set
K19(K20(((X2) /\ (Y)),COMPLEX)) is set
X is set
X2 is functional () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) /" (Y2 . f2) is Relation-like Function-like complex-valued ext-real-valued real-valued set
(Y2 . f2) " is Relation-like Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) (#) ((Y2 . f2) ") is Relation-like Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),REAL) is Relation-like complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),REAL)) is set
X is set
X2 is functional () () () () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
X1 is set
Y is functional () () () () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
Y1 is Relation-like X -defined X2 -valued Function-like () () () () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () () () () Element of K19(K20(X1,Y))
(X2,Y,Y1,Y2) is Relation-like Function-like set
X /\ X1 is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () () () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
(((X2) /\ (Y))) is functional () () () set
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
rng (X,X1,X2,Y,Y1,Y2) is functional () () () Element of K19((((X2) /\ (Y))))
K19((((X2) /\ (Y)))) is set
f1 is set
f2 is set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued ext-real-valued real-valued set
Y1 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
Y2 . f2 is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) /" (Y2 . f2) is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(Y2 . f2) " is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
(Y1 . f2) (#) ((Y2 . f2) ") is Relation-like RAT -valued Function-like complex-valued ext-real-valued real-valued set
f3 is Relation-like Function-like set
rng f3 is set
f4 is set
dom (Y2 . f2) is set
dom (Y1 . f2) is set
dom f3 is set
(dom (Y1 . f2)) /\ (dom (Y2 . f2)) is set
K20(((X2) /\ (Y)),RAT) is Relation-like RAT -valued complex-valued ext-real-valued real-valued set
K19(K20(((X2) /\ (Y)),RAT)) is set
X is set
X1 is set
X /\ X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
((X2)) is functional () set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
(X,X2,Y1) is Relation-like X -defined ((X2)) -valued Function-like () Element of K19(K20(X,((X2))))
K20(X,((X2))) is Relation-like set
K19(K20(X,((X2)))) is set
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X,X1,((X2)),Y,(X,X2,Y1),Y2) is Relation-like X /\ X1 -defined (((((X2))) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2))) /\ (Y)))))
(((X2))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((X2)) : verum } is set
(((X2))) /\ (Y) is set
(((((X2))) /\ (Y))) is functional () set
K20((X /\ X1),(((((X2))) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((((X2))) /\ (Y))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Relation-like X /\ X1 -defined (((((X2) /\ (Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2) /\ (Y)))))))
((((X2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
(((((X2) /\ (Y))))) is functional () set
K20((X /\ X1),(((((X2) /\ (Y)))))) is Relation-like set
K19(K20((X /\ X1),(((((X2) /\ (Y))))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X,X2,Y1) is Element of K19(X)
dom (X,X1,((X2)),Y,(X,X2,Y1),Y2) is Element of K19((X /\ X1))
(dom (X,X2,Y1)) /\ (dom Y2) is Element of K19(X1)
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Element of K19((X /\ X1))
dom (X,X1,((X2)),Y,(X,X2,Y1),Y2) is set
f2 is set
(X,X1,((X2)),Y,(X,X2,Y1),Y2) . f2 is Relation-like Function-like complex-valued set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) . f2 is Relation-like Function-like complex-valued set
(X,X2,Y1) . f2 is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
((X,X2,Y1) . f2) /" (Y2 . f2) is Relation-like Function-like complex-valued set
