:: DIFF_1 semantic presentation

REAL is non empty V32() V57() V58() V59() V63() set
NAT is non empty epsilon-transitive epsilon-connected ordinal V57() V58() V59() V60() V61() V62() V63() Element of bool REAL
bool REAL is set
[:NAT,REAL:] is V13() complex-valued ext-real-valued real-valued set
bool [:NAT,REAL:] is set
COMPLEX is non empty V32() V57() V63() set
omega is non empty epsilon-transitive epsilon-connected ordinal V57() V58() V59() V60() V61() V62() V63() set
bool omega is set
bool NAT is set
RAT is non empty V32() V57() V58() V59() V60() V63() set
INT is non empty V32() V57() V58() V59() V60() V61() V63() set
ExtREAL is non empty V58() set
{} is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real V13() non-empty empty-yielding V17( RAT ) ext-real complex-valued ext-real-valued real-valued natural-valued V57() V58() V59() V60() V61() V62() V63() set
1 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive V56() V57() V58() V59() V60() V61() V62() Element of NAT
{{},1} is non empty V57() V58() V59() V60() V61() V62() set
0 is empty epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real V13() non-empty empty-yielding V17( RAT ) V30() ext-real complex-valued ext-real-valued real-valued natural-valued V56() V57() V58() V59() V60() V61() V62() V63() Element of NAT
- 1 is V11() real ext-real Element of REAL
PFuncs (REAL,REAL) is non empty functional set
[:NAT,(PFuncs (REAL,REAL)):] is V13() set
bool [:NAT,(PFuncs (REAL,REAL)):] is set
[:REAL,REAL:] is V13() complex-valued ext-real-valued real-valued set
bool [:REAL,REAL:] is set
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom x is V57() V58() V59() Element of bool REAL
h is V11() real ext-real set
- h is V11() real ext-real set
(- h) ++ (dom x) is V57() V58() V59() Element of bool REAL
f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom f2 is V57() V58() V59() Element of bool REAL
S is set
S is set
S is V11() real ext-real Element of REAL
f2 . S is V11() real ext-real Element of REAL
S + h is V11() real ext-real Element of REAL
x . (S + h) is V11() real ext-real Element of REAL
S is V11() real ext-real Element of REAL
f2 . S is V11() real ext-real Element of REAL
S + h is V11() real ext-real Element of REAL
x . (S + h) is V11() real ext-real Element of REAL
f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom f is V57() V58() V59() Element of bool REAL
f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom f2 is V57() V58() V59() Element of bool REAL
k is V11() real ext-real Element of REAL
f . k is V11() real ext-real Element of REAL
f2 . k is V11() real ext-real Element of REAL
k + h is V11() real ext-real Element of REAL
x . (k + h) is V11() real ext-real Element of REAL
x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (x,h) is V57() V58() V59() Element of bool REAL
dom x is non empty V57() V58() V59() Element of bool REAL
- h is V11() real ext-real set
(- h) ++ (dom x) is V57() V58() V59() Element of bool REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (x,h) is V57() V58() V59() Element of bool REAL
f2 is V11() real ext-real Element of REAL
dom x is non empty V57() V58() V59() Element of bool REAL
- h is V11() real ext-real set
(- h) ++ (dom x) is V57() V58() V59() Element of bool REAL
f . f2 is V11() real ext-real Element of REAL
f2 + h is V11() real ext-real Element of REAL
x . (f2 + h) is V11() real ext-real Element of REAL
dom f is non empty V57() V58() V59() Element of bool REAL
f2 is V11() real ext-real Element of REAL
f . f2 is V11() real ext-real Element of REAL
(x,h) . f2 is V11() real ext-real Element of REAL
f2 + h is V11() real ext-real Element of REAL
x . (f2 + h) is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is V11() real ext-real Element of REAL
f . f2 is V11() real ext-real Element of REAL
f2 + h is V11() real ext-real Element of REAL
x . (f2 + h) is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) - x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- x is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
- 1 is V11() real ext-real set
(- 1) (#) x is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(x,h) + (- x) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) - x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- x is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) x is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(x,h) + (- x) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
dom (x,h) is V57() V58() V59() Element of bool REAL
(x,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (x,h) is non empty V57() V58() V59() Element of bool REAL
dom x is non empty V57() V58() V59() Element of bool REAL
(dom (x,h)) /\ (dom x) is V57() V58() V59() Element of bool REAL
REAL /\ (dom x) is V57() V58() V59() Element of bool REAL
REAL /\ REAL is V57() V58() V59() set
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
- h is V11() real ext-real set
(x,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x - (x,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (x,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x + (- (x,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
(x,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x - (x,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (x,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x + (- (x,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
dom (x,h) is V57() V58() V59() Element of bool REAL
(x,(- h)) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (x,(- h)) is non empty V57() V58() V59() Element of bool REAL
dom x is non empty V57() V58() V59() Element of bool REAL
(dom (x,(- h))) /\ (dom x) is V57() V58() V59() Element of bool REAL
REAL /\ (dom x) is V57() V58() V59() Element of bool REAL
REAL /\ REAL is V57() V58() V59() set
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
2 is non empty epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real positive V56() V57() V58() V59() V60() V61() V62() Element of NAT
h / 2 is V11() real ext-real Element of REAL
(x,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(x,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,(h / 2)) - (x,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (x,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(x,(h / 2)) + (- (x,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(x,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(x,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,(h / 2)) - (x,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (x,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(x,(h / 2)) + (- (x,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
dom (x,h) is V57() V58() V59() Element of bool REAL
(x,(h / 2)) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (x,(h / 2)) is non empty V57() V58() V59() Element of bool REAL
(x,(- (h / 2))) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (x,(- (h / 2))) is non empty V57() V58() V59() Element of bool REAL
(dom (x,(h / 2))) /\ (dom (x,(- (h / 2)))) is V57() V58() V59() Element of bool REAL
REAL /\ (dom (x,(- (h / 2)))) is V57() V58() V59() Element of bool REAL
REAL /\ REAL is V57() V58() V59() set
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
S is Element of PFuncs (REAL,REAL)
k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,h) - k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- k is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) k is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(k,h) + (- k) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is Element of PFuncs (REAL,REAL)
r2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,h) - r2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- r2 is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) r2 is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(r2,h) + (- r2) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f is Element of PFuncs (REAL,REAL)
f2 is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
S . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
S . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S . k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S . k),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S . k),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S . k),h) - (S . k) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (S . k) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (S . k) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S . k),h) + (- (S . k)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) - x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- x is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) x is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(x,h) + (- x) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f . S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f . S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f . S),h) - (f . S) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f . S) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f . S) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f . S),h) + (- (f . S)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
x + h is V11() real ext-real Element of REAL
f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom f is V57() V58() V59() Element of bool REAL
(f,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,h) - f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) f is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,h) + (- f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,h) . x is V11() real ext-real Element of REAL
f . (x + h) is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
(f . (x + h)) - (f . x) is V11() real ext-real Element of REAL
dom (f,h) is V57() V58() V59() Element of bool REAL
- h is V11() real ext-real Element of REAL
(- h) ++ (dom f) is V57() V58() V59() Element of bool REAL
(- h) + (x + h) is V11() real ext-real Element of REAL
(f,h) . x is V11() real ext-real Element of REAL
(dom (f,h)) /\ (dom f) is V57() V58() V59() Element of bool REAL
dom (f,h) is V57() V58() V59() Element of bool REAL
x is V11() real ext-real Element of REAL
h is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(h,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
(h,x) . f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(h,x) . (f + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h,x) . f),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h,x) . f),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h,x) . f),x) - ((h,x) . f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((h,x) . f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((h,x) . f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((h,x) . f),x) + (- ((h,x) . f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(h,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
(h,x) . f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
h + x is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) - f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f,x) + (- f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
f . (h + x) is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
(f . (h + x)) - (f . h) is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) - f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) + (- f) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
dom ((f,x) - f) is non empty V57() V58() V59() Element of bool REAL
(f,x) . h is V11() real ext-real Element of REAL
((f,x) . h) - (f . h) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
h - x is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- x is V11() real ext-real set
(f,(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f - (f,(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f + (- (f,(- x))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
f . (h - x) is V11() real ext-real Element of REAL
(f . h) - (f . (h - x)) is V11() real ext-real Element of REAL
- x is V11() real ext-real Element of REAL
(f,(- x)) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- x)) - f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f,(- x)) + (- f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
- (f,(- x)) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(- 1) (#) (f,(- x)) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- (f,(- x))) . h is V11() real ext-real Element of REAL
(f,(- x)) . h is V11() real ext-real Element of REAL
- ((f,(- x)) . h) is V11() real ext-real Element of REAL
h + (- x) is V11() real ext-real Element of REAL
f . (h + (- x)) is V11() real ext-real Element of REAL
(f . (h + (- x))) - (f . h) is V11() real ext-real Element of REAL
- ((f . (h + (- x))) - (f . h)) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
x / 2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
h + (x / 2) is V11() real ext-real Element of REAL
h - (x / 2) is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x / 2 is V11() real ext-real Element of REAL
(f,(x / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x / 2) is V11() real ext-real Element of REAL
(f,(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(x / 2)) - (f,(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,(x / 2)) + (- (f,(- (x / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
f . (h + (x / 2)) is V11() real ext-real Element of REAL
f . (h - (x / 2)) is V11() real ext-real Element of REAL
(f . (h + (x / 2))) - (f . (h - (x / 2))) is V11() real ext-real Element of REAL
(f,(x / 2)) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x / 2) is V11() real ext-real Element of REAL
(f,(- (x / 2))) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(x / 2)) - (f,(- (x / 2))) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- (x / 2))) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- (x / 2))) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f,(x / 2)) + (- (f,(- (x / 2)))) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
dom ((f,(x / 2)) - (f,(- (x / 2)))) is non empty V57() V58() V59() Element of bool REAL
(f,(x / 2)) . h is V11() real ext-real Element of REAL
(f,(- (x / 2))) . h is V11() real ext-real Element of REAL
((f,(x / 2)) . h) - ((f,(- (x / 2))) . h) is V11() real ext-real Element of REAL
(f . (h + (x / 2))) - ((f,(- (x / 2))) . h) is V11() real ext-real Element of REAL
h + (- (x / 2)) is V11() real ext-real Element of REAL
f . (h + (- (x / 2))) is V11() real ext-real Element of REAL
(f . (h + (x / 2))) - (f . (h + (- (x / 2)))) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is V11() real ext-real Element of REAL
f2 + h is V11() real ext-real Element of REAL
f . (f2 + h) is V11() real ext-real Element of REAL
f . f2 is V11() real ext-real Element of REAL
(f . (f2 + h)) - (f . f2) is V11() real ext-real Element of REAL
dom f is non empty V57() V58() V59() Element of bool REAL
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f2 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (f2 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2 + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . ((f2 + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is V11() real ext-real Element of REAL
((f,h) . ((f2 + 1) + 1)) . S is V11() real ext-real Element of REAL
S + h is V11() real ext-real Element of REAL
((f,h) . (f2 + 1)) . (S + h) is V11() real ext-real Element of REAL
f2 + 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (f2 + 2) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,h) . (f2 + 2)) . S is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . (f2 + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . (f2 + 1)),h) - ((f,h) . (f2 + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f,h) . (f2 + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f,h) . (f2 + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . (f2 + 1)),h) + (- ((f,h) . (f2 + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . (f2 + 1)),h) . S is V11() real ext-real Element of REAL
((f,h) . (f2 + 1)) . S is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)) . (S + h)) - (((f,h) . (f2 + 1)) . S) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is V11() real ext-real Element of REAL
((f,h) . (0 + 1)) . f2 is V11() real ext-real Element of REAL
(f,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . 0),h) - ((f,h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . 0),h) + (- ((f,h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . 0),h) . f2 is V11() real ext-real Element of REAL
(f,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,h) - f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f,h) + (- f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,h) . f2 is V11() real ext-real Element of REAL
f2 + h is V11() real ext-real Element of REAL
f . (f2 + h) is V11() real ext-real Element of REAL
f . f2 is V11() real ext-real Element of REAL
(f . (f2 + h)) - (f . f2) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
((f,h) . (x + 1)) . f2 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
((f,h) . (x + 1)) . f2 is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h (#) S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((h (#) S),f) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) S),f) . (x + 1)) . f2 is V11() real ext-real Element of REAL
(S,f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,f) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,f) . (x + 1)) . f2 is V11() real ext-real Element of REAL
h * (((S,f) . (x + 1)) . f2) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((h (#) S),f) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,f) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
h * (((S,f) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
(((h (#) S),f) . (k + 1)) . x is V11() real ext-real Element of REAL
((S,f) . (k + 1)) . x is V11() real ext-real Element of REAL
h * (((S,f) . (k + 1)) . x) is V11() real ext-real Element of REAL
x + f is V11() real ext-real Element of REAL
(((h (#) S),f) . (k + 1)) . (x + f) is V11() real ext-real Element of REAL
((S,f) . (k + 1)) . (x + f) is V11() real ext-real Element of REAL
h * (((S,f) . (k + 1)) . (x + f)) is V11() real ext-real Element of REAL
((((h (#) S),f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . (k + 1)),f) - (((h (#) S),f) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((h (#) S),f) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((h (#) S),f) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . (k + 1)),f) + (- (((h (#) S),f) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . (k + 1)),f) . x is V11() real ext-real Element of REAL
(h * (((S,f) . (k + 1)) . (x + f))) - (h * (((S,f) . (k + 1)) . x)) is V11() real ext-real Element of REAL
(((S,f) . (k + 1)) . (x + f)) - (((S,f) . (k + 1)) . x) is V11() real ext-real Element of REAL
h * ((((S,f) . (k + 1)) . (x + f)) - (((S,f) . (k + 1)) . x)) is V11() real ext-real Element of REAL
(((S,f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (k + 1)),f) - ((S,f) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S,f) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S,f) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . (k + 1)),f) + (- ((S,f) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . (k + 1)),f) . x is V11() real ext-real Element of REAL
h * ((((S,f) . (k + 1)),f) . x) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((h (#) S),f) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,f) . (0 + 1)) . k is V11() real ext-real Element of REAL
h * (((S,f) . (0 + 1)) . k) is V11() real ext-real Element of REAL
dom (h (#) S) is non empty V57() V58() V59() Element of bool REAL
k + f is V11() real ext-real Element of REAL
((h (#) S),f) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . 0),f) - (((h (#) S),f) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((h (#) S),f) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((h (#) S),f) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . 0),f) + (- (((h (#) S),f) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . 0),f) . k is V11() real ext-real Element of REAL
((h (#) S),f) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),f) - (h (#) S) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h (#) S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (h (#) S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