(Y2 . f2) " is Relation-like Function-like complex-valued set
((X,X2,Y1) . f2) (#) ((Y2 . f2) ") is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued set
- (Y1 . f2) is Relation-like Function-like complex-valued set
(- 1) (#) (Y1 . f2) is Relation-like Function-like complex-valued set
(- (Y1 . f2)) /" (Y2 . f2) is Relation-like Function-like complex-valued set
(- (Y1 . f2)) (#) ((Y2 . f2) ") is Relation-like Function-like complex-valued set
(Y1 . f2) /" (Y2 . f2) is Relation-like Function-like complex-valued set
(Y1 . f2) (#) ((Y2 . f2) ") is Relation-like Function-like complex-valued set
- ((Y1 . f2) /" (Y2 . f2)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y1 . f2) /" (Y2 . f2)) is Relation-like Function-like complex-valued set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is functional () set
K20(X,X2) is Relation-like set
K19(K20(X,X2)) is set
(X2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of X2 : verum } is set
Y is functional () set
K20(X1,Y) is Relation-like set
K19(K20(X1,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
((Y)) is functional () set
(X2) /\ (Y) is set
(((X2) /\ (Y))) is functional () set
Y1 is Relation-like X -defined X2 -valued Function-like () Element of K19(K20(X,X2))
Y2 is Relation-like X1 -defined Y -valued Function-like () Element of K19(K20(X1,Y))
(X1,Y,Y2) is Relation-like X1 -defined ((Y)) -valued Function-like () Element of K19(K20(X1,((Y))))
K20(X1,((Y))) is Relation-like set
K19(K20(X1,((Y)))) is set
(X,X1,X2,((Y)),Y1,(X1,Y,Y2)) is Relation-like X /\ X1 -defined (((X2) /\ (((Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (((Y)))))))
(((Y))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of ((Y)) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of ((Y)) : verum } is set
(X2) /\ (((Y))) is set
(((X2) /\ (((Y))))) is functional () set
K20((X /\ X1),(((X2) /\ (((Y)))))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (((Y))))))) is set
(X,X1,X2,Y,Y1,Y2) is Relation-like X /\ X1 -defined (((X2) /\ (Y))) -valued Function-like () Element of K19(K20((X /\ X1),(((X2) /\ (Y)))))
K20((X /\ X1),(((X2) /\ (Y)))) is Relation-like set
K19(K20((X /\ X1),(((X2) /\ (Y))))) is set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Relation-like X /\ X1 -defined (((((X2) /\ (Y))))) -valued Function-like () Element of K19(K20((X /\ X1),(((((X2) /\ (Y)))))))
((((X2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((X2) /\ (Y))) : verum } is set
(((((X2) /\ (Y))))) is functional () set
K20((X /\ X1),(((((X2) /\ (Y)))))) is Relation-like set
K19(K20((X /\ X1),(((((X2) /\ (Y))))))) is set
dom (X,X1,X2,Y,Y1,Y2) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom Y1 is Element of K19(X)
K19(X) is set
dom Y2 is Element of K19(X1)
K19(X1) is set
(dom Y1) /\ (dom Y2) is Element of K19(X1)
dom (X1,Y,Y2) is Element of K19(X1)
dom (X,X1,X2,((Y)),Y1,(X1,Y,Y2)) is Element of K19((X /\ X1))
(dom Y1) /\ (dom (X1,Y,Y2)) is Element of K19(X1)
dom ((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) is Element of K19((X /\ X1))
dom (X,X1,X2,((Y)),Y1,(X1,Y,Y2)) is set
f2 is set
(X,X1,X2,((Y)),Y1,(X1,Y,Y2)) . f2 is Relation-like Function-like complex-valued set
((X /\ X1),(((X2) /\ (Y))),(X,X1,X2,Y,Y1,Y2)) . f2 is Relation-like Function-like complex-valued set
Y1 . f2 is Relation-like Function-like complex-valued set
(X1,Y,Y2) . f2 is Relation-like Function-like complex-valued set
(Y1 . f2) /" ((X1,Y,Y2) . f2) is Relation-like Function-like complex-valued set
((X1,Y,Y2) . f2) " is Relation-like Function-like complex-valued set
(Y1 . f2) (#) (((X1,Y,Y2) . f2) ") is Relation-like Function-like complex-valued set
Y2 . f2 is Relation-like Function-like complex-valued set
- (Y2 . f2) is Relation-like Function-like complex-valued set
(- 1) (#) (Y2 . f2) is Relation-like Function-like complex-valued set
(Y1 . f2) /" (- (Y2 . f2)) is Relation-like Function-like complex-valued set
(- (Y2 . f2)) " is Relation-like Function-like complex-valued set
(Y1 . f2) (#) ((- (Y2 . f2)) ") is Relation-like Function-like complex-valued set
(Y1 . f2) /" (Y2 . f2) is Relation-like Function-like complex-valued set
(Y2 . f2) " is Relation-like Function-like complex-valued set
(Y1 . f2) (#) ((Y2 . f2) ") is Relation-like Function-like complex-valued set
- ((Y1 . f2) /" (Y2 . f2)) is Relation-like Function-like complex-valued set
(- 1) (#) ((Y1 . f2) /" (Y2 . f2)) is Relation-like Function-like complex-valued set
(X,X1,X2,Y,Y1,Y2) . f2 is Relation-like Function-like complex-valued set
- ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
(- 1) (#) ((X,X1,X2,Y,Y1,Y2) . f2) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) /" (f2 . f5) is Relation-like Function-like complex-valued set
(f2 . f5) " is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) (#) ((f2 . f5) ") is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) (#) (f1 . f5) is Relation-like Function-like complex-valued set
((f . f5) (#) (f1 . f5)) /" (f2 . f5) is Relation-like Function-like complex-valued set
((f . f5) (#) (f1 . f5)) (#) ((f2 . f5) ") is Relation-like Function-like complex-valued set
(f1 . f5) /" (f2 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) (#) ((f2 . f5) ") is Relation-like Function-like complex-valued set
(f . f5) (#) ((f1 . f5) /" (f2 . f5)) is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . f5 is Relation-like Function-like complex-valued set
(f . f5) (#) ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y) /\ (Y2) is set
(((Y) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X,X2,Y,Y2,f,f2) is Relation-like X /\ X2 -defined (((Y) /\ (Y2))) -valued Function-like () Element of K19(K20((X /\ X2),(((Y) /\ (Y2)))))
K20((X /\ X2),(((Y) /\ (Y2)))) is Relation-like set
K19(K20((X /\ X2),(((Y) /\ (Y2))))) is set
((X /\ X2),X1,(((Y) /\ (Y2))),Y1,(X,X2,Y,Y2,f,f2),f1) is Relation-like (X /\ X2) /\ X1 -defined ((((((Y) /\ (Y2)))) /\ (Y1))) -valued Function-like () Element of K19(K20(((X /\ X2) /\ X1),((((((Y) /\ (Y2)))) /\ (Y1)))))
(X /\ X2) /\ X1 is set
((((Y) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y2))) : verum } is set
((((Y) /\ (Y2)))) /\ (Y1) is set
((((((Y) /\ (Y2)))) /\ (Y1))) is functional () set
K20(((X /\ X2) /\ X1),((((((Y) /\ (Y2)))) /\ (Y1)))) is Relation-like set
K19(K20(((X /\ X2) /\ X1),((((((Y) /\ (Y2)))) /\ (Y1))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X2),X1,(((Y) /\ (Y2))),Y1,(X,X2,Y,Y2,f,f2),f1) is Element of K19(((X /\ X2) /\ X1))
K19(((X /\ X2) /\ X1)) is set
dom (X,X2,Y,Y2,f,f2) is Element of K19((X /\ X2))
K19((X /\ X2)) is set
dom f1 is Element of K19(X1)
K19(X1) is set
(dom (X,X2,Y,Y2,f,f2)) /\ (dom f1) is Element of K19(X1)
dom f is Element of K19(X)
K19(X) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
((X /\ X2),X1,(((Y) /\ (Y2))),Y1,(X,X2,Y,Y2,f,f2),f1) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) (#) (f2 . f5) is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) /" (f1 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) " is Relation-like Function-like complex-valued set
(f . f5) (#) ((f1 . f5) ") is Relation-like Function-like complex-valued set
((f . f5) /" (f1 . f5)) (#) (f2 . f5) is Relation-like Function-like complex-valued set
(f . f5) (#) (f2 . f5) is Relation-like Function-like complex-valued set
((f . f5) (#) (f2 . f5)) /" (f1 . f5) is Relation-like Function-like complex-valued set
((f . f5) (#) (f2 . f5)) (#) ((f1 . f5) ") is Relation-like Function-like complex-valued set