((h (#) S),f) + (- (h (#) S)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((h (#) S),f) . k is V11() real ext-real Element of REAL
(h (#) S) . (k + f) is V11() real ext-real Element of REAL
(h (#) S) . k is V11() real ext-real Element of REAL
((h (#) S) . (k + f)) - ((h (#) S) . k) is V11() real ext-real Element of REAL
S . (k + f) is V11() real ext-real Element of REAL
h * (S . (k + f)) is V11() real ext-real Element of REAL
(h * (S . (k + f))) - ((h (#) S) . k) is V11() real ext-real Element of REAL
S . k is V11() real ext-real Element of REAL
h * (S . k) is V11() real ext-real Element of REAL
(h * (S . (k + f))) - (h * (S . k)) is V11() real ext-real Element of REAL
(S . (k + f)) - (S . k) is V11() real ext-real Element of REAL
h * ((S . (k + f)) - (S . k)) is V11() real ext-real Element of REAL
(S,f) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) - S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(S,f) + (- S) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,f) . k is V11() real ext-real Element of REAL
h * ((S,f) . k) is V11() real ext-real Element of REAL
(S,f) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),f) - ((S,f) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S,f) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S,f) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . 0),f) + (- ((S,f) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . 0),f) . k is V11() real ext-real Element of REAL
h * ((((S,f) . 0),f) . k) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (x + 1)) . f is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 + S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f2 + S),h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 + S),h) . (x + 1)) . f is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (x + 1)) . f is V11() real ext-real Element of REAL
(((f2,h) . (x + 1)) . f) + (((S,h) . (x + 1)) . f) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((f2 + S),h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) + (((S,h) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
(((f2 + S),h) . (k + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . x is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . x) + (((S,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
x + h is V11() real ext-real Element of REAL
(((f2 + S),h) . (k + 1)) . (x + h) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x + h) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x + h) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + h)) + (((S,h) . (k + 1)) . (x + h)) is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . (k + 1)),h) - (((f2 + S),h) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2 + S),h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2 + S),h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . (k + 1)),h) + (- (((f2 + S),h) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)) . (x + h)) - ((((f2 + S),h) . (k + 1)) . x) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + h)) - (((f2,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)) . (x + h)) - (((S,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)) . (x + h)) - (((f2,h) . (k + 1)) . x)) + ((((S,h) . (k + 1)) . (x + h)) - (((S,h) . (k + 1)) . x)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),h) - ((f2,h) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) + (- ((f2,h) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) + ((((S,h) . (k + 1)) . (x + h)) - (((S,h) . (k + 1)) . x)) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),h) - ((S,h) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) + (- ((S,h) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) + ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) + ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((f2 + S),h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((f2,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) + (((S,h) . (0 + 1)) . k) is V11() real ext-real Element of REAL
((f2 + S),h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . 0),h) - (((f2 + S),h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2 + S),h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2 + S),h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . 0),h) + (- (((f2 + S),h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . 0),h) . k is V11() real ext-real Element of REAL
((f2 + S),h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),h) - (f2 + S) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f2 + S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f2 + S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
((f2 + S),h) + (- (f2 + S)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 + S),h) . k is V11() real ext-real Element of REAL
k + h is V11() real ext-real Element of REAL
(f2 + S) . (k + h) is V11() real ext-real Element of REAL
(f2 + S) . k is V11() real ext-real Element of REAL
((f2 + S) . (k + h)) - ((f2 + S) . k) is V11() real ext-real Element of REAL
f2 . (k + h) is V11() real ext-real Element of REAL
S . (k + h) is V11() real ext-real Element of REAL
(f2 . (k + h)) + (S . (k + h)) is V11() real ext-real Element of REAL
((f2 . (k + h)) + (S . (k + h))) - ((f2 + S) . k) is V11() real ext-real Element of REAL
f2 . k is V11() real ext-real Element of REAL
S . k is V11() real ext-real Element of REAL
(f2 . k) + (S . k) is V11() real ext-real Element of REAL
((f2 . (k + h)) + (S . (k + h))) - ((f2 . k) + (S . k)) is V11() real ext-real Element of REAL
(f2 . (k + h)) - (f2 . k) is V11() real ext-real Element of REAL
(S . (k + h)) - (S . k) is V11() real ext-real Element of REAL
((f2 . (k + h)) - (f2 . k)) + ((S . (k + h)) - (S . k)) is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) - f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f2,h) + (- f2) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) + ((S . (k + h)) - (S . k)) is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) - S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(S,h) + (- S) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) + ((S,h) . k) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) - ((f2,h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) + (- ((f2,h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) + ((S,h) . k) is V11() real ext-real Element of REAL
(S,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) - ((S,h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) + (- ((S,h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) + ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) + ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (x + 1)) . f is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 - S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
f2 + (- S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
((f2 - S),h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f2 - S),h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 - S),h) . (x + 1)) . f is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (x + 1)) . f is V11() real ext-real Element of REAL
(((f2,h) . (x + 1)) . f) - (((S,h) . (x + 1)) . f) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((f2 - S),h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((f2,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) - (((S,h) . (0 + 1)) . k) is V11() real ext-real Element of REAL
dom f2 is non empty V57() V58() V59() Element of bool REAL
dom S is non empty V57() V58() V59() Element of bool REAL
(dom f2) /\ (dom S) is V57() V58() V59() Element of bool REAL
dom (f2 - S) is non empty V57() V58() V59() Element of bool REAL
k + h is V11() real ext-real Element of REAL
((f2 - S),h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . 0),h) - (((f2 - S),h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2 - S),h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2 - S),h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . 0),h) + (- (((f2 - S),h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . 0),h) . k is V11() real ext-real Element of REAL
((f2 - S),h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 - S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 - S),h) - (f2 - S) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f2 - S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f2 - S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
((f2 - S),h) + (- (f2 - S)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 - S),h) . k is V11() real ext-real Element of REAL
(f2 - S) . (k + h) is V11() real ext-real Element of REAL
(f2 - S) . k is V11() real ext-real Element of REAL
((f2 - S) . (k + h)) - ((f2 - S) . k) is V11() real ext-real Element of REAL
f2 . (k + h) is V11() real ext-real Element of REAL
S . (k + h) is V11() real ext-real Element of REAL
(f2 . (k + h)) - (S . (k + h)) is V11() real ext-real Element of REAL
((f2 . (k + h)) - (S . (k + h))) - ((f2 - S) . k) is V11() real ext-real Element of REAL
f2 . k is V11() real ext-real Element of REAL
S . k is V11() real ext-real Element of REAL
(f2 . k) - (S . k) is V11() real ext-real Element of REAL
((f2 . (k + h)) - (S . (k + h))) - ((f2 . k) - (S . k)) is V11() real ext-real Element of REAL
(f2 . (k + h)) - (f2 . k) is V11() real ext-real Element of REAL
(S . (k + h)) - (S . k) is V11() real ext-real Element of REAL
((f2 . (k + h)) - (f2 . k)) - ((S . (k + h)) - (S . k)) is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) - f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f2,h) + (- f2) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) - ((S . (k + h)) - (S . k)) is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) - S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) + (- S) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) - ((S,h) . k) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) - ((f2,h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) + (- ((f2,h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) - ((S,h) . k) is V11() real ext-real Element of REAL
(S,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) - ((S,h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) + (- ((S,h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) - ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) - ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((f2 - S),h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) - (((S,h) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
(((f2 - S),h) . (k + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . x is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
x + h is V11() real ext-real Element of REAL
(((f2 - S),h) . (k + 1)) . (x + h) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x + h) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x + h) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + h)) - (((S,h) . (k + 1)) . (x + h)) is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . (k + 1)),h) - (((f2 - S),h) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2 - S),h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2 - S),h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . (k + 1)),h) + (- (((f2 - S),h) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)) . (x + h)) - ((((f2 - S),h) . (k + 1)) . x) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + h)) - (((f2,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)) . (x + h)) - (((S,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)) . (x + h)) - (((f2,h) . (k + 1)) . x)) - ((((S,h) . (k + 1)) . (x + h)) - (((S,h) . (k + 1)) . x)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),h) - ((f2,h) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) + (- ((f2,h) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) - ((((S,h) . (k + 1)) . (x + h)) - (((S,h) . (k + 1)) . x)) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),h) - ((S,h) . (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S,h) . (k + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) + (- ((S,h) . (k + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) - ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) - ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is V11() real ext-real Element of REAL
k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h (#) k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(k,f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((k,f2) . (x + 1)) . S is V11() real ext-real Element of REAL
h * (((k,f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f (#) x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(h (#) k) + (f (#) x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) k) + (f (#) x)),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(((h (#) k) + (f (#) x)),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) k) + (f (#) x)),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
(x,f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(x,f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((x,f2) . (x + 1)) . S is V11() real ext-real Element of REAL
f * (((x,f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
(h * (((k,f2) . (x + 1)) . S)) + (f * (((x,f2) . (x + 1)) . S)) is V11() real ext-real Element of REAL
((h (#) k),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((h (#) k),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) k),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
((f (#) x),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f (#) x),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) x),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
((((h (#) k),f2) . (x + 1)) . S) + ((((f (#) x),f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
(h * (((k,f2) . (x + 1)) . S)) + ((((f (#) x),f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f,x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 1) . h is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) . h is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
((f,x) . h) - (f . h) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,x) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . (0 + 1)) . h is V11() real ext-real Element of REAL
(f,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) - ((f,x) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) + (- ((f,x) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) . h is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) - f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f,x) + (- f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
h + x is V11() real ext-real Element of REAL
f . (h + x) is V11() real ext-real Element of REAL
(f . (h + x)) - (f . h) is V11() real ext-real Element of REAL
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
S is Element of PFuncs (REAL,REAL)
k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
(k,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k - (k,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (k,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (k,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
k + (- (k,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is Element of PFuncs (REAL,REAL)
r2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
r2 - (r2,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (r2,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (r2,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
r2 + (- (r2,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f is Element of PFuncs (REAL,REAL)
f2 is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
S . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
S . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S . k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S . k),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
((S . k),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S . k) - ((S . k),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S . k),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S . k),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S . k) + (- ((S . k),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x - (x,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (x,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x + (- (x,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f . S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
((f . S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f . S) - ((f . S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f . S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f . S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f . S) + (- ((f . S),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is V11() real ext-real Element of REAL
h is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(h,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
(h,x) . f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(h,x) . (f + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h,x) . f),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- x is V11() real ext-real set
(((h,x) . f),(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h,x) . f) - (((h,x) . f),(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((h,x) . f),(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((h,x) . f),(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((h,x) . f) + (- (((h,x) . f),(- x))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(h,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
(h,x) . f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is V11() real ext-real Element of REAL
f . f2 is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
f . (f2 - h) is V11() real ext-real Element of REAL
(f . f2) - (f . (f2 - h)) is V11() real ext-real Element of REAL
dom f is non empty V57() V58() V59() Element of bool REAL
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f2 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (f2 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2 + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . ((f2 + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is V11() real ext-real Element of REAL
((f,h) . ((f2 + 1) + 1)) . S is V11() real ext-real Element of REAL
S - h is V11() real ext-real Element of REAL
((f,h) . (f2 + 1)) . (S - h) is V11() real ext-real Element of REAL
f2 + 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (f2 + 2) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,h) . (f2 + 2)) . S is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
(((f,h) . (f2 + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,h) . (f2 + 1)) - (((f,h) . (f2 + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f,h) . (f2 + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f,h) . (f2 + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f,h) . (f2 + 1)) + (- (((f,h) . (f2 + 1)),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . (f2 + 1)),h) . S is V11() real ext-real Element of REAL
((f,h) . (f2 + 1)) . S is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)) . S) - (((f,h) . (f2 + 1)) . (S - h)) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is V11() real ext-real Element of REAL
((f,h) . (0 + 1)) . f2 is V11() real ext-real Element of REAL
(f,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
(((f,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,h) . 0) - (((f,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f,h) . 0) + (- (((f,h) . 0),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . 0),h) . f2 is V11() real ext-real Element of REAL
(f,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f - (f,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f + (- (f,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,h) . f2 is V11() real ext-real Element of REAL
f . f2 is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
f . (f2 - h) is V11() real ext-real Element of REAL
(f . f2) - (f . (f2 - h)) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
((f,h) . (x + 1)) . f2 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