(X,X2,Y,Y2,f,f2) . f5 is Relation-like Function-like complex-valued set
((X,X2,Y,Y2,f,f2) . f5) /" (f1 . f5) is Relation-like Function-like complex-valued set
((X,X2,Y,Y2,f,f2) . f5) (#) ((f1 . f5) ") is Relation-like Function-like complex-valued set
X is set
X1 is set
X /\ X1 is set
X2 is set
X1 /\ X2 is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y) /\ (Y1) is set
(((Y) /\ (Y1))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X,X1,Y,Y1,f,f1) is Relation-like X /\ X1 -defined (((Y) /\ (Y1))) -valued Function-like () Element of K19(K20((X /\ X1),(((Y) /\ (Y1)))))
K20((X /\ X1),(((Y) /\ (Y1)))) is Relation-like set
K19(K20((X /\ X1),(((Y) /\ (Y1))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Relation-like (X /\ X1) /\ X2 -defined ((((((Y) /\ (Y1)))) /\ (Y2))) -valued Function-like () Element of K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))))
(X /\ X1) /\ X2 is set
((((Y) /\ (Y1)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y) /\ (Y1))) : verum } is set
((((Y) /\ (Y1)))) /\ (Y2) is set
((((((Y) /\ (Y1)))) /\ (Y2))) is functional () set
K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2)))) is Relation-like set
K19(K20(((X /\ X1) /\ X2),((((((Y) /\ (Y1)))) /\ (Y2))))) is set
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Relation-like X /\ (X1 /\ X2) -defined (((Y) /\ ((((Y1) /\ (Y2)))))) -valued Function-like () Element of K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))))
X /\ (X1 /\ X2) is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
(Y) /\ ((((Y1) /\ (Y2)))) is set
(((Y) /\ ((((Y1) /\ (Y2)))))) is functional () set
K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2))))))) is Relation-like set
K19(K20((X /\ (X1 /\ X2)),(((Y) /\ ((((Y1) /\ (Y2)))))))) is set
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is Element of K19(((X /\ X1) /\ X2))
K19(((X /\ X1) /\ X2)) is set
dom (X,X1,Y,Y1,f,f1) is Element of K19((X /\ X1))
K19((X /\ X1)) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom (X,X1,Y,Y1,f,f1)) /\ (dom f2) is Element of K19(X2)
dom (X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) is Element of K19((X /\ (X1 /\ X2)))
K19((X /\ (X1 /\ X2))) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
(dom f) /\ (dom f1) is Element of K19(X1)
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) is set
f5 is set
((X /\ X1),X2,(((Y) /\ (Y1))),Y2,(X,X1,Y,Y1,f,f1),f2) . f5 is Relation-like Function-like complex-valued set
(X,(X1 /\ X2),Y,(((Y1) /\ (Y2))),f,(X1,X2,Y1,Y2,f1,f2)) . f5 is Relation-like Function-like complex-valued set
(X,X1,Y,Y1,f,f1) . f5 is Relation-like Function-like complex-valued set
f2 . f5 is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) /" (f2 . f5) is Relation-like Function-like complex-valued set
(f2 . f5) " is Relation-like Function-like complex-valued set
((X,X1,Y,Y1,f,f1) . f5) (#) ((f2 . f5) ") is Relation-like Function-like complex-valued set
f . f5 is Relation-like Function-like complex-valued set
f1 . f5 is Relation-like Function-like complex-valued set
(f . f5) /" (f1 . f5) is Relation-like Function-like complex-valued set
(f1 . f5) " is Relation-like Function-like complex-valued set
(f . f5) (#) ((f1 . f5) ") is Relation-like Function-like complex-valued set
((f . f5) /" (f1 . f5)) /" (f2 . f5) is Relation-like Function-like complex-valued set
((f . f5) /" (f1 . f5)) (#) ((f2 . f5) ") is Relation-like Function-like complex-valued set
(f1 . f5) (#) (f2 . f5) is Relation-like Function-like complex-valued set
(f . f5) /" ((f1 . f5) (#) (f2 . f5)) is Relation-like Function-like complex-valued set
((f1 . f5) (#) (f2 . f5)) " is Relation-like Function-like complex-valued set
(f . f5) (#) (((f1 . f5) (#) (f2 . f5)) ") is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . f5 is Relation-like Function-like complex-valued set
(f . f5) /" ((X1,X2,Y1,Y2,f1,f2) . f5) is Relation-like Function-like complex-valued set
((X1,X2,Y1,Y2,f1,f2) . f5) " is Relation-like Function-like complex-valued set
(f . f5) (#) (((X1,X2,Y1,Y2,f1,f2) . f5) ") is Relation-like Function-like complex-valued set
X is set
X1 is set
X1 /\ X is set
X2 is set
X1 /\ X2 is set
X2 /\ X is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y1) /\ (Y) is set
(((Y1) /\ (Y))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
(Y2) /\ (Y) is set
(((Y2) /\ (Y))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X1,X,Y1,Y,f1,f) is Relation-like X1 /\ X -defined (((Y1) /\ (Y))) -valued Function-like () Element of K19(K20((X1 /\ X),(((Y1) /\ (Y)))))
K20((X1 /\ X),(((Y1) /\ (Y)))) is Relation-like set
K19(K20((X1 /\ X),(((Y1) /\ (Y))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is Relation-like (X1 /\ X2) /\ X -defined ((((((Y1) /\ (Y2)))) /\ (Y))) -valued Function-like () Element of K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))))
(X1 /\ X2) /\ X is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
((((Y1) /\ (Y2)))) /\ (Y) is set
((((((Y1) /\ (Y2)))) /\ (Y))) is functional () set
K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))) is Relation-like set
K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y))))) is set
(X2,X,Y2,Y,f2,f) is Relation-like X2 /\ X -defined (((Y2) /\ (Y))) -valued Function-like () Element of K19(K20((X2 /\ X),(((Y2) /\ (Y)))))
K20((X2 /\ X),(((Y2) /\ (Y)))) is Relation-like set
K19(K20((X2 /\ X),(((Y2) /\ (Y))))) is set
((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) is Relation-like (X1 /\ X) /\ (X2 /\ X) -defined ((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) -valued Function-like () Element of K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))))
(X1 /\ X) /\ (X2 /\ X) is set
((((Y1) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
((((Y2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))) is set
((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) is functional () set
K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))) is Relation-like set
K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))))) is set
dom ((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is Element of K19(((X1 /\ X2) /\ X))
K19(((X1 /\ X2) /\ X)) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) is Element of K19(((X1 /\ X) /\ (X2 /\ X)))
K19(((X1 /\ X) /\ (X2 /\ X))) is set
dom (X1,X,Y1,Y,f1,f) is Element of K19((X1 /\ X))
K19((X1 /\ X)) is set
dom (X2,X,Y2,Y,f2,f) is Element of K19((X2 /\ X))
K19((X2 /\ X)) is set
(dom (X1,X,Y1,Y,f1,f)) /\ (dom (X2,X,Y2,Y,f2,f)) is Element of K19((X2 /\ X))
(dom f1) /\ (dom f) is Element of K19(X)
(dom f2) /\ (dom f) is Element of K19(X)
dom ((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is set
x is set
((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) . x is Relation-like Function-like complex-valued set
((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) . x is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . x is Relation-like Function-like complex-valued set
f . x is Relation-like Function-like complex-valued set
((X1,X2,Y1,Y2,f1,f2) . x) /" (f . x) is Relation-like Function-like complex-valued set
(f . x) " is Relation-like Function-like complex-valued set
((X1,X2,Y1,Y2,f1,f2) . x) (#) ((f . x) ") is Relation-like Function-like complex-valued set
f1 . x is Relation-like Function-like complex-valued set
f2 . x is Relation-like Function-like complex-valued set
(f1 . x) + (f2 . x) is Relation-like Function-like complex-valued set
((f1 . x) + (f2 . x)) /" (f . x) is Relation-like Function-like complex-valued set