((f,h) . (x + 1)) . f2 is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h (#) S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((h (#) S),f) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) S),f) . (x + 1)) . f2 is V11() real ext-real Element of REAL
(S,f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,f) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,f) . (x + 1)) . f2 is V11() real ext-real Element of REAL
h * (((S,f) . (x + 1)) . f2) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((h (#) S),f) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,f) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
h * (((S,f) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
(((h (#) S),f) . (k + 1)) . x is V11() real ext-real Element of REAL
((S,f) . (k + 1)) . x is V11() real ext-real Element of REAL
h * (((S,f) . (k + 1)) . x) is V11() real ext-real Element of REAL
x - f is V11() real ext-real Element of REAL
(((h (#) S),f) . (k + 1)) . (x - f) is V11() real ext-real Element of REAL
((S,f) . (k + 1)) . (x - f) is V11() real ext-real Element of REAL
h * (((S,f) . (k + 1)) . (x - f)) is V11() real ext-real Element of REAL
((((h (#) S),f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V11() real ext-real set
((((h (#) S),f) . (k + 1)),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) S),f) . (k + 1)) - ((((h (#) S),f) . (k + 1)),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((h (#) S),f) . (k + 1)),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((h (#) S),f) . (k + 1)),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((h (#) S),f) . (k + 1)) + (- ((((h (#) S),f) . (k + 1)),(- f))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . (k + 1)),f) . x is V11() real ext-real Element of REAL
((((h (#) S),f) . (k + 1)) . x) - ((((h (#) S),f) . (k + 1)) . (x - f)) is V11() real ext-real Element of REAL
(((S,f) . (k + 1)) . x) - (((S,f) . (k + 1)) . (x - f)) is V11() real ext-real Element of REAL
h * ((((S,f) . (k + 1)) . x) - (((S,f) . (k + 1)) . (x - f))) is V11() real ext-real Element of REAL
(((S,f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (k + 1)),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,f) . (k + 1)) - (((S,f) . (k + 1)),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,f) . (k + 1)),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,f) . (k + 1)),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S,f) . (k + 1)) + (- (((S,f) . (k + 1)),(- f))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . (k + 1)),f) . x is V11() real ext-real Element of REAL
h * ((((S,f) . (k + 1)),f) . x) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((h (#) S),f) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,f) . (0 + 1)) . k is V11() real ext-real Element of REAL
h * (((S,f) . (0 + 1)) . k) is V11() real ext-real Element of REAL
dom (h (#) S) is non empty V57() V58() V59() Element of bool REAL
k - f is V11() real ext-real Element of REAL
((h (#) S),f) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V11() real ext-real set
((((h (#) S),f) . 0),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) S),f) . 0) - ((((h (#) S),f) . 0),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((h (#) S),f) . 0),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((h (#) S),f) . 0),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((h (#) S),f) . 0) + (- ((((h (#) S),f) . 0),(- f))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . 0),f) . k is V11() real ext-real Element of REAL
((h (#) S),f) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(h (#) S) - ((h (#) S),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((h (#) S),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((h (#) S),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(h (#) S) + (- ((h (#) S),(- f))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((h (#) S),f) . k is V11() real ext-real Element of REAL
(h (#) S) . k is V11() real ext-real Element of REAL
(h (#) S) . (k - f) is V11() real ext-real Element of REAL
((h (#) S) . k) - ((h (#) S) . (k - f)) is V11() real ext-real Element of REAL
S . (k - f) is V11() real ext-real Element of REAL
h * (S . (k - f)) is V11() real ext-real Element of REAL
((h (#) S) . k) - (h * (S . (k - f))) is V11() real ext-real Element of REAL
S . k is V11() real ext-real Element of REAL
h * (S . k) is V11() real ext-real Element of REAL
(h * (S . k)) - (h * (S . (k - f))) is V11() real ext-real Element of REAL
(S . k) - (S . (k - f)) is V11() real ext-real Element of REAL
h * ((S . k) - (S . (k - f))) is V11() real ext-real Element of REAL
(S,f) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S - (S,(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (S,(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (S,(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
S + (- (S,(- f))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,f) . k is V11() real ext-real Element of REAL
h * ((S,f) . k) is V11() real ext-real Element of REAL
(S,f) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,f) . 0) - (((S,f) . 0),(- f)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,f) . 0),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,f) . 0),(- f)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S,f) . 0) + (- (((S,f) . 0),(- f))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . 0),f) . k is V11() real ext-real Element of REAL
h * ((((S,f) . 0),f) . k) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (x + 1)) . f is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 + S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f2 + S),h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 + S),h) . (x + 1)) . f is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (x + 1)) . f is V11() real ext-real Element of REAL
(((f2,h) . (x + 1)) . f) + (((S,h) . (x + 1)) . f) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((f2 + S),h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) + (((S,h) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
(((f2 + S),h) . (k + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . x is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . x) + (((S,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
x - h is V11() real ext-real Element of REAL
(((f2 + S),h) . (k + 1)) . (x - h) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x - h) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x - h) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x - h)) + (((S,h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
((((f2 + S),h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 + S),h) . (k + 1)) - ((((f2 + S),h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 + S),h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 + S),h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2 + S),h) . (k + 1)) + (- ((((f2 + S),h) . (k + 1)),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)) . x) - ((((f2 + S),h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . x) - (((f2,h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)) . x) - (((f2,h) . (k + 1)) . (x - h))) + ((((S,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . (x - h))) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (k + 1)) - (((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2,h) . (k + 1)) + (- (((f2,h) . (k + 1)),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) + ((((S,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . (x - h))) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (k + 1)) - (((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S,h) . (k + 1)) + (- (((S,h) . (k + 1)),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) + ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) + ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((f2 + S),h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((f2,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) + (((S,h) . (0 + 1)) . k) is V11() real ext-real Element of REAL
((f2 + S),h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
((((f2 + S),h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 + S),h) . 0) - ((((f2 + S),h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 + S),h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 + S),h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2 + S),h) . 0) + (- ((((f2 + S),h) . 0),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . 0),h) . k is V11() real ext-real Element of REAL
((f2 + S),h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2 + S) - ((f2 + S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2 + S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2 + S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2 + S) + (- ((f2 + S),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 + S),h) . k is V11() real ext-real Element of REAL
(f2 + S) . k is V11() real ext-real Element of REAL
k - h is V11() real ext-real Element of REAL
(f2 + S) . (k - h) is V11() real ext-real Element of REAL
((f2 + S) . k) - ((f2 + S) . (k - h)) is V11() real ext-real Element of REAL
f2 . k is V11() real ext-real Element of REAL
S . k is V11() real ext-real Element of REAL
(f2 . k) + (S . k) is V11() real ext-real Element of REAL
((f2 . k) + (S . k)) - ((f2 + S) . (k - h)) is V11() real ext-real Element of REAL
f2 . (k - h) is V11() real ext-real Element of REAL
S . (k - h) is V11() real ext-real Element of REAL
(f2 . (k - h)) + (S . (k - h)) is V11() real ext-real Element of REAL
((f2 . k) + (S . k)) - ((f2 . (k - h)) + (S . (k - h))) is V11() real ext-real Element of REAL
(f2 . k) - (f2 . (k - h)) is V11() real ext-real Element of REAL
(S . k) - (S . (k - h)) is V11() real ext-real Element of REAL
((f2 . k) - (f2 . (k - h))) + ((S . k) - (S . (k - h))) is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 - (f2,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f2,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f2,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f2 + (- (f2,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) + ((S . k) - (S . (k - h))) is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S - (S,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (S,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (S,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
S + (- (S,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) + ((S,h) . k) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . 0) - (((f2,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2,h) . 0) + (- (((f2,h) . 0),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) + ((S,h) . k) is V11() real ext-real Element of REAL
(S,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . 0) - (((S,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S,h) . 0) + (- (((S,h) . 0),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) + ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) + ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (x + 1)) . f is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 - S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
f2 + (- S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
((f2 - S),h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f2 - S),h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 - S),h) . (x + 1)) . f is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (x + 1)) . f is V11() real ext-real Element of REAL
(((f2,h) . (x + 1)) . f) - (((S,h) . (x + 1)) . f) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((f2 - S),h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((f2,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) - (((S,h) . (0 + 1)) . k) is V11() real ext-real Element of REAL
dom f2 is non empty V57() V58() V59() Element of bool REAL
dom S is non empty V57() V58() V59() Element of bool REAL
(dom f2) /\ (dom S) is V57() V58() V59() Element of bool REAL
dom (f2 - S) is non empty V57() V58() V59() Element of bool REAL
k - h is V11() real ext-real Element of REAL
((f2 - S),h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
((((f2 - S),h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 - S),h) . 0) - ((((f2 - S),h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 - S),h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 - S),h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2 - S),h) . 0) + (- ((((f2 - S),h) . 0),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . 0),h) . k is V11() real ext-real Element of REAL
((f2 - S),h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 - S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2 - S) - ((f2 - S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2 - S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2 - S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2 - S) + (- ((f2 - S),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 - S),h) . k is V11() real ext-real Element of REAL
(f2 - S) . k is V11() real ext-real Element of REAL
(f2 - S) . (k - h) is V11() real ext-real Element of REAL
((f2 - S) . k) - ((f2 - S) . (k - h)) is V11() real ext-real Element of REAL
f2 . k is V11() real ext-real Element of REAL
S . k is V11() real ext-real Element of REAL
(f2 . k) - (S . k) is V11() real ext-real Element of REAL
((f2 . k) - (S . k)) - ((f2 - S) . (k - h)) is V11() real ext-real Element of REAL
f2 . (k - h) is V11() real ext-real Element of REAL
S . (k - h) is V11() real ext-real Element of REAL
(f2 . (k - h)) - (S . (k - h)) is V11() real ext-real Element of REAL
((f2 . k) - (S . k)) - ((f2 . (k - h)) - (S . (k - h))) is V11() real ext-real Element of REAL
(f2 . k) - (f2 . (k - h)) is V11() real ext-real Element of REAL
(S . k) - (S . (k - h)) is V11() real ext-real Element of REAL
((f2 . k) - (f2 . (k - h))) - ((S . k) - (S . (k - h))) is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 - (f2,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f2,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f2,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f2 + (- (f2,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) - ((S . k) - (S . (k - h))) is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S - (S,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (S,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (S,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
S + (- (S,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) - ((S,h) . k) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . 0) - (((f2,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2,h) . 0) + (- (((f2,h) . 0),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) - ((S,h) . k) is V11() real ext-real Element of REAL
(S,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . 0) - (((S,h) . 0),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . 0),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S,h) . 0) + (- (((S,h) . 0),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) - ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) - ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((f2 - S),h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) - (((S,h) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
(((f2 - S),h) . (k + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . x is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . x) is V11() real ext-real Element of REAL
x - h is V11() real ext-real Element of REAL
(((f2 - S),h) . (k + 1)) . (x - h) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x - h) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x - h) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x - h)) - (((S,h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
((((f2 - S),h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 - S),h) . (k + 1)) - ((((f2 - S),h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 - S),h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 - S),h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2 - S),h) . (k + 1)) + (- ((((f2 - S),h) . (k + 1)),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)) . x) - ((((f2 - S),h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . x) - (((f2,h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . (x - h)) is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)) . x) - (((f2,h) . (k + 1)) . (x - h))) - ((((S,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . (x - h))) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (k + 1)) - (((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2,h) . (k + 1)) + (- (((f2,h) . (k + 1)),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) - ((((S,h) . (k + 1)) . x) - (((S,h) . (k + 1)) . (x - h))) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (k + 1)) - (((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . (k + 1)),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S,h) . (k + 1)) + (- (((S,h) . (k + 1)),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) - ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) - ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is V11() real ext-real Element of REAL
k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h (#) k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(k,f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((k,f2) . (x + 1)) . S is V11() real ext-real Element of REAL
h * (((k,f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f (#) x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(h (#) k) + (f (#) x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) k) + (f (#) x)),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(((h (#) k) + (f (#) x)),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) k) + (f (#) x)),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
(x,f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(x,f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((x,f2) . (x + 1)) . S is V11() real ext-real Element of REAL
f * (((x,f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
(h * (((k,f2) . (x + 1)) . S)) + (f * (((x,f2) . (x + 1)) . S)) is V11() real ext-real Element of REAL
((h (#) k),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((h (#) k),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) k),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
((f (#) x),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f (#) x),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) x),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
((((h (#) k),f2) . (x + 1)) . S) + ((((f (#) x),f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
(h * (((k,f2) . (x + 1)) . S)) + ((((f (#) x),f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
- x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f,x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 1) . h is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
(f,(- x)) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- x)) . h is V11() real ext-real Element of REAL
(f . h) - ((f,(- x)) . h) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,x) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . (0 + 1)) . h is V11() real ext-real Element of REAL
(f,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- x is V11() real ext-real set
(((f,x) . 0),(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 0) - (((f,x) . 0),(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f,x) . 0),(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f,x) . 0),(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f,x) . 0) + (- (((f,x) . 0),(- x))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) . h is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f - (f,(- x)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- x)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f + (- (f,(- x))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
h - x is V11() real ext-real Element of REAL
f . (h - x) is V11() real ext-real Element of REAL
(f . h) - (f . (h - x)) is V11() real ext-real Element of REAL
h + (- x) is V11() real ext-real Element of REAL
f . (h + (- x)) is V11() real ext-real Element of REAL
(f . h) - (f . (h + (- x))) is V11() real ext-real Element of REAL
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h is V11() real ext-real set