((f1 . x) + (f2 . x)) (#) ((f . x) ") is Relation-like Function-like complex-valued set
(f1 . x) /" (f . x) is Relation-like Function-like complex-valued set
(f1 . x) (#) ((f . x) ") is Relation-like Function-like complex-valued set
(f2 . x) /" (f . x) is Relation-like Function-like complex-valued set
(f2 . x) (#) ((f . x) ") is Relation-like Function-like complex-valued set
((f1 . x) /" (f . x)) + ((f2 . x) /" (f . x)) is Relation-like Function-like complex-valued set
(X1,X,Y1,Y,f1,f) . x is Relation-like Function-like complex-valued set
((X1,X,Y1,Y,f1,f) . x) + ((f2 . x) /" (f . x)) is Relation-like Function-like complex-valued set
(X2,X,Y2,Y,f2,f) . x is Relation-like Function-like complex-valued set
((X1,X,Y1,Y,f1,f) . x) + ((X2,X,Y2,Y,f2,f) . x) is Relation-like Function-like complex-valued set
X is set
X1 is set
X1 /\ X is set
X2 is set
X1 /\ X2 is set
X2 /\ X is set
Y is functional () set
K20(X,Y) is Relation-like set
K19(K20(X,Y)) is set
(Y) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y : verum } is set
Y1 is functional () set
K20(X1,Y1) is Relation-like set
K19(K20(X1,Y1)) is set
(Y1) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y1 : verum } is set
(Y1) /\ (Y) is set
(((Y1) /\ (Y))) is functional () set
Y2 is functional () set
K20(X2,Y2) is Relation-like set
K19(K20(X2,Y2)) is set
(Y2) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of Y2 : verum } is set
(Y1) /\ (Y2) is set
(((Y1) /\ (Y2))) is functional () set
(Y2) /\ (Y) is set
(((Y2) /\ (Y))) is functional () set
f is Relation-like X -defined Y -valued Function-like () Element of K19(K20(X,Y))
f1 is Relation-like X1 -defined Y1 -valued Function-like () Element of K19(K20(X1,Y1))
(X1,X,Y1,Y,f1,f) is Relation-like X1 /\ X -defined (((Y1) /\ (Y))) -valued Function-like () Element of K19(K20((X1 /\ X),(((Y1) /\ (Y)))))
K20((X1 /\ X),(((Y1) /\ (Y)))) is Relation-like set
K19(K20((X1 /\ X),(((Y1) /\ (Y))))) is set
f2 is Relation-like X2 -defined Y2 -valued Function-like () Element of K19(K20(X2,Y2))
(X1,X2,Y1,Y2,f1,f2) is Relation-like X1 /\ X2 -defined (((Y1) /\ (Y2))) -valued Function-like () Element of K19(K20((X1 /\ X2),(((Y1) /\ (Y2)))))
K20((X1 /\ X2),(((Y1) /\ (Y2)))) is Relation-like set
K19(K20((X1 /\ X2),(((Y1) /\ (Y2))))) is set
((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is Relation-like (X1 /\ X2) /\ X -defined ((((((Y1) /\ (Y2)))) /\ (Y))) -valued Function-like () Element of K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))))
(X1 /\ X2) /\ X is set
((((Y1) /\ (Y2)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y2))) : verum } is set
((((Y1) /\ (Y2)))) /\ (Y) is set
((((((Y1) /\ (Y2)))) /\ (Y))) is functional () set
K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y)))) is Relation-like set
K19(K20(((X1 /\ X2) /\ X),((((((Y1) /\ (Y2)))) /\ (Y))))) is set
(X2,X,Y2,Y,f2,f) is Relation-like X2 /\ X -defined (((Y2) /\ (Y))) -valued Function-like () Element of K19(K20((X2 /\ X),(((Y2) /\ (Y)))))
K20((X2 /\ X),(((Y2) /\ (Y)))) is Relation-like set
K19(K20((X2 /\ X),(((Y2) /\ (Y))))) is set
((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) is Relation-like (X1 /\ X) /\ (X2 /\ X) -defined ((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) -valued Function-like () Element of K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))))
(X1 /\ X) /\ (X2 /\ X) is set
((((Y1) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y1) /\ (Y))) : verum } is set
((((Y2) /\ (Y)))) is set
{ (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
union { (dom b₁) where b₁ is Relation-like Function-like Element of (((Y2) /\ (Y))) : verum } is set
((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))) is set