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
S is Element of PFuncs (REAL,REAL)
k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(k,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(k,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,(h / 2)) - (k,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (k,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (k,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(k,(h / 2)) + (- (k,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is Element of PFuncs (REAL,REAL)
r2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(r2,(h / 2)) - (r2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (r2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (r2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(r2,(h / 2)) + (- (r2,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f is Element of PFuncs (REAL,REAL)
f2 is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
S . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
S . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S . k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S . k),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
((S . k),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
((S . k),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S . k),(h / 2)) - ((S . k),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S . k),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S . k),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((S . k),(h / 2)) + (- ((S . k),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x,(h / 2)) - (x,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (x,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(x,(h / 2)) + (- (x,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f . S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
((f . S),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
((f . S),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f . S),(h / 2)) - ((f . S),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f . S),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f . S),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f . S),(h / 2)) + (- ((f . S),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
x is V11() real ext-real Element of REAL
h is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(h,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
(h,x) . f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(h,x) . (f + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h,x) . f),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x / 2 is V11() real ext-real Element of REAL
(((h,x) . f),(x / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x / 2) is V11() real ext-real Element of REAL
(((h,x) . f),(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h,x) . f),(x / 2)) - (((h,x) . f),(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((h,x) . f),(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((h,x) . f),(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((h,x) . f),(x / 2)) + (- (((h,x) . f),(- (x / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(h,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real set
(h,x) . f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f2 + (h / 2) is V11() real ext-real Element of REAL
f . (f2 + (h / 2)) is V11() real ext-real Element of REAL
f2 - (h / 2) is V11() real ext-real Element of REAL
f . (f2 - (h / 2)) is V11() real ext-real Element of REAL
(f . (f2 + (h / 2))) - (f . (f2 - (h / 2))) is V11() real ext-real Element of REAL
dom f is non empty V57() V58() V59() Element of bool REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 is V11() real ext-real Element of REAL
((f,h) . (0 + 1)) . f2 is V11() real ext-real Element of REAL
(f,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(((f,h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(((f,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . 0),(h / 2)) - (((f,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . 0),(h / 2)) + (- (((f,h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . 0),h) . f2 is V11() real ext-real Element of REAL
(f,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(h / 2)) - (f,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,(h / 2)) + (- (f,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,h) . f2 is V11() real ext-real Element of REAL
f2 + (h / 2) is V11() real ext-real Element of REAL
f . (f2 + (h / 2)) is V11() real ext-real Element of REAL
f2 - (h / 2) is V11() real ext-real Element of REAL
f . (f2 - (h / 2)) is V11() real ext-real Element of REAL
(f . (f2 + (h / 2))) - (f . (f2 - (h / 2))) is V11() real ext-real Element of REAL
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f2 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (f2 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2 + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . ((f2 + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S is V11() real ext-real Element of REAL
((f,h) . ((f2 + 1) + 1)) . S is V11() real ext-real Element of REAL
S - (h / 2) is V11() real ext-real Element of REAL
((f,h) . (f2 + 1)) . (S - (h / 2)) is V11() real ext-real Element of REAL
f2 + 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,h) . (f2 + 2) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,h) . (f2 + 2)) . S is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,h) . (f2 + 1)),(h / 2)) - (((f,h) . (f2 + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f,h) . (f2 + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f,h) . (f2 + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . (f2 + 1)),(h / 2)) + (- (((f,h) . (f2 + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,h) . (f2 + 1)),h) . S is V11() real ext-real Element of REAL
S + (h / 2) is V11() real ext-real Element of REAL
((f,h) . (f2 + 1)) . (S + (h / 2)) is V11() real ext-real Element of REAL
(((f,h) . (f2 + 1)) . (S + (h / 2))) - (((f,h) . (f2 + 1)) . (S - (h / 2))) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
((f,h) . (x + 1)) . f2 is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h (#) S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((h (#) S),f) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) S),f) . (x + 1)) . f2 is V11() real ext-real Element of REAL
(S,f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,f) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,f) . (x + 1)) . f2 is V11() real ext-real Element of REAL
h * (((S,f) . (x + 1)) . f2) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((h (#) S),f) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,f) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
h * (((S,f) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
f / 2 is V11() real ext-real Element of REAL
x - (f / 2) is V11() real ext-real Element of REAL
(((h (#) S),f) . (k + 1)) . (x - (f / 2)) is V11() real ext-real Element of REAL
((S,f) . (k + 1)) . (x - (f / 2)) is V11() real ext-real Element of REAL
h * (((S,f) . (k + 1)) . (x - (f / 2))) is V11() real ext-real Element of REAL
x + (f / 2) is V11() real ext-real Element of REAL
(((h (#) S),f) . (k + 1)) . (x + (f / 2)) is V11() real ext-real Element of REAL
((S,f) . (k + 1)) . (x + (f / 2)) is V11() real ext-real Element of REAL
h * (((S,f) . (k + 1)) . (x + (f / 2))) is V11() real ext-real Element of REAL
((((h (#) S),f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f / 2 is V11() real ext-real Element of REAL
((((h (#) S),f) . (k + 1)),(f / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f / 2) is V11() real ext-real Element of REAL
((((h (#) S),f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . (k + 1)),(f / 2)) - ((((h (#) S),f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((h (#) S),f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((h (#) S),f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . (k + 1)),(f / 2)) + (- ((((h (#) S),f) . (k + 1)),(- (f / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . (k + 1)),f) . x is V11() real ext-real Element of REAL
((((h (#) S),f) . (k + 1)) . (x + (f / 2))) - ((((h (#) S),f) . (k + 1)) . (x - (f / 2))) is V11() real ext-real Element of REAL
(((S,f) . (k + 1)) . (x + (f / 2))) - (((S,f) . (k + 1)) . (x - (f / 2))) is V11() real ext-real Element of REAL
h * ((((S,f) . (k + 1)) . (x + (f / 2))) - (((S,f) . (k + 1)) . (x - (f / 2)))) is V11() real ext-real Element of REAL
(((S,f) . (k + 1)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (k + 1)),(f / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (k + 1)),(f / 2)) - (((S,f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,f) . (k + 1)),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . (k + 1)),(f / 2)) + (- (((S,f) . (k + 1)),(- (f / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . (k + 1)),f) . x is V11() real ext-real Element of REAL
h * ((((S,f) . (k + 1)),f) . x) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((h (#) S),f) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((h (#) S),f) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,f) . (0 + 1)) . k is V11() real ext-real Element of REAL
h * (((S,f) . (0 + 1)) . k) is V11() real ext-real Element of REAL
f / 2 is V11() real ext-real Element of REAL
k + (f / 2) is V11() real ext-real Element of REAL
dom (h (#) S) is non empty V57() V58() V59() Element of bool REAL
k - (f / 2) is V11() real ext-real Element of REAL
((h (#) S),f) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f / 2 is V11() real ext-real Element of REAL
((((h (#) S),f) . 0),(f / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f / 2) is V11() real ext-real Element of REAL
((((h (#) S),f) . 0),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) S),f) . 0),(f / 2)) - ((((h (#) S),f) . 0),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((h (#) S),f) . 0),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((h (#) S),f) . 0),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . 0),(f / 2)) + (- ((((h (#) S),f) . 0),(- (f / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((h (#) S),f) . 0),f) . k is V11() real ext-real Element of REAL
((h (#) S),f) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),(f / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((h (#) S),(f / 2)) - ((h (#) S),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((h (#) S),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((h (#) S),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((h (#) S),(f / 2)) + (- ((h (#) S),(- (f / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((h (#) S),f) . k is V11() real ext-real Element of REAL
(h (#) S) . (k + (f / 2)) is V11() real ext-real Element of REAL
(h (#) S) . (k - (f / 2)) is V11() real ext-real Element of REAL
((h (#) S) . (k + (f / 2))) - ((h (#) S) . (k - (f / 2))) is V11() real ext-real Element of REAL
S . (k + (f / 2)) is V11() real ext-real Element of REAL
h * (S . (k + (f / 2))) is V11() real ext-real Element of REAL
(h * (S . (k + (f / 2)))) - ((h (#) S) . (k - (f / 2))) is V11() real ext-real Element of REAL
S . (k - (f / 2)) is V11() real ext-real Element of REAL
h * (S . (k - (f / 2))) is V11() real ext-real Element of REAL
(h * (S . (k + (f / 2)))) - (h * (S . (k - (f / 2)))) is V11() real ext-real Element of REAL
(S . (k + (f / 2))) - (S . (k - (f / 2))) is V11() real ext-real Element of REAL
h * ((S . (k + (f / 2))) - (S . (k - (f / 2)))) is V11() real ext-real Element of REAL
(S,f) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(f / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(f / 2)) - (S,(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (S,(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (S,(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,(f / 2)) + (- (S,(- (f / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,f) . k is V11() real ext-real Element of REAL
h * ((S,f) . k) is V11() real ext-real Element of REAL
(S,f) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),(f / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . 0),(f / 2)) - (((S,f) . 0),(- (f / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,f) . 0),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,f) . 0),(- (f / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . 0),(f / 2)) + (- (((S,f) . 0),(- (f / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . 0),f) . k is V11() real ext-real Element of REAL
h * ((((S,f) . 0),f) . k) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (x + 1)) . f is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 + S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f2 + S),h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 + S),h) . (x + 1)) . f is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (x + 1)) . f is V11() real ext-real Element of REAL
(((f2,h) . (x + 1)) . f) + (((S,h) . (x + 1)) . f) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((f2 + S),h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) + (((S,h) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
h / 2 is V11() real ext-real Element of REAL
x - (h / 2) is V11() real ext-real Element of REAL
(((f2 + S),h) . (k + 1)) . (x - (h / 2)) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x - (h / 2)) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x - (h / 2))) + (((S,h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
x + (h / 2) is V11() real ext-real Element of REAL
(((f2 + S),h) . (k + 1)) . (x + (h / 2)) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x + (h / 2)) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x + (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + (h / 2))) + (((S,h) . (k + 1)) . (x + (h / 2))) is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . (k + 1)),(h / 2)) - ((((f2 + S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 + S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 + S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . (k + 1)),(h / 2)) + (- ((((f2 + S),h) . (k + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2 + S),h) . (k + 1)) . (x + (h / 2))) - ((((f2 + S),h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + (h / 2))) - (((f2,h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)) . (x + (h / 2))) - (((S,h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)) . (x + (h / 2))) - (((f2,h) . (k + 1)) . (x - (h / 2)))) + ((((S,h) . (k + 1)) . (x + (h / 2))) - (((S,h) . (k + 1)) . (x - (h / 2)))) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(h / 2)) - (((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),(h / 2)) + (- (((f2,h) . (k + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) + ((((S,h) . (k + 1)) . (x + (h / 2))) - (((S,h) . (k + 1)) . (x - (h / 2)))) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(h / 2)) - (((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),(h / 2)) + (- (((S,h) . (k + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) + ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) + ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 + S),h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((f2 + S),h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((f2,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) + (((S,h) . (0 + 1)) . k) is V11() real ext-real Element of REAL
((f2 + S),h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
((((f2 + S),h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
((((f2 + S),h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 + S),h) . 0),(h / 2)) - ((((f2 + S),h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 + S),h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 + S),h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . 0),(h / 2)) + (- ((((f2 + S),h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 + S),h) . 0),h) . k is V11() real ext-real Element of REAL
((f2 + S),h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 + S),(h / 2)) - ((f2 + S),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2 + S),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2 + S),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 + S),(h / 2)) + (- ((f2 + S),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 + S),h) . k is V11() real ext-real Element of REAL
h / 2 is V11() real ext-real Element of REAL
k + (h / 2) is V11() real ext-real Element of REAL
(f2 + S) . (k + (h / 2)) is V11() real ext-real Element of REAL
k - (h / 2) is V11() real ext-real Element of REAL
(f2 + S) . (k - (h / 2)) is V11() real ext-real Element of REAL
((f2 + S) . (k + (h / 2))) - ((f2 + S) . (k - (h / 2))) is V11() real ext-real Element of REAL
f2 . (k + (h / 2)) is V11() real ext-real Element of REAL
S . (k + (h / 2)) is V11() real ext-real Element of REAL
(f2 . (k + (h / 2))) + (S . (k + (h / 2))) is V11() real ext-real Element of REAL
((f2 . (k + (h / 2))) + (S . (k + (h / 2)))) - ((f2 + S) . (k - (h / 2))) is V11() real ext-real Element of REAL
f2 . (k - (h / 2)) is V11() real ext-real Element of REAL
S . (k - (h / 2)) is V11() real ext-real Element of REAL
(f2 . (k - (h / 2))) + (S . (k - (h / 2))) is V11() real ext-real Element of REAL
((f2 . (k + (h / 2))) + (S . (k + (h / 2)))) - ((f2 . (k - (h / 2))) + (S . (k - (h / 2)))) is V11() real ext-real Element of REAL
(f2 . (k + (h / 2))) - (f2 . (k - (h / 2))) is V11() real ext-real Element of REAL
(S . (k + (h / 2))) - (S . (k - (h / 2))) is V11() real ext-real Element of REAL
((f2 . (k + (h / 2))) - (f2 . (k - (h / 2)))) + ((S . (k + (h / 2))) - (S . (k - (h / 2)))) is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(h / 2)) - (f2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,(h / 2)) + (- (f2,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) + ((S . (k + (h / 2))) - (S . (k - (h / 2)))) is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(h / 2)) - (S,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (S,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (S,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,(h / 2)) + (- (S,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) + ((S,h) . k) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(h / 2)) - (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),(h / 2)) + (- (((f2,h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) + ((S,h) . k) is V11() real ext-real Element of REAL
(S,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(h / 2)) - (((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),(h / 2)) + (- (((S,h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) + ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) + ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (x + 1)) . f is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f2 - S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) S is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
f2 + (- S) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
((f2 - S),h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f2 - S),h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2 - S),h) . (x + 1)) . f is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,h) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,h) . (x + 1)) . f is V11() real ext-real Element of REAL
(((f2,h) . (x + 1)) . f) - (((S,h) . (x + 1)) . f) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
(((f2 - S),h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((f2,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
((S,h) . (0 + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) - (((S,h) . (0 + 1)) . k) is V11() real ext-real Element of REAL
h / 2 is V11() real ext-real Element of REAL
k - (h / 2) is V11() real ext-real Element of REAL
dom f2 is non empty V57() V58() V59() Element of bool REAL
dom S is non empty V57() V58() V59() Element of bool REAL
(dom f2) /\ (dom S) is V57() V58() V59() Element of bool REAL
dom (f2 - S) is non empty V57() V58() V59() Element of bool REAL
k + (h / 2) is V11() real ext-real Element of REAL
((f2 - S),h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
((((f2 - S),h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
((((f2 - S),h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . 0),(h / 2)) - ((((f2 - S),h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 - S),h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 - S),h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . 0),(h / 2)) + (- ((((f2 - S),h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . 0),h) . k is V11() real ext-real Element of REAL
((f2 - S),h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 - S),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 - S),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2 - S),(h / 2)) - ((f2 - S),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2 - S),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2 - S),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 - S),(h / 2)) + (- ((f2 - S),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2 - S),h) . k is V11() real ext-real Element of REAL
(f2 - S) . (k + (h / 2)) is V11() real ext-real Element of REAL
(f2 - S) . (k - (h / 2)) is V11() real ext-real Element of REAL
((f2 - S) . (k + (h / 2))) - ((f2 - S) . (k - (h / 2))) is V11() real ext-real Element of REAL
f2 . (k + (h / 2)) is V11() real ext-real Element of REAL
S . (k + (h / 2)) is V11() real ext-real Element of REAL
(f2 . (k + (h / 2))) - (S . (k + (h / 2))) is V11() real ext-real Element of REAL
((f2 . (k + (h / 2))) - (S . (k + (h / 2)))) - ((f2 - S) . (k - (h / 2))) is V11() real ext-real Element of REAL
f2 . (k - (h / 2)) is V11() real ext-real Element of REAL
S . (k - (h / 2)) is V11() real ext-real Element of REAL
(f2 . (k - (h / 2))) - (S . (k - (h / 2))) is V11() real ext-real Element of REAL
((f2 . (k + (h / 2))) - (S . (k + (h / 2)))) - ((f2 . (k - (h / 2))) - (S . (k - (h / 2)))) is V11() real ext-real Element of REAL
(f2 . (k + (h / 2))) - (f2 . (k - (h / 2))) is V11() real ext-real Element of REAL
(S . (k + (h / 2))) - (S . (k - (h / 2))) is V11() real ext-real Element of REAL
((f2 . (k + (h / 2))) - (f2 . (k - (h / 2)))) - ((S . (k + (h / 2))) - (S . (k - (h / 2)))) is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(h / 2)) - (f2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,(h / 2)) + (- (f2,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) - ((S . (k + (h / 2))) - (S . (k - (h / 2)))) is V11() real ext-real Element of REAL
(S,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,(h / 2)) - (S,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (S,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (S,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,(h / 2)) + (- (S,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(S,h) . k is V11() real ext-real Element of REAL
((f2,h) . k) - ((S,h) . k) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(h / 2)) - (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),(h / 2)) + (- (((f2,h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) - ((S,h) . k) is V11() real ext-real Element of REAL
(S,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . 0),(h / 2)) - (((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),(h / 2)) + (- (((S,h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . 0),h) . k is V11() real ext-real Element of REAL
((((f2,h) . 0),h) . k) - ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . (0 + 1)) . k) - ((((S,h) . 0),h) . k) is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f2 - S),h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,h) . ((k + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
(((f2 - S),h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((f2,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
((S,h) . ((k + 1) + 1)) . x is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) - (((S,h) . ((k + 1) + 1)) . x) is V11() real ext-real Element of REAL
h / 2 is V11() real ext-real Element of REAL
x - (h / 2) is V11() real ext-real Element of REAL
(((f2 - S),h) . (k + 1)) . (x - (h / 2)) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x - (h / 2)) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x - (h / 2))) - (((S,h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
x + (h / 2) is V11() real ext-real Element of REAL
(((f2 - S),h) . (k + 1)) . (x + (h / 2)) is V11() real ext-real Element of REAL
((f2,h) . (k + 1)) . (x + (h / 2)) is V11() real ext-real Element of REAL
((S,h) . (k + 1)) . (x + (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + (h / 2))) - (((S,h) . (k + 1)) . (x + (h / 2))) is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f2 - S),h) . (k + 1)),(h / 2)) - ((((f2 - S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((f2 - S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((f2 - S),h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . (k + 1)),(h / 2)) + (- ((((f2 - S),h) . (k + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f2 - S),h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2 - S),h) . (k + 1)) . (x + (h / 2))) - ((((f2 - S),h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)) . (x + (h / 2))) - (((f2,h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)) . (x + (h / 2))) - (((S,h) . (k + 1)) . (x - (h / 2))) is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)) . (x + (h / 2))) - (((f2,h) . (k + 1)) . (x - (h / 2)))) - ((((S,h) . (k + 1)) . (x + (h / 2))) - (((S,h) . (k + 1)) . (x - (h / 2)))) is V11() real ext-real Element of REAL
(((f2,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (k + 1)),(h / 2)) - (((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),(h / 2)) + (- (((f2,h) . (k + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) - ((((S,h) . (k + 1)) . (x + (h / 2))) - (((S,h) . (k + 1)) . (x - (h / 2)))) is V11() real ext-real Element of REAL
(((S,h) . (k + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,h) . (k + 1)),(h / 2)) - (((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((S,h) . (k + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),(h / 2)) + (- (((S,h) . (k + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,h) . (k + 1)),h) . x is V11() real ext-real Element of REAL
((((f2,h) . (k + 1)),h) . x) - ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
(((f2,h) . ((k + 1) + 1)) . x) - ((((S,h) . (k + 1)),h) . x) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is V11() real ext-real Element of REAL
k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h (#) k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(k,f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(k,f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((k,f2) . (x + 1)) . S is V11() real ext-real Element of REAL
h * (((k,f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f (#) x is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(h (#) k) + (f (#) x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) k) + (f (#) x)),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(((h (#) k) + (f (#) x)),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((h (#) k) + (f (#) x)),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
(x,f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(x,f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((x,f2) . (x + 1)) . S is V11() real ext-real Element of REAL
f * (((x,f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
(h * (((k,f2) . (x + 1)) . S)) + (f * (((x,f2) . (x + 1)) . S)) is V11() real ext-real Element of REAL
((h (#) k),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((h (#) k),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((h (#) k),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
((f (#) x),f2) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f (#) x),f2) . (x + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) x),f2) . (x + 1)) . S is V11() real ext-real Element of REAL
((((h (#) k),f2) . (x + 1)) . S) + ((((f (#) x),f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
(h * (((k,f2) . (x + 1)) . S)) + ((((f (#) x),f2) . (x + 1)) . S) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
x / 2 is V11() real ext-real Element of REAL
- (x / 2) is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f,x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 1) . h is V11() real ext-real Element of REAL
(f,(x / 2)) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(x / 2)) . h is V11() real ext-real Element of REAL
(f,(- (x / 2))) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- (x / 2))) . h is V11() real ext-real Element of REAL
((f,(x / 2)) . h) - ((f,(- (x / 2))) . h) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,x) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . (0 + 1)) . h is V11() real ext-real Element of REAL
(f,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x / 2 is V11() real ext-real Element of REAL
(((f,x) . 0),(x / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (x / 2) is V11() real ext-real Element of REAL
(((f,x) . 0),(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),(x / 2)) - (((f,x) . 0),(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f,x) . 0),(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f,x) . 0),(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),(x / 2)) + (- (((f,x) . 0),(- (x / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) . h is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(x / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(x / 2)) - (f,(- (x / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- (x / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,(x / 2)) + (- (f,(- (x / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
h + (x / 2) is V11() real ext-real Element of REAL
f . (h + (x / 2)) is V11() real ext-real Element of REAL
h - (x / 2) is V11() real ext-real Element of REAL
f . (h - (x / 2)) is V11() real ext-real Element of REAL
(f . (h + (x / 2))) - (f . (h - (x / 2))) is V11() real ext-real Element of REAL
h + (- (x / 2)) is V11() real ext-real Element of REAL
f . (h + (- (x / 2))) is V11() real ext-real Element of REAL
((f,(x / 2)) . h) - (f . (h + (- (x / 2)))) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
x * h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f + (x * h) is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . x) . f is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . x) . (f + (x * h)) is V11() real ext-real Element of REAL
S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . S is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S * h is V11() real ext-real Element of REAL
S + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (S + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S + 1) * h is V11() real ext-real Element of REAL
S * h is V11() real ext-real Element of REAL
k is V11() real ext-real Element of REAL
((f2,h) . (S + 1)) . k is V11() real ext-real Element of REAL
k + ((S + 1) * h) is V11() real ext-real Element of REAL
((f2,h) . (S + 1)) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
k + h is V11() real ext-real Element of REAL
((f2,h) . S) . (k + h) is V11() real ext-real Element of REAL
(k + h) + (S * h) is V11() real ext-real Element of REAL
((f2,h) . S) . ((k + h) + (S * h)) is V11() real ext-real Element of REAL
(((f2,h) . S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . S),h) - ((f2,h) . S) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . S) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . S) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . S),h) + (- ((f2,h) . S)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . S),h) . k is V11() real ext-real Element of REAL
((f2,h) . S) . k is V11() real ext-real Element of REAL
(((f2,h) . S) . (k + h)) - (((f2,h) . S) . k) is V11() real ext-real Element of REAL
k + (S * h) is V11() real ext-real Element of REAL
((f2,h) . S) . (k + (S * h)) is V11() real ext-real Element of REAL
(((f2,h) . S) . ((k + h) + (S * h))) - (((f2,h) . S) . (k + (S * h))) is V11() real ext-real Element of REAL
(S + 1) * h is V11() real ext-real Element of REAL
k + ((S + 1) * h) is V11() real ext-real Element of REAL
((f2,h) . S) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
(k + ((S + 1) * h)) - h is V11() real ext-real Element of REAL
((f2,h) . S) . ((k + ((S + 1) * h)) - h) is V11() real ext-real Element of REAL
(((f2,h) . S) . (k + ((S + 1) * h))) - (((f2,h) . S) . ((k + ((S + 1) * h)) - h)) is V11() real ext-real Element of REAL
(((f2,h) . S),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
(((f2,h) . S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . S) - (((f2,h) . S),(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . S),(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f2,h) . S) + (- (((f2,h) . S),(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . S),h) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
((f2,h) . (S + 1)) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
0 * h is V11() real ext-real Element of REAL
S is V11() real ext-real Element of REAL
((f2,h) . 0) . S is V11() real ext-real Element of REAL
S + (0 * h) is V11() real ext-real Element of REAL
((f2,h) . 0) . (S + (0 * h)) is V11() real ext-real Element of REAL
f2 . S is V11() real ext-real Element of REAL
0 * h is V11() real ext-real Element of REAL
S + (0 * h) is V11() real ext-real Element of REAL
((f2,h) . 0) . (S + (0 * h)) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 * x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
x * h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f + (x * h) is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (2 * x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (2 * x)) . f is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . (2 * x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (2 * x)) . (f + (x * h)) is V11() real ext-real Element of REAL
S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 * S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . (2 * S) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (2 * S) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S * h is V11() real ext-real Element of REAL
S + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 * (S + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . (2 * (S + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (2 * (S + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S + 1) * h is V11() real ext-real Element of REAL
k is V11() real ext-real Element of REAL
((f2,h) . (2 * (S + 1))) . k is V11() real ext-real Element of REAL
k + ((S + 1) * h) is V11() real ext-real Element of REAL
((f2,h) . (2 * (S + 1))) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
k + h is V11() real ext-real Element of REAL
(k + h) + h is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . ((k + h) + h) is V11() real ext-real Element of REAL
((k + h) + h) + (S * h) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (((k + h) + h) + (S * h)) is V11() real ext-real Element of REAL
S + 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(S + 2) * h is V11() real ext-real Element of REAL
k + ((S + 2) * h) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (k + ((S + 2) * h)) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (k + h) is V11() real ext-real Element of REAL
(k + h) + (S * h) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . ((k + h) + (S * h)) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
k + (S * h) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (k + (S * h)) is V11() real ext-real Element of REAL
(2 * S) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . ((2 * S) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((2 * S) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(k + ((S + 1) * h)) - (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * S)),(h / 2)) - (((f2,h) . (2 * S)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . (2 * S)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . (2 * S)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * S)),(h / 2)) + (- (((f2,h) . (2 * S)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * S)),h) . ((k + ((S + 1) * h)) - (h / 2)) is V11() real ext-real Element of REAL
((k + ((S + 1) * h)) - (h / 2)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) - (h / 2)) + (h / 2)) is V11() real ext-real Element of REAL
((k + ((S + 1) * h)) - (h / 2)) - (h / 2) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) - (h / 2)) - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) - (h / 2)) + (h / 2))) - (((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) - (h / 2)) - (h / 2))) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)) . (k + ((S + 1) * h))) - (((f2,h) . (2 * S)) . (k + (S * h))) is V11() real ext-real Element of REAL
(k + ((S + 1) * h)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) + (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)),h) . ((k + ((S + 1) * h)) + (h / 2)) is V11() real ext-real Element of REAL
((k + ((S + 1) * h)) + (h / 2)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) + (h / 2)) + (h / 2)) is V11() real ext-real Element of REAL
((k + ((S + 1) * h)) + (h / 2)) - (h / 2) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) + (h / 2)) - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) + (h / 2)) + (h / 2))) - (((f2,h) . (2 * S)) . (((k + ((S + 1) * h)) + (h / 2)) - (h / 2))) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)) . (k + ((S + 2) * h))) - (((f2,h) . (2 * S)) . (k + ((S + 1) * h))) is V11() real ext-real Element of REAL
((2 * S) + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . (((2 * S) + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (((2 * S) + 1) + 1)) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),(h / 2)) - (((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),(h / 2)) + (- (((f2,h) . ((2 * S) + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),h) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
((((f2,h) . (2 * S)) . (k + ((S + 2) * h))) - (((f2,h) . (2 * S)) . (k + ((S + 1) * h)))) - ((((f2,h) . (2 * S)) . (k + ((S + 1) * h))) - (((f2,h) . (2 * S)) . (k + (S * h)))) is V11() real ext-real Element of REAL
(f2,h) . (((2 * S) + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (((2 * S) + 1) + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),h) - ((f2,h) . ((2 * S) + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . ((2 * S) + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . ((2 * S) + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),h) + (- ((f2,h) . ((2 * S) + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),h) . k is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . (k + h) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)) . (k + h)) - (((f2,h) . ((2 * S) + 1)) . k) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * S)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * S)),h) - ((f2,h) . (2 * S)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . (2 * S)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . (2 * S)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * S)),h) + (- ((f2,h) . (2 * S))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * S)),h) . (k + h) is V11() real ext-real Element of REAL
((((f2,h) . (2 * S)),h) . (k + h)) - (((f2,h) . ((2 * S) + 1)) . k) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)),h) . k is V11() real ext-real Element of REAL
((((f2,h) . (2 * S)),h) . (k + h)) - ((((f2,h) . (2 * S)),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)) . ((k + h) + h)) - (((f2,h) . (2 * S)) . (k + h)) is V11() real ext-real Element of REAL
((((f2,h) . (2 * S)) . ((k + h) + h)) - (((f2,h) . (2 * S)) . (k + h))) - ((((f2,h) . (2 * S)),h) . k) is V11() real ext-real Element of REAL
((f2,h) . (2 * S)) . k is V11() real ext-real Element of REAL
(((f2,h) . (2 * S)) . (k + h)) - (((f2,h) . (2 * S)) . k) is V11() real ext-real Element of REAL
((((f2,h) . (2 * S)) . ((k + h) + h)) - (((f2,h) . (2 * S)) . (k + h))) - ((((f2,h) . (2 * S)) . (k + h)) - (((f2,h) . (2 * S)) . k)) is V11() real ext-real Element of REAL
2 * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . (2 * 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (2 * 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
0 * h is V11() real ext-real Element of REAL
S is V11() real ext-real Element of REAL