((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))) is functional () set
K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y))))))) is Relation-like set
K19(K20(((X1 /\ X) /\ (X2 /\ X)),((((((Y1) /\ (Y)))) /\ ((((Y2) /\ (Y)))))))) is set
dom ((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is Element of K19(((X1 /\ X2) /\ X))
K19(((X1 /\ X2) /\ X)) is set
dom f is Element of K19(X)
K19(X) is set
dom (X1,X2,Y1,Y2,f1,f2) is Element of K19((X1 /\ X2))
K19((X1 /\ X2)) is set
(dom f) /\ (dom (X1,X2,Y1,Y2,f1,f2)) is Element of K19((X1 /\ X2))
dom f1 is Element of K19(X1)
K19(X1) is set
dom f2 is Element of K19(X2)
K19(X2) is set
(dom f1) /\ (dom f2) is Element of K19(X2)
dom ((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) is Element of K19(((X1 /\ X) /\ (X2 /\ X)))
K19(((X1 /\ X) /\ (X2 /\ X))) is set
dom (X1,X,Y1,Y,f1,f) is Element of K19((X1 /\ X))
K19((X1 /\ X)) is set
dom (X2,X,Y2,Y,f2,f) is Element of K19((X2 /\ X))
K19((X2 /\ X)) is set
(dom (X1,X,Y1,Y,f1,f)) /\ (dom (X2,X,Y2,Y,f2,f)) is Element of K19((X2 /\ X))
(dom f1) /\ (dom f) is Element of K19(X)
(dom f2) /\ (dom f) is Element of K19(X)
dom ((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) is set
x is set
((X1 /\ X2),X,(((Y1) /\ (Y2))),Y,(X1,X2,Y1,Y2,f1,f2),f) . x is Relation-like Function-like complex-valued set
((X1 /\ X),(X2 /\ X),(((Y1) /\ (Y))),(((Y2) /\ (Y))),(X1,X,Y1,Y,f1,f),(X2,X,Y2,Y,f2,f)) . x is Relation-like Function-like complex-valued set
(X1,X2,Y1,Y2,f1,f2) . x is Relation-like Function-like complex-valued set
f . x is Relation-like Function-like complex-valued set
((X1,X2,Y1,Y2,f1,f2) . x) /" (f . x) is Relation-like Function-like complex-valued set
(f . x) " is Relation-like Function-like complex-valued set
((X1,X2,Y1,Y2,f1,f2) . x) (#) ((f . x) ") is Relation-like Function-like complex-valued set
f1 . x is Relation-like Function-like complex-valued set
f2 . x is Relation-like Function-like complex-valued set
(f1 . x) - (f2 . x) is Relation-like Function-like complex-valued set
- (f2 . x) is Relation-like Function-like complex-valued set
(- 1) (#) (f2 . x) is Relation-like Function-like complex-valued set
(f1 . x) + (- (f2 . x)) is Relation-like Function-like complex-valued set
((f1 . x) - (f2 . x)) /" (f . x) is Relation-like Function-like complex-valued set
((f1 . x) - (f2 . x)) (#) ((f . x) ") is Relation-like Function-like complex-valued set
(f1 . x) /" (f . x) is Relation-like Function-like complex-valued set
(f1 . x) (#) ((f . x) ") is Relation-like Function-like complex-valued set
(f2 . x) /" (f . x) is Relation-like Function-like complex-valued set
(f2 . x) (#) ((f . x) ") is Relation-like Function-like complex-valued set
((f1 . x) /" (f . x)) - ((f2 . x) /" (f . x)) is Relation-like Function-like complex-valued set
- ((f2 . x) /" (f . x)) is Relation-like Function-like complex-valued set
(- 1) (#) ((f2 . x) /" (f . x)) is Relation-like Function-like complex-valued set
((f1 . x) /" (f . x)) + (- ((f2 . x) /" (f . x))) is Relation-like Function-like complex-valued set
(X1,X,Y1,Y,f1,f) . x is Relation-like Function-like complex-valued set
((X1,X,Y1,Y,f1,f) . x) - ((f2 . x) /" (f . x)) is Relation-like Function-like complex-valued set
((X1,X,Y1,Y,f1,f) . x) + (- ((f2 . x) /" (f . x))) is Relation-like Function-like complex-valued set
(X2,X,Y2,Y,f2,f) . x is Relation-like Function-like complex-valued set
((X1,X,Y1,Y,f1,f) . x) - ((X2,X,Y2,Y,f2,f) . x) is Relation-like Function-like complex-valued set
- ((X2,X,Y2,Y,f2,f) . x) is Relation-like Function-like complex-valued set
(- 1) (#) ((X2,X,Y2,Y,f2,f) . x) is Relation-like Function-like complex-valued set
((X1,X,Y1,Y,f1,f) . x) + (- ((X2,X,Y2,Y,f2,f) . x)) is Relation-like Function-like complex-valued set