((f2,h) . (2 * 0)) . S is V11() real ext-real Element of REAL
S + (0 * h) is V11() real ext-real Element of REAL
((f2,h) . (2 * 0)) . (S + (0 * h)) is V11() real ext-real Element of REAL
f2 . S is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 * x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(2 * x) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is V11() real ext-real Element of REAL
x * h is V11() real ext-real Element of REAL
h / 2 is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f + (x * h) is V11() real ext-real Element of REAL
(f + (x * h)) + (h / 2) is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . ((2 * x) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . ((2 * x) + 1)) . f is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,h) . ((2 * x) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . ((2 * x) + 1)) . ((f + (x * h)) + (h / 2)) is V11() real ext-real Element of REAL
S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 * S is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(2 * S) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . ((2 * S) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((2 * S) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
S * h is V11() real ext-real Element of REAL
S + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 * (S + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(2 * (S + 1)) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . ((2 * (S + 1)) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((2 * (S + 1)) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S + 1) * h is V11() real ext-real Element of REAL
k is V11() real ext-real Element of REAL
((f2,h) . ((2 * (S + 1)) + 1)) . k is V11() real ext-real Element of REAL
k + ((S + 1) * h) is V11() real ext-real Element of REAL
(k + ((S + 1) * h)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * (S + 1)) + 1)) . ((k + ((S + 1) * h)) + (h / 2)) is V11() real ext-real Element of REAL
k + h is V11() real ext-real Element of REAL
(k + h) + h is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + h) + h) is V11() real ext-real Element of REAL
((k + h) + h) + (S * h) is V11() real ext-real Element of REAL
(((k + h) + h) + (S * h)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((((k + h) + h) + (S * h)) + (h / 2)) is V11() real ext-real Element of REAL
S + 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(S + 2) * h is V11() real ext-real Element of REAL
k + ((S + 2) * h) is V11() real ext-real Element of REAL
(k + ((S + 2) * h)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + ((S + 2) * h)) + (h / 2)) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . (k + h) is V11() real ext-real Element of REAL
(k + h) + (S * h) is V11() real ext-real Element of REAL
((k + h) + (S * h)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . (((k + h) + (S * h)) + (h / 2)) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) + (h / 2)) is V11() real ext-real Element of REAL
k + (S * h) is V11() real ext-real Element of REAL
(k + (S * h)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + (S * h)) + (h / 2)) is V11() real ext-real Element of REAL
(f2,h) . (2 * (S + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . (2 * (S + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (2 * (S + 1))) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
((2 * S) + 1) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . (((2 * S) + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (((2 * S) + 1) + 1)) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),(h / 2)) - (((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . ((2 * S) + 1)),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),(h / 2)) + (- (((f2,h) . ((2 * S) + 1)),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),h) . (k + ((S + 1) * h)) is V11() real ext-real Element of REAL
(k + ((S + 1) * h)) - (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) + (h / 2))) - (((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) - (h / 2))) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) + (h / 2))) - (((f2,h) . ((2 * S) + 1)) . ((k + (S * h)) + (h / 2))) is V11() real ext-real Element of REAL
((f2,h) . (2 * (S + 1))) . (k + ((S + 2) * h)) is V11() real ext-real Element of REAL
((f2,h) . (((2 * S) + 1) + 1)) . (k + ((S + 2) * h)) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),h) . (k + ((S + 2) * h)) is V11() real ext-real Element of REAL
(k + ((S + 2) * h)) - (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . ((k + ((S + 2) * h)) - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)) . ((k + ((S + 2) * h)) + (h / 2))) - (((f2,h) . ((2 * S) + 1)) . ((k + ((S + 2) * h)) - (h / 2))) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)) . ((k + ((S + 2) * h)) + (h / 2))) - (((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) + (h / 2))) is V11() real ext-real Element of REAL
(((f2,h) . (2 * (S + 1))),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * (S + 1))),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * (S + 1))),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * (S + 1))),(h / 2)) - (((f2,h) . (2 * (S + 1))),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . (2 * (S + 1))),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . (2 * (S + 1))),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * (S + 1))),(h / 2)) + (- (((f2,h) . (2 * (S + 1))),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * (S + 1))),h) . ((k + ((S + 1) * h)) + (h / 2)) is V11() real ext-real Element of REAL
((k + ((S + 1) * h)) + (h / 2)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . (2 * (S + 1))) . (((k + ((S + 1) * h)) + (h / 2)) + (h / 2)) is V11() real ext-real Element of REAL
((k + ((S + 1) * h)) + (h / 2)) - (h / 2) is V11() real ext-real Element of REAL
((f2,h) . (2 * (S + 1))) . (((k + ((S + 1) * h)) + (h / 2)) - (h / 2)) is V11() real ext-real Element of REAL
(((f2,h) . (2 * (S + 1))) . (((k + ((S + 1) * h)) + (h / 2)) + (h / 2))) - (((f2,h) . (2 * (S + 1))) . (((k + ((S + 1) * h)) + (h / 2)) - (h / 2))) is V11() real ext-real Element of REAL
((((f2,h) . ((2 * S) + 1)) . ((k + ((S + 2) * h)) + (h / 2))) - (((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) + (h / 2)))) - ((((f2,h) . ((2 * S) + 1)) . ((k + ((S + 1) * h)) + (h / 2))) - (((f2,h) . ((2 * S) + 1)) . ((k + (S * h)) + (h / 2)))) is V11() real ext-real Element of REAL
(((f2,h) . (2 * (S + 1))),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * (S + 1))),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . (2 * (S + 1))),h) - ((f2,h) . (2 * (S + 1))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . (2 * (S + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . (2 * (S + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * (S + 1))),h) + (- ((f2,h) . (2 * (S + 1)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . (2 * (S + 1))),h) . k is V11() real ext-real Element of REAL
((f2,h) . (2 * (S + 1))) . (k + h) is V11() real ext-real Element of REAL
((f2,h) . (2 * (S + 1))) . k is V11() real ext-real Element of REAL
(((f2,h) . (2 * (S + 1))) . (k + h)) - (((f2,h) . (2 * (S + 1))) . k) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . ((2 * S) + 1)),h) - ((f2,h) . ((2 * S) + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . ((2 * S) + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . ((2 * S) + 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),h) + (- ((f2,h) . ((2 * S) + 1))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . ((2 * S) + 1)),h) . (k + h) is V11() real ext-real Element of REAL
(f2,h) . (((2 * S) + 1) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,h) . (((2 * S) + 1) + 1)) . k is V11() real ext-real Element of REAL
((((f2,h) . ((2 * S) + 1)),h) . (k + h)) - (((f2,h) . (((2 * S) + 1) + 1)) . k) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)),h) . k is V11() real ext-real Element of REAL
((((f2,h) . ((2 * S) + 1)),h) . (k + h)) - ((((f2,h) . ((2 * S) + 1)),h) . k) is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)) . ((k + h) + h)) - (((f2,h) . ((2 * S) + 1)) . (k + h)) is V11() real ext-real Element of REAL
((((f2,h) . ((2 * S) + 1)) . ((k + h) + h)) - (((f2,h) . ((2 * S) + 1)) . (k + h))) - ((((f2,h) . ((2 * S) + 1)),h) . k) is V11() real ext-real Element of REAL
((f2,h) . ((2 * S) + 1)) . k is V11() real ext-real Element of REAL
(((f2,h) . ((2 * S) + 1)) . (k + h)) - (((f2,h) . ((2 * S) + 1)) . k) is V11() real ext-real Element of REAL
((((f2,h) . ((2 * S) + 1)) . ((k + h) + h)) - (((f2,h) . ((2 * S) + 1)) . (k + h))) - ((((f2,h) . ((2 * S) + 1)) . (k + h)) - (((f2,h) . ((2 * S) + 1)) . k)) is V11() real ext-real Element of REAL
2 * 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(2 * 0) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f2,h) . ((2 * 0) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) . ((2 * 0) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
0 * h is V11() real ext-real Element of REAL
S is V11() real ext-real Element of REAL
((f2,h) . ((2 * 0) + 1)) . S is V11() real ext-real Element of REAL
S + (0 * h) is V11() real ext-real Element of REAL
(S + (0 * h)) + (h / 2) is V11() real ext-real Element of REAL
((f2,h) . ((2 * 0) + 1)) . ((S + (0 * h)) + (h / 2)) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) - ((f2,h) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,h) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) + (- ((f2,h) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . S is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,h) - f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f2,h) + (- f2) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . S is V11() real ext-real Element of REAL
S + h is V11() real ext-real Element of REAL
f2 . (S + h) is V11() real ext-real Element of REAL
f2 . S is V11() real ext-real Element of REAL
(f2 . (S + h)) - (f2 . S) is V11() real ext-real Element of REAL
S + (h / 2) is V11() real ext-real Element of REAL
(S + (h / 2)) + (h / 2) is V11() real ext-real Element of REAL
f2 . ((S + (h / 2)) + (h / 2)) is V11() real ext-real Element of REAL
(S + (h / 2)) - (h / 2) is V11() real ext-real Element of REAL
f2 . ((S + (h / 2)) - (h / 2)) is V11() real ext-real Element of REAL
(f2 . ((S + (h / 2)) + (h / 2))) - (f2 . ((S + (h / 2)) - (h / 2))) is V11() real ext-real Element of REAL
(f2,h) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(f2,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(f2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,(h / 2)) - (f2,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f2,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,(h / 2)) + (- (f2,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,h) . (S + (h / 2)) is V11() real ext-real Element of REAL
(f2,h) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,h) . 0),(h / 2)) - (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f2,h) . 0),(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),(h / 2)) + (- (((f2,h) . 0),(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,h) . 0),h) . (S + (h / 2)) is V11() real ext-real Element of REAL
x is V13() Function-like complex-valued ext-real-valued real-valued set
h is V11() real ext-real set
x . h is V11() real ext-real Element of REAL
f is V11() real ext-real set
x . f is V11() real ext-real Element of REAL
(x . h) - (x . f) is V11() real ext-real Element of REAL
h - f is V11() real ext-real set
((x . h) - (x . f)) / (h - f) is V11() real ext-real Element of REAL
x is V13() Function-like complex-valued ext-real-valued real-valued set
h is V11() real ext-real set
f is V11() real ext-real set
(x,h,f) is V11() real ext-real Element of REAL
x . h is V11() real ext-real Element of REAL
x . f is V11() real ext-real Element of REAL
(x . h) - (x . f) is V11() real ext-real Element of REAL
h - f is V11() real ext-real set
((x . h) - (x . f)) / (h - f) is V11() real ext-real Element of REAL
f2 is V11() real ext-real set
(x,f,f2) is V11() real ext-real Element of REAL
x . f2 is V11() real ext-real Element of REAL
(x . f) - (x . f2) is V11() real ext-real Element of REAL
f - f2 is V11() real ext-real set
((x . f) - (x . f2)) / (f - f2) is V11() real ext-real Element of REAL
(x,h,f) - (x,f,f2) is V11() real ext-real Element of REAL
h - f2 is V11() real ext-real set
((x,h,f) - (x,f,f2)) / (h - f2) is V11() real ext-real Element of REAL
x is V13() Function-like complex-valued ext-real-valued real-valued set
h is V11() real ext-real set
f is V11() real ext-real set
f2 is V11() real ext-real set
(x,h,f,f2) is V11() real ext-real Element of REAL
(x,h,f) is V11() real ext-real Element of REAL
x . h is V11() real ext-real Element of REAL
x . f is V11() real ext-real Element of REAL
(x . h) - (x . f) is V11() real ext-real Element of REAL
h - f is V11() real ext-real set
((x . h) - (x . f)) / (h - f) is V11() real ext-real Element of REAL
(x,f,f2) is V11() real ext-real Element of REAL
x . f2 is V11() real ext-real Element of REAL
(x . f) - (x . f2) is V11() real ext-real Element of REAL
f - f2 is V11() real ext-real set
((x . f) - (x . f2)) / (f - f2) is V11() real ext-real Element of REAL
(x,h,f) - (x,f,f2) is V11() real ext-real Element of REAL
h - f2 is V11() real ext-real set
((x,h,f) - (x,f,f2)) / (h - f2) is V11() real ext-real Element of REAL
S is V11() real ext-real set
(x,f,f2,S) is V11() real ext-real Element of REAL
(x,f2,S) is V11() real ext-real Element of REAL
x . S is V11() real ext-real Element of REAL
(x . f2) - (x . S) is V11() real ext-real Element of REAL
f2 - S is V11() real ext-real set
((x . f2) - (x . S)) / (f2 - S) is V11() real ext-real Element of REAL
(x,f,f2) - (x,f2,S) is V11() real ext-real Element of REAL
f - S is V11() real ext-real set
((x,f,f2) - (x,f2,S)) / (f - S) is V11() real ext-real Element of REAL
(x,h,f,f2) - (x,f,f2,S) is V11() real ext-real Element of REAL
h - S is V11() real ext-real set
((x,h,f,f2) - (x,f,f2,S)) / (h - S) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x,h) is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
(f . x) - (f . h) is V11() real ext-real Element of REAL
x - h is V11() real ext-real set
((f . x) - (f . h)) / (x - h) is V11() real ext-real Element of REAL
(f,h,x) is V11() real ext-real Element of REAL
(f . h) - (f . x) is V11() real ext-real Element of REAL
h - x is V11() real ext-real set
((f . h) - (f . x)) / (h - x) is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
(f . h) - (f . x) is V11() real ext-real Element of REAL
- ((f . h) - (f . x)) is V11() real ext-real Element of REAL
h - x is V11() real ext-real Element of REAL
- (h - x) is V11() real ext-real Element of REAL
(- ((f . h) - (f . x))) / (- (h - x)) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x,h) is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
(f . x) - (f . h) is V11() real ext-real Element of REAL
x - h is V11() real ext-real set
((f . x) - (f . h)) / (x - h) is V11() real ext-real Element of REAL
dom f is non empty V57() V58() V59() Element of bool REAL
f . x is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x (#) f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((x (#) f2),h,f) is V11() real ext-real Element of REAL
(x (#) f2) . h is V11() real ext-real Element of REAL
(x (#) f2) . f is V11() real ext-real Element of REAL
((x (#) f2) . h) - ((x (#) f2) . f) is V11() real ext-real Element of REAL
h - f is V11() real ext-real set
(((x (#) f2) . h) - ((x (#) f2) . f)) / (h - f) is V11() real ext-real Element of REAL
(f2,h,f) is V11() real ext-real Element of REAL
f2 . h is V11() real ext-real Element of REAL
f2 . f is V11() real ext-real Element of REAL
(f2 . h) - (f2 . f) is V11() real ext-real Element of REAL
((f2 . h) - (f2 . f)) / (h - f) is V11() real ext-real Element of REAL
x * (f2,h,f) is V11() real ext-real Element of REAL
dom (x (#) f2) is non empty V57() V58() V59() Element of bool REAL
f2 . h is V11() real ext-real Element of REAL
x * (f2 . h) is V11() real ext-real Element of REAL
(x (#) f2) . f is V11() real ext-real Element of REAL
(x * (f2 . h)) - ((x (#) f2) . f) is V11() real ext-real Element of REAL
h - f is V11() real ext-real Element of REAL
((x * (f2 . h)) - ((x (#) f2) . f)) / (h - f) is V11() real ext-real Element of REAL
f2 . f is V11() real ext-real Element of REAL
x * (f2 . f) is V11() real ext-real Element of REAL
(x * (f2 . h)) - (x * (f2 . f)) is V11() real ext-real Element of REAL
((x * (f2 . h)) - (x * (f2 . f))) / (h - f) is V11() real ext-real Element of REAL
(f2 . h) - (f2 . f) is V11() real ext-real Element of REAL
x * ((f2 . h) - (f2 . f)) is V11() real ext-real Element of REAL
(x * ((f2 . h) - (f2 . f))) / (h - f) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x,h) is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
(f . x) - (f . h) is V11() real ext-real Element of REAL
x - h is V11() real ext-real set
((f . x) - (f . h)) / (x - h) is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f + f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f + f2),x,h) is V11() real ext-real Element of REAL
(f + f2) . x is V11() real ext-real Element of REAL
(f + f2) . h is V11() real ext-real Element of REAL
((f + f2) . x) - ((f + f2) . h) is V11() real ext-real Element of REAL
(((f + f2) . x) - ((f + f2) . h)) / (x - h) is V11() real ext-real Element of REAL
(f2,x,h) is V11() real ext-real Element of REAL
f2 . x is V11() real ext-real Element of REAL
f2 . h is V11() real ext-real Element of REAL
(f2 . x) - (f2 . h) is V11() real ext-real Element of REAL
((f2 . x) - (f2 . h)) / (x - h) is V11() real ext-real Element of REAL
(f,x,h) + (f2,x,h) is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
f2 . x is V11() real ext-real Element of REAL
(f . x) + (f2 . x) is V11() real ext-real Element of REAL
(f + f2) . h is V11() real ext-real Element of REAL
((f . x) + (f2 . x)) - ((f + f2) . h) is V11() real ext-real Element of REAL
x - h is V11() real ext-real Element of REAL
(((f . x) + (f2 . x)) - ((f + f2) . h)) / (x - h) is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
f2 . h is V11() real ext-real Element of REAL
(f . h) + (f2 . h) is V11() real ext-real Element of REAL
((f . x) + (f2 . x)) - ((f . h) + (f2 . h)) is V11() real ext-real Element of REAL
(((f . x) + (f2 . x)) - ((f . h) + (f2 . h))) / (x - h) is V11() real ext-real Element of REAL
(f . x) - (f . h) is V11() real ext-real Element of REAL
(f2 . x) - (f2 . h) is V11() real ext-real Element of REAL
((f . x) - (f . h)) + ((f2 . x) - (f2 . h)) is V11() real ext-real Element of REAL
(((f . x) - (f . h)) + ((f2 . x) - (f2 . h))) / (x - h) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x (#) S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f,f2) is V11() real ext-real Element of REAL
S . f is V11() real ext-real Element of REAL
S . f2 is V11() real ext-real Element of REAL
(S . f) - (S . f2) is V11() real ext-real Element of REAL
f - f2 is V11() real ext-real set
((S . f) - (S . f2)) / (f - f2) is V11() real ext-real Element of REAL
x * (S,f,f2) is V11() real ext-real Element of REAL
k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h (#) k is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(x (#) S) + (h (#) k) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((x (#) S) + (h (#) k)),f,f2) is V11() real ext-real Element of REAL
((x (#) S) + (h (#) k)) . f is V11() real ext-real Element of REAL
((x (#) S) + (h (#) k)) . f2 is V11() real ext-real Element of REAL
(((x (#) S) + (h (#) k)) . f) - (((x (#) S) + (h (#) k)) . f2) is V11() real ext-real Element of REAL
((((x (#) S) + (h (#) k)) . f) - (((x (#) S) + (h (#) k)) . f2)) / (f - f2) is V11() real ext-real Element of REAL
(k,f,f2) is V11() real ext-real Element of REAL
k . f is V11() real ext-real Element of REAL
k . f2 is V11() real ext-real Element of REAL
(k . f) - (k . f2) is V11() real ext-real Element of REAL
((k . f) - (k . f2)) / (f - f2) is V11() real ext-real Element of REAL
h * (k,f,f2) is V11() real ext-real Element of REAL
(x * (S,f,f2)) + (h * (k,f,f2)) is V11() real ext-real Element of REAL
((x (#) S),f,f2) is V11() real ext-real Element of REAL
(x (#) S) . f is V11() real ext-real Element of REAL
(x (#) S) . f2 is V11() real ext-real Element of REAL
((x (#) S) . f) - ((x (#) S) . f2) is V11() real ext-real Element of REAL
(((x (#) S) . f) - ((x (#) S) . f2)) / (f - f2) is V11() real ext-real Element of REAL
((h (#) k),f,f2) is V11() real ext-real Element of REAL
(h (#) k) . f is V11() real ext-real Element of REAL
(h (#) k) . f2 is V11() real ext-real Element of REAL
((h (#) k) . f) - ((h (#) k) . f2) is V11() real ext-real Element of REAL
(((h (#) k) . f) - ((h (#) k) . f2)) / (f - f2) is V11() real ext-real Element of REAL
((x (#) S),f,f2) + ((h (#) k),f,f2) is V11() real ext-real Element of REAL
(x * (S,f,f2)) + ((h (#) k),f,f2) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,x,h,f) is V11() real ext-real Element of REAL
(f2,x,h) is V11() real ext-real Element of REAL
f2 . x is V11() real ext-real Element of REAL
f2 . h is V11() real ext-real Element of REAL
(f2 . x) - (f2 . h) is V11() real ext-real Element of REAL
x - h is V11() real ext-real set
((f2 . x) - (f2 . h)) / (x - h) is V11() real ext-real Element of REAL
(f2,h,f) is V11() real ext-real Element of REAL
f2 . f is V11() real ext-real Element of REAL
(f2 . h) - (f2 . f) is V11() real ext-real Element of REAL
h - f is V11() real ext-real set
((f2 . h) - (f2 . f)) / (h - f) is V11() real ext-real Element of REAL
(f2,x,h) - (f2,h,f) is V11() real ext-real Element of REAL
x - f is V11() real ext-real set
((f2,x,h) - (f2,h,f)) / (x - f) is V11() real ext-real Element of REAL
(f2,h,f,x) is V11() real ext-real Element of REAL
(f2,f,x) is V11() real ext-real Element of REAL
(f2 . f) - (f2 . x) is V11() real ext-real Element of REAL
f - x is V11() real ext-real set
((f2 . f) - (f2 . x)) / (f - x) is V11() real ext-real Element of REAL
(f2,h,f) - (f2,f,x) is V11() real ext-real Element of REAL
h - x is V11() real ext-real set
((f2,h,f) - (f2,f,x)) / (h - x) is V11() real ext-real Element of REAL
(f2,f,h,x) is V11() real ext-real Element of REAL
(f2,f,h) is V11() real ext-real Element of REAL
(f2 . f) - (f2 . h) is V11() real ext-real Element of REAL
f - h is V11() real ext-real set
((f2 . f) - (f2 . h)) / (f - h) is V11() real ext-real Element of REAL
(f2,h,x) is V11() real ext-real Element of REAL
(f2 . h) - (f2 . x) is V11() real ext-real Element of REAL
((f2 . h) - (f2 . x)) / (h - x) is V11() real ext-real Element of REAL
(f2,f,h) - (f2,h,x) is V11() real ext-real Element of REAL
((f2,f,h) - (f2,h,x)) / (f - x) is V11() real ext-real Element of REAL
h - x is V11() real ext-real Element of REAL
f - x is V11() real ext-real Element of REAL
h - f is V11() real ext-real Element of REAL
f2 . x is V11() real ext-real Element of REAL
f2 . h is V11() real ext-real Element of REAL
(f2 . x) - (f2 . h) is V11() real ext-real Element of REAL
- (h - x) is V11() real ext-real Element of REAL
((f2 . x) - (f2 . h)) / (- (h - x)) is V11() real ext-real Element of REAL
f2 . f is V11() real ext-real Element of REAL
(f2 . h) - (f2 . f) is V11() real ext-real Element of REAL
((f2 . h) - (f2 . f)) / (h - f) is V11() real ext-real Element of REAL
(((f2 . x) - (f2 . h)) / (- (h - x))) - (((f2 . h) - (f2 . f)) / (h - f)) is V11() real ext-real Element of REAL
- (f - x) is V11() real ext-real Element of REAL
((((f2 . x) - (f2 . h)) / (- (h - x))) - (((f2 . h) - (f2 . f)) / (h - f))) / (- (f - x)) is V11() real ext-real Element of REAL
((f2 . x) - (f2 . h)) / (h - x) is V11() real ext-real Element of REAL
- (((f2 . x) - (f2 . h)) / (h - x)) is V11() real ext-real Element of REAL
(- (((f2 . x) - (f2 . h)) / (h - x))) - (((f2 . h) - (f2 . f)) / (h - f)) is V11() real ext-real Element of REAL
((- (((f2 . x) - (f2 . h)) / (h - x))) - (((f2 . h) - (f2 . f)) / (h - f))) / (- (f - x)) is V11() real ext-real Element of REAL
(((f2 . x) - (f2 . h)) / (h - x)) + (((f2 . h) - (f2 . f)) / (h - f)) is V11() real ext-real Element of REAL
- ((((f2 . x) - (f2 . h)) / (h - x)) + (((f2 . h) - (f2 . f)) / (h - f))) is V11() real ext-real Element of REAL
(- ((((f2 . x) - (f2 . h)) / (h - x)) + (((f2 . h) - (f2 . f)) / (h - f)))) / (- (f - x)) is V11() real ext-real Element of REAL
((((f2 . x) - (f2 . h)) / (h - x)) + (((f2 . h) - (f2 . f)) / (h - f))) / (f - x) is V11() real ext-real Element of REAL
((f2 . x) - (f2 . h)) * (h - f) is V11() real ext-real Element of REAL
((f2 . h) - (f2 . f)) * (h - x) is V11() real ext-real Element of REAL
(((f2 . x) - (f2 . h)) * (h - f)) + (((f2 . h) - (f2 . f)) * (h - x)) is V11() real ext-real Element of REAL
(h - x) * (h - f) is V11() real ext-real Element of REAL
((((f2 . x) - (f2 . h)) * (h - f)) + (((f2 . h) - (f2 . f)) * (h - x))) / ((h - x) * (h - f)) is V11() real ext-real Element of REAL
(((((f2 . x) - (f2 . h)) * (h - f)) + (((f2 . h) - (f2 . f)) * (h - x))) / ((h - x) * (h - f))) / (f - x) is V11() real ext-real Element of REAL
(f2 . x) * (h - f) is V11() real ext-real Element of REAL
(f2 . h) * (f - x) is V11() real ext-real Element of REAL
((f2 . x) * (h - f)) + ((f2 . h) * (f - x)) is V11() real ext-real Element of REAL
(f2 . f) * (h - x) is V11() real ext-real Element of REAL
(((f2 . x) * (h - f)) + ((f2 . h) * (f - x))) - ((f2 . f) * (h - x)) is V11() real ext-real Element of REAL
((h - x) * (h - f)) * (f - x) is V11() real ext-real Element of REAL
((((f2 . x) * (h - f)) + ((f2 . h) * (f - x))) - ((f2 . f) * (h - x))) / (((h - x) * (h - f)) * (f - x)) is V11() real ext-real Element of REAL
- ((f2 . h) - (f2 . f)) is V11() real ext-real Element of REAL
- (h - f) is V11() real ext-real Element of REAL
(- ((f2 . h) - (f2 . f))) / (- (h - f)) is V11() real ext-real Element of REAL
(f2 . h) - (f2 . x) is V11() real ext-real Element of REAL
((f2 . h) - (f2 . x)) / (h - x) is V11() real ext-real Element of REAL
((- ((f2 . h) - (f2 . f))) / (- (h - f))) - (((f2 . h) - (f2 . x)) / (h - x)) is V11() real ext-real Element of REAL
(((- ((f2 . h) - (f2 . f))) / (- (h - f))) - (((f2 . h) - (f2 . x)) / (h - x))) / (f - x) is V11() real ext-real Element of REAL
(((f2 . h) - (f2 . f)) / (h - f)) - (((f2 . h) - (f2 . x)) / (h - x)) is V11() real ext-real Element of REAL
((((f2 . h) - (f2 . f)) / (h - f)) - (((f2 . h) - (f2 . x)) / (h - x))) / (f - x) is V11() real ext-real Element of REAL
((f2 . h) - (f2 . x)) * (h - f) is V11() real ext-real Element of REAL
(((f2 . h) - (f2 . f)) * (h - x)) - (((f2 . h) - (f2 . x)) * (h - f)) is V11() real ext-real Element of REAL
(h - f) * (h - x) is V11() real ext-real Element of REAL
((((f2 . h) - (f2 . f)) * (h - x)) - (((f2 . h) - (f2 . x)) * (h - f))) / ((h - f) * (h - x)) is V11() real ext-real Element of REAL
(((((f2 . h) - (f2 . f)) * (h - x)) - (((f2 . h) - (f2 . x)) * (h - f))) / ((h - f) * (h - x))) / (f - x) is V11() real ext-real Element of REAL
((f2 . h) - (f2 . f)) * (f - x) is V11() real ext-real Element of REAL
(f2 . f) - (f2 . x) is V11() real ext-real Element of REAL
((f2 . f) - (f2 . x)) * (h - f) is V11() real ext-real Element of REAL
(((f2 . h) - (f2 . f)) * (f - x)) - (((f2 . f) - (f2 . x)) * (h - f)) is V11() real ext-real Element of REAL
(h - f) * (f - x) is V11() real ext-real Element of REAL
((((f2 . h) - (f2 . f)) * (f - x)) - (((f2 . f) - (f2 . x)) * (h - f))) / ((h - f) * (f - x)) is V11() real ext-real Element of REAL
(((((f2 . h) - (f2 . f)) * (f - x)) - (((f2 . f) - (f2 . x)) * (h - f))) / ((h - f) * (f - x))) / (h - x) is V11() real ext-real Element of REAL
((h - f) * (f - x)) * (h - x) is V11() real ext-real Element of REAL
((((f2 . x) * (h - f)) + ((f2 . h) * (f - x))) - ((f2 . f) * (h - x))) / (((h - f) * (f - x)) * (h - x)) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,x,h,f) is V11() real ext-real Element of REAL
(f2,x,h) is V11() real ext-real Element of REAL
f2 . x is V11() real ext-real Element of REAL
f2 . h is V11() real ext-real Element of REAL
(f2 . x) - (f2 . h) is V11() real ext-real Element of REAL
x - h is V11() real ext-real set
((f2 . x) - (f2 . h)) / (x - h) is V11() real ext-real Element of REAL
(f2,h,f) is V11() real ext-real Element of REAL
f2 . f is V11() real ext-real Element of REAL
(f2 . h) - (f2 . f) is V11() real ext-real Element of REAL
h - f is V11() real ext-real set
((f2 . h) - (f2 . f)) / (h - f) is V11() real ext-real Element of REAL
(f2,x,h) - (f2,h,f) is V11() real ext-real Element of REAL
x - f is V11() real ext-real set
((f2,x,h) - (f2,h,f)) / (x - f) is V11() real ext-real Element of REAL
(f2,f,x,h) is V11() real ext-real Element of REAL
(f2,f,x) is V11() real ext-real Element of REAL
(f2 . f) - (f2 . x) is V11() real ext-real Element of REAL
f - x is V11() real ext-real set
((f2 . f) - (f2 . x)) / (f - x) is V11() real ext-real Element of REAL
(f2,f,x) - (f2,x,h) is V11() real ext-real Element of REAL
f - h is V11() real ext-real set
((f2,f,x) - (f2,x,h)) / (f - h) is V11() real ext-real Element of REAL
(f2,h,x,f) is V11() real ext-real Element of REAL
(f2,h,x) is V11() real ext-real Element of REAL
(f2 . h) - (f2 . x) is V11() real ext-real Element of REAL
h - x is V11() real ext-real set
((f2 . h) - (f2 . x)) / (h - x) is V11() real ext-real Element of REAL
(f2,x,f) is V11() real ext-real Element of REAL
(f2 . x) - (f2 . f) is V11() real ext-real Element of REAL
((f2 . x) - (f2 . f)) / (x - f) is V11() real ext-real Element of REAL
(f2,h,x) - (f2,x,f) is V11() real ext-real Element of REAL
((f2,h,x) - (f2,x,f)) / (h - f) is V11() real ext-real Element of REAL
x is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
h is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x + h is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
S is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(S,f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,f) . x is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . x),f) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(((S,f) . x),f) . h is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((S,f) . x),f) . h) . f2 is V11() real ext-real Element of REAL
(S,f) . (x + h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,f) . (x + h)) . f2 is V11() real ext-real Element of REAL
k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(((S,f) . x),f) . k is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x + k is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(S,f) . (x + k) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(((S,f) . x),f) . (k + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x + (k + 1) is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(S,f) . (x + (k + 1)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is V11() real ext-real Element of REAL
((((S,f) . x),f) . (k + 1)) . x is V11() real ext-real Element of REAL
((S,f) . (x + (k + 1))) . x is V11() real ext-real Element of REAL
(((((S,f) . x),f) . k),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((((S,f) . x),f) . k),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((((S,f) . x),f) . k),f) - ((((S,f) . x),f) . k) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((((S,f) . x),f) . k) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((((S,f) . x),f) . k) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((((S,f) . x),f) . k),f) + (- ((((S,f) . x),f) . k)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((((S,f) . x),f) . k),f) . x is V11() real ext-real Element of REAL
x + f is V11() real ext-real Element of REAL
((((S,f) . x),f) . k) . (x + f) is V11() real ext-real Element of REAL
((((S,f) . x),f) . k) . x is V11() real ext-real Element of REAL
(((((S,f) . x),f) . k) . (x + f)) - (((((S,f) . x),f) . k) . x) is V11() real ext-real Element of REAL
((S,f) . (x + k)) . (x + f) is V11() real ext-real Element of REAL
(((S,f) . (x + k)) . (x + f)) - (((((S,f) . x),f) . k) . x) is V11() real ext-real Element of REAL
((S,f) . (x + k)) . x is V11() real ext-real Element of REAL
(((S,f) . (x + k)) . (x + f)) - (((S,f) . (x + k)) . x) is V11() real ext-real Element of REAL
(((S,f) . (x + k)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (x + k)),f) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((S,f) . (x + k)),f) - ((S,f) . (x + k)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((S,f) . (x + k)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((S,f) . (x + k)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . (x + k)),f) + (- ((S,f) . (x + k))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((S,f) . (x + k)),f) . x is V11() real ext-real Element of REAL
(x + k) + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(S,f) . ((x + k) + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((S,f) . ((x + k) + 1)) . x is V11() real ext-real Element of REAL
(((S,f) . x),f) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(S,f) . (x + 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
k is V11() real ext-real Element of REAL
((((S,f) . x),f) . 0) . k is V11() real ext-real Element of REAL
((S,f) . (x + 0)) . k is V11() real ext-real Element of REAL
NAT --> 1 is non empty V13() V16( NAT ) V17( NAT ) V17( RAT ) V17( INT ) Function-like total quasi_total complex-valued ext-real-valued real-valued natural-valued Element of bool [:NAT,NAT:]
[:NAT,NAT:] is V13() V17( RAT ) V17( INT ) complex-valued ext-real-valued real-valued natural-valued set
bool [:NAT,NAT:] is set
NAT --> (NAT --> 1) is non empty V13() V16( NAT ) V17({(NAT --> 1)}) Function-like total quasi_total Element of bool [:NAT,{(NAT --> 1)}:]
{(NAT --> 1)} is non empty set
[:NAT,{(NAT --> 1)}:] is V13() set
bool [:NAT,{(NAT --> 1)}:] is set
dom (NAT --> (NAT --> 1)) is non empty V57() V58() V59() V60() V61() V62() Element of bool NAT
f is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(NAT --> (NAT --> 1)) . f is Element of {(NAT --> 1)}
dom (NAT --> 1) is non empty V57() V58() V59() V60() V61() V62() Element of bool NAT
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(NAT --> 1) . f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
f . f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
x is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
x is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
x is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total () Element of bool [:NAT,(PFuncs (REAL,REAL)):]
h is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
x . h is set
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
h + x is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f . h is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f,x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 1) . h is V11() real ext-real Element of REAL
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f (#) f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f (#) f2),x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f (#) f2),x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) f2),x) . 1) . h is V11() real ext-real Element of REAL
(f2,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(f2,x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . 1) . h is V11() real ext-real Element of REAL
(f . h) * (((f2,x) . 1) . h) is V11() real ext-real Element of REAL
f2 . (h + x) is V11() real ext-real Element of REAL
(((f,x) . 1) . h) * (f2 . (h + x)) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . 1) . h)) + ((((f,x) . 1) . h) * (f2 . (h + x))) is V11() real ext-real Element of REAL
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f (#) f2),x) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) f2),x) . (0 + 1)) . h is V11() real ext-real Element of REAL
((f (#) f2),x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f (#) f2),x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f (#) f2),x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f (#) f2),x) . 0),x) - (((f (#) f2),x) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f (#) f2),x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f (#) f2),x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f (#) f2),x) . 0),x) + (- (((f (#) f2),x) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f (#) f2),x) . 0),x) . h is V11() real ext-real Element of REAL
((f (#) f2),x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f (#) f2),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f (#) f2),x) - (f (#) f2) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f (#) f2) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) (f (#) f2) is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
((f (#) f2),x) + (- (f (#) f2)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((f (#) f2),x) . h is V11() real ext-real Element of REAL
(f (#) f2) . (h + x) is V11() real ext-real Element of REAL
(f (#) f2) . h is V11() real ext-real Element of REAL
((f (#) f2) . (h + x)) - ((f (#) f2) . h) is V11() real ext-real Element of REAL
f . (h + x) is V11() real ext-real Element of REAL
(f . (h + x)) * (f2 . (h + x)) is V11() real ext-real Element of REAL
((f . (h + x)) * (f2 . (h + x))) - ((f (#) f2) . h) is V11() real ext-real Element of REAL
f2 . h is V11() real ext-real Element of REAL
(f . h) * (f2 . h) is V11() real ext-real Element of REAL
((f . (h + x)) * (f2 . (h + x))) - ((f . h) * (f2 . h)) is V11() real ext-real Element of REAL
(f2 . (h + x)) - (f2 . h) is V11() real ext-real Element of REAL
(f . h) * ((f2 . (h + x)) - (f2 . h)) is V11() real ext-real Element of REAL
(f . (h + x)) - (f . h) is V11() real ext-real Element of REAL
((f . (h + x)) - (f . h)) * (f2 . (h + x)) is V11() real ext-real Element of REAL
((f . h) * ((f2 . (h + x)) - (f2 . h))) + (((f . (h + x)) - (f . h)) * (f2 . (h + x))) is V11() real ext-real Element of REAL
(f2,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,x) - f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f2,x) + (- f2) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,x) . h is V11() real ext-real Element of REAL
(f . h) * ((f2,x) . h) is V11() real ext-real Element of REAL
((f . h) * ((f2,x) . h)) + (((f . (h + x)) - (f . h)) * (f2 . (h + x))) is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) - f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f,x) + (- f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
((f,x) . h) * (f2 . (h + x)) is V11() real ext-real Element of REAL
((f . h) * ((f2,x) . h)) + (((f,x) . h) * (f2 . (h + x))) is V11() real ext-real Element of REAL
(f2,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 0),x) - ((f2,x) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,x) . 0),x) + (- ((f2,x) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,x) . 0),x) . h is V11() real ext-real Element of REAL
(f . h) * ((((f2,x) . 0),x) . h) is V11() real ext-real Element of REAL
((f . h) * ((((f2,x) . 0),x) . h)) + (((f,x) . h) * (f2 . (h + x))) is V11() real ext-real Element of REAL
(f,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) - ((f,x) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) + (- ((f,x) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) . h is V11() real ext-real Element of REAL
((((f,x) . 0),x) . h) * (f2 . (h + x)) is V11() real ext-real Element of REAL
((f . h) * ((((f2,x) . 0),x) . h)) + (((((f,x) . 0),x) . h) * (f2 . (h + x))) is V11() real ext-real Element of REAL
(f2,x) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . (0 + 1)) . h is V11() real ext-real Element of REAL
(f . h) * (((f2,x) . (0 + 1)) . h) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . (0 + 1)) . h)) + (((((f,x) . 0),x) . h) * (f2 . (h + x))) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
f is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
f (#) f2 is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f (#) f2),x) is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total Element of bool [:NAT,(PFuncs (REAL,REAL)):]
((f (#) f2),x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) f2),x) . 1) . h is V11() real ext-real Element of REAL
((f (#) f2),x) . 2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) f2),x) . 2) . h is V11() real ext-real Element of REAL
S is non empty V13() V16( NAT ) V17( PFuncs (REAL,REAL)) Function-like total quasi_total () Element of bool [:NAT,(PFuncs (REAL,REAL)):]
(S,1) is non empty V13() V16( NAT ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
Sum ((S,1),1) is V11() real ext-real Element of REAL
(S,2) is non empty V13() V16( NAT ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
Sum ((S,2),2) is V11() real ext-real Element of REAL
1 -' 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative V56() V57() V58() V59() V60() V61() V62() Element of NAT
1 - 0 is V11() real ext-real Element of REAL
1 -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative V56() V57() V58() V59() V60() V61() V62() Element of NAT
1 - 1 is V11() real ext-real Element of REAL
2 -' 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 - 1 is V11() real ext-real Element of REAL
(f2,x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
2 -' 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 - 2 is V11() real ext-real Element of REAL
(S,2) . 1 is V11() real ext-real Element of REAL
2 choose 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,x) . 1 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 1) . h is V11() real ext-real Element of REAL
(2 choose 1) * (((f,x) . 1) . h) is V11() real ext-real Element of REAL
(f2,x) . (2 -' 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
1 * x is V11() real ext-real Element of REAL
h + (1 * x) is V11() real ext-real Element of REAL
((f2,x) . (2 -' 1)) . (h + (1 * x)) is V11() real ext-real Element of REAL
((2 choose 1) * (((f,x) . 1) . h)) * (((f2,x) . (2 -' 1)) . (h + (1 * x))) is V11() real ext-real Element of REAL
2 * (((f,x) . 1) . h) is V11() real ext-real Element of REAL
h + x is V11() real ext-real Element of REAL
((f2,x) . 1) . (h + x) is V11() real ext-real Element of REAL
(2 * (((f,x) . 1) . h)) * (((f2,x) . 1) . (h + x)) is V11() real ext-real Element of REAL
(S,1) . 1 is V11() real ext-real Element of REAL
1 choose 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(1 choose 1) * (((f,x) . 1) . h) is V11() real ext-real Element of REAL
(f2,x) . (1 -' 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . (1 -' 1)) . (h + (1 * x)) is V11() real ext-real Element of REAL
((1 choose 1) * (((f,x) . 1) . h)) * (((f2,x) . (1 -' 1)) . (h + (1 * x))) is V11() real ext-real Element of REAL
1 * (((f,x) . 1) . h) is V11() real ext-real Element of REAL
(1 * (((f,x) . 1) . h)) * (((f2,x) . (1 -' 1)) . (h + (1 * x))) is V11() real ext-real Element of REAL
f2 . (h + x) is V11() real ext-real Element of REAL
(((f,x) . 1) . h) * (f2 . (h + x)) is V11() real ext-real Element of REAL
(S,1) . 0 is V11() real ext-real Element of REAL
1 choose 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(f,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 0) . h is V11() real ext-real Element of REAL
(1 choose 0) * (((f,x) . 0) . h) is V11() real ext-real Element of REAL
(f2,x) . (1 -' 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
0 * x is V11() real ext-real Element of REAL
h + (0 * x) is V11() real ext-real Element of REAL
((f2,x) . (1 -' 0)) . (h + (0 * x)) is V11() real ext-real Element of REAL
((1 choose 0) * (((f,x) . 0) . h)) * (((f2,x) . (1 -' 0)) . (h + (0 * x))) is V11() real ext-real Element of REAL
1 * (((f,x) . 0) . h) is V11() real ext-real Element of REAL
(1 * (((f,x) . 0) . h)) * (((f2,x) . (1 -' 0)) . (h + (0 * x))) is V11() real ext-real Element of REAL
f . h is V11() real ext-real Element of REAL
((f2,x) . 1) . h is V11() real ext-real Element of REAL
(f . h) * (((f2,x) . 1) . h) is V11() real ext-real Element of REAL
Partial_Sums (S,1) is non empty V13() V16( NAT ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
0 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(Partial_Sums (S,1)) . (0 + 1) is V11() real ext-real Element of REAL
(Partial_Sums (S,1)) . 0 is V11() real ext-real Element of REAL
((Partial_Sums (S,1)) . 0) + ((S,1) . 1) is V11() real ext-real Element of REAL
((S,1) . 0) + ((S,1) . 1) is V11() real ext-real Element of REAL
1 + 1 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
((f (#) f2),x) . (1 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f (#) f2),x) . (1 + 1)) . h is V11() real ext-real Element of REAL
((((f (#) f2),x) . 1),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f (#) f2),x) . 1),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((((f (#) f2),x) . 1),x) - (((f (#) f2),x) . 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (((f (#) f2),x) . 1) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (((f (#) f2),x) . 1) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f (#) f2),x) . 1),x) + (- (((f (#) f2),x) . 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
((((f (#) f2),x) . 1),x) . h is V11() real ext-real Element of REAL
(((f (#) f2),x) . 1) . (h + x) is V11() real ext-real Element of REAL
((((f (#) f2),x) . 1) . (h + x)) - ((((f (#) f2),x) . 1) . h) is V11() real ext-real Element of REAL
f . (h + x) is V11() real ext-real Element of REAL
(f . (h + x)) * (((f2,x) . 1) . (h + x)) is V11() real ext-real Element of REAL
((f,x) . 1) . (h + x) is V11() real ext-real Element of REAL
(h + x) + x is V11() real ext-real Element of REAL
f2 . ((h + x) + x) is V11() real ext-real Element of REAL
(((f,x) . 1) . (h + x)) * (f2 . ((h + x) + x)) is V11() real ext-real Element of REAL
((f . (h + x)) * (((f2,x) . 1) . (h + x))) + ((((f,x) . 1) . (h + x)) * (f2 . ((h + x) + x))) is V11() real ext-real Element of REAL
(((f . (h + x)) * (((f2,x) . 1) . (h + x))) + ((((f,x) . 1) . (h + x)) * (f2 . ((h + x) + x)))) - ((((f (#) f2),x) . 1) . h) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . 1) . h)) + ((((f,x) . 1) . h) * (f2 . (h + x))) is V11() real ext-real Element of REAL
(((f . (h + x)) * (((f2,x) . 1) . (h + x))) + ((((f,x) . 1) . (h + x)) * (f2 . ((h + x) + x)))) - (((f . h) * (((f2,x) . 1) . h)) + ((((f,x) . 1) . h) * (f2 . (h + x)))) is V11() real ext-real Element of REAL
(((f2,x) . 1) . (h + x)) - (((f2,x) . 1) . h) is V11() real ext-real Element of REAL
(f . h) * ((((f2,x) . 1) . (h + x)) - (((f2,x) . 1) . h)) is V11() real ext-real Element of REAL
(f . (h + x)) - (f . h) is V11() real ext-real Element of REAL
((f . (h + x)) - (f . h)) * (((f2,x) . 1) . (h + x)) is V11() real ext-real Element of REAL
((f . h) * ((((f2,x) . 1) . (h + x)) - (((f2,x) . 1) . h))) + (((f . (h + x)) - (f . h)) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(((f,x) . 1) . (h + x)) - (((f,x) . 1) . h) is V11() real ext-real Element of REAL
((((f,x) . 1) . (h + x)) - (((f,x) . 1) . h)) * (f2 . ((h + x) + x)) is V11() real ext-real Element of REAL
(((f . h) * ((((f2,x) . 1) . (h + x)) - (((f2,x) . 1) . h))) + (((f . (h + x)) - (f . h)) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1) . (h + x)) - (((f,x) . 1) . h)) * (f2 . ((h + x) + x))) is V11() real ext-real Element of REAL
(f2 . ((h + x) + x)) - (f2 . (h + x)) is V11() real ext-real Element of REAL
(((f,x) . 1) . h) * ((f2 . ((h + x) + x)) - (f2 . (h + x))) is V11() real ext-real Element of REAL
((((f . h) * ((((f2,x) . 1) . (h + x)) - (((f2,x) . 1) . h))) + (((f . (h + x)) - (f . h)) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1) . (h + x)) - (((f,x) . 1) . h)) * (f2 . ((h + x) + x)))) + ((((f,x) . 1) . h) * ((f2 . ((h + x) + x)) - (f2 . (h + x)))) is V11() real ext-real Element of REAL
(((f2,x) . 1),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 1),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 1),x) - ((f2,x) . 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,x) . 1) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,x) . 1) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,x) . 1),x) + (- ((f2,x) . 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,x) . 1),x) . h is V11() real ext-real Element of REAL
(f . h) * ((((f2,x) . 1),x) . h) is V11() real ext-real Element of REAL
((f . h) * ((((f2,x) . 1),x) . h)) + (((f . (h + x)) - (f . h)) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(((f . h) * ((((f2,x) . 1),x) . h)) + (((f . (h + x)) - (f . h)) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1) . (h + x)) - (((f,x) . 1) . h)) * (f2 . ((h + x) + x))) is V11() real ext-real Element of REAL
((((f . h) * ((((f2,x) . 1),x) . h)) + (((f . (h + x)) - (f . h)) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1) . (h + x)) - (((f,x) . 1) . h)) * (f2 . ((h + x) + x)))) + ((((f,x) . 1) . h) * ((f2 . ((h + x) + x)) - (f2 . (h + x)))) is V11() real ext-real Element of REAL
(f,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,x) - f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f,x) + (- f) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,x) . h is V11() real ext-real Element of REAL
((f,x) . h) * (((f2,x) . 1) . (h + x)) is V11() real ext-real Element of REAL
((f . h) * ((((f2,x) . 1),x) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(((f . h) * ((((f2,x) . 1),x) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1) . (h + x)) - (((f,x) . 1) . h)) * (f2 . ((h + x) + x))) is V11() real ext-real Element of REAL
((((f . h) * ((((f2,x) . 1),x) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1) . (h + x)) - (((f,x) . 1) . h)) * (f2 . ((h + x) + x)))) + ((((f,x) . 1) . h) * ((f2 . ((h + x) + x)) - (f2 . (h + x)))) is V11() real ext-real Element of REAL
(((f,x) . 1),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 1),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 1),x) - ((f,x) . 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f,x) . 1) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f,x) . 1) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 1),x) + (- ((f,x) . 1)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 1),x) . h is V11() real ext-real Element of REAL
((((f,x) . 1),x) . h) * (f2 . ((h + x) + x)) is V11() real ext-real Element of REAL
(((f . h) * ((((f2,x) . 1),x) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1),x) . h) * (f2 . ((h + x) + x))) is V11() real ext-real Element of REAL
((((f . h) * ((((f2,x) . 1),x) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1),x) . h) * (f2 . ((h + x) + x)))) + ((((f,x) . 1) . h) * ((f2 . ((h + x) + x)) - (f2 . (h + x)))) is V11() real ext-real Element of REAL
(f2,x) is non empty V13() V16( REAL ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f2,x) - f2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) (#) f2 is V13() V16( REAL ) Function-like total complex-valued ext-real-valued real-valued set
(f2,x) + (- f2) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f2,x) . (h + x) is V11() real ext-real Element of REAL
(((f,x) . 1) . h) * ((f2,x) . (h + x)) is V11() real ext-real Element of REAL
((((f . h) * ((((f2,x) . 1),x) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1),x) . h) * (f2 . ((h + x) + x)))) + ((((f,x) . 1) . h) * ((f2,x) . (h + x))) is V11() real ext-real Element of REAL
(f2,x) . (1 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . (1 + 1)) . h is V11() real ext-real Element of REAL
(f . h) * (((f2,x) . (1 + 1)) . h) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . (1 + 1)) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(((f . h) * (((f2,x) . (1 + 1)) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1),x) . h) * (f2 . ((h + x) + x))) is V11() real ext-real Element of REAL
((((f . h) * (((f2,x) . (1 + 1)) . h)) + (((f,x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1),x) . h) * (f2 . ((h + x) + x)))) + ((((f,x) . 1) . h) * ((f2,x) . (h + x))) is V11() real ext-real Element of REAL
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f,x) . 0),x) - ((f,x) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) + (- ((f,x) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f,x) . 0),x) . h is V11() real ext-real Element of REAL
((((f,x) . 0),x) . h) * (((f2,x) . 1) . (h + x)) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . (1 + 1)) . h)) + (((((f,x) . 0),x) . h) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(((f . h) * (((f2,x) . (1 + 1)) . h)) + (((((f,x) . 0),x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1),x) . h) * (f2 . ((h + x) + x))) is V11() real ext-real Element of REAL
((((f . h) * (((f2,x) . (1 + 1)) . h)) + (((((f,x) . 0),x) . h) * (((f2,x) . 1) . (h + x)))) + (((((f,x) . 1),x) . h) * (f2 . ((h + x) + x)))) + ((((f,x) . 1) . h) * ((f2,x) . (h + x))) is V11() real ext-real Element of REAL
(f2,x) . 2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . 2) . h is V11() real ext-real Element of REAL
(f . h) * (((f2,x) . 2) . h) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . 2) . h)) + (((((f,x) . 0),x) . h) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(f,x) . 2 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . 2) . h is V11() real ext-real Element of REAL
2 * x is V11() real ext-real Element of REAL
h + (2 * x) is V11() real ext-real Element of REAL
f2 . (h + (2 * x)) is V11() real ext-real Element of REAL
(((f,x) . 2) . h) * (f2 . (h + (2 * x))) is V11() real ext-real Element of REAL
(((f . h) * (((f2,x) . 2) . h)) + (((((f,x) . 0),x) . h) * (((f2,x) . 1) . (h + x)))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x)))) is V11() real ext-real Element of REAL
((((f . h) * (((f2,x) . 2) . h)) + (((((f,x) . 0),x) . h) * (((f2,x) . 1) . (h + x)))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x))))) + ((((f,x) . 1) . h) * ((f2,x) . (h + x))) is V11() real ext-real Element of REAL
(f,x) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f,x) . (0 + 1)) . h is V11() real ext-real Element of REAL
(((f,x) . (0 + 1)) . h) * (((f2,x) . 1) . (h + x)) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . 2) . h)) + ((((f,x) . (0 + 1)) . h) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(((f . h) * (((f2,x) . 2) . h)) + ((((f,x) . (0 + 1)) . h) * (((f2,x) . 1) . (h + x)))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x)))) is V11() real ext-real Element of REAL
((((f . h) * (((f2,x) . 2) . h)) + ((((f,x) . (0 + 1)) . h) * (((f2,x) . 1) . (h + x)))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x))))) + ((((f,x) . 1) . h) * ((f2,x) . (h + x))) is V11() real ext-real Element of REAL
(((f,x) . 1) . h) * (((f2,x) . 1) . (h + x)) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . 2) . h)) + ((((f,x) . 1) . h) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
(((f . h) * (((f2,x) . 2) . h)) + ((((f,x) . 1) . h) * (((f2,x) . 1) . (h + x)))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x)))) is V11() real ext-real Element of REAL
(f2,x) . 0 is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 0),x) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(((f2,x) . 0),x) - ((f2,x) . 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- ((f2,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) ((f2,x) . 0) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,x) . 0),x) + (- ((f2,x) . 0)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(((f2,x) . 0),x) . (h + x) is V11() real ext-real Element of REAL
(((f,x) . 1) . h) * ((((f2,x) . 0),x) . (h + x)) is V11() real ext-real Element of REAL
((((f . h) * (((f2,x) . 2) . h)) + ((((f,x) . 1) . h) * (((f2,x) . 1) . (h + x)))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x))))) + ((((f,x) . 1) . h) * ((((f2,x) . 0),x) . (h + x))) is V11() real ext-real Element of REAL
(f2,x) . (0 + 1) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . (0 + 1)) . (h + x) is V11() real ext-real Element of REAL
(((f,x) . 1) . h) * (((f2,x) . (0 + 1)) . (h + x)) is V11() real ext-real Element of REAL
((((f . h) * (((f2,x) . 2) . h)) + ((((f,x) . 1) . h) * (((f2,x) . 1) . (h + x)))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x))))) + ((((f,x) . 1) . h) * (((f2,x) . (0 + 1)) . (h + x))) is V11() real ext-real Element of REAL
2 * ((((f,x) . 1) . h) * (((f2,x) . 1) . (h + x))) is V11() real ext-real Element of REAL
((f . h) * (((f2,x) . 2) . h)) + (2 * ((((f,x) . 1) . h) * (((f2,x) . 1) . (h + x)))) is V11() real ext-real Element of REAL
(((f . h) * (((f2,x) . 2) . h)) + (2 * ((((f,x) . 1) . h) * (((f2,x) . 1) . (h + x))))) + ((((f,x) . 2) . h) * (f2 . (h + (2 * x)))) is V11() real ext-real Element of REAL
2 -' 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real non negative V56() V57() V58() V59() V60() V61() V62() Element of NAT
2 - 0 is V11() real ext-real Element of REAL
(S,2) . 2 is V11() real ext-real Element of REAL
2 choose 2 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(2 choose 2) * (((f,x) . 2) . h) is V11() real ext-real Element of REAL
(f2,x) . (2 -' 2) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . (2 -' 2)) . (h + (2 * x)) is V11() real ext-real Element of REAL
((2 choose 2) * (((f,x) . 2) . h)) * (((f2,x) . (2 -' 2)) . (h + (2 * x))) is V11() real ext-real Element of REAL
1 * (((f,x) . 2) . h) is V11() real ext-real Element of REAL
(1 * (((f,x) . 2) . h)) * (((f2,x) . (2 -' 2)) . (h + (2 * x))) is V11() real ext-real Element of REAL
(S,2) . 0 is V11() real ext-real Element of REAL
2 choose 0 is epsilon-transitive epsilon-connected ordinal natural V11() real V30() ext-real V56() V57() V58() V59() V60() V61() V62() Element of NAT
(2 choose 0) * (((f,x) . 0) . h) is V11() real ext-real Element of REAL
(f2,x) . (2 -' 0) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
((f2,x) . (2 -' 0)) . (h + (0 * x)) is V11() real ext-real Element of REAL
((2 choose 0) * (((f,x) . 0) . h)) * (((f2,x) . (2 -' 0)) . (h + (0 * x))) is V11() real ext-real Element of REAL
(1 * (((f,x) . 0) . h)) * (((f2,x) . (2 -' 0)) . (h + (0 * x))) is V11() real ext-real Element of REAL
Partial_Sums (S,2) is non empty V13() V16( NAT ) V17( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of bool [:NAT,REAL:]
(Partial_Sums (S,2)) . (1 + 1) is V11() real ext-real Element of REAL
(Partial_Sums (S,2)) . (0 + 1) is V11() real ext-real Element of REAL
((Partial_Sums (S,2)) . (0 + 1)) + ((S,2) . 2) is V11() real ext-real Element of REAL
(Partial_Sums (S,2)) . 0 is V11() real ext-real Element of REAL
((Partial_Sums (S,2)) . 0) + ((S,2) . 1) is V11() real ext-real Element of REAL
(((Partial_Sums (S,2)) . 0) + ((S,2) . 1)) + ((S,2) . 2) is V11() real ext-real Element of REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
x - h is V11() real ext-real Element of REAL
f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom f is V57() V58() V59() Element of bool REAL
(f,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- h is V11() real ext-real set
(f,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
f - (f,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- h)) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
f + (- (f,(- h))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,h) . x is V11() real ext-real Element of REAL
f . x is V11() real ext-real Element of REAL
f . (x - h) is V11() real ext-real Element of REAL
(f . x) - (f . (x - h)) is V11() real ext-real Element of REAL
- h is V11() real ext-real Element of REAL
(f,(- h)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (f,(- h)) is V57() V58() V59() Element of bool REAL
- (- h) is V11() real ext-real Element of REAL
(- (- h)) ++ (dom f) is V57() V58() V59() Element of bool REAL
x - (- (- h)) is V11() real ext-real Element of REAL
h + (x - (- (- h))) is V11() real ext-real Element of REAL
(f,(- h)) . x is V11() real ext-real Element of REAL
x + (- h) is V11() real ext-real Element of REAL
f . (x + (- h)) is V11() real ext-real Element of REAL
(dom (f,(- h))) /\ (dom f) is V57() V58() V59() Element of bool REAL
dom (f,h) is V57() V58() V59() Element of bool REAL
x is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
h / 2 is V11() real ext-real Element of REAL
x + (h / 2) is V11() real ext-real Element of REAL
x - (h / 2) is V11() real ext-real Element of REAL
f is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom f is V57() V58() V59() Element of bool REAL
(f,h) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
h / 2 is V11() real ext-real Element of REAL
(f,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (h / 2) is V11() real ext-real Element of REAL
(f,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
(f,(h / 2)) - (f,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
- (f,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(- 1) (#) (f,(- (h / 2))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,(h / 2)) + (- (f,(- (h / 2)))) is V13() V16( REAL ) Function-like complex-valued ext-real-valued real-valued set
(f,h) . x is V11() real ext-real Element of REAL
f . (x + (h / 2)) is V11() real ext-real Element of REAL
f . (x - (h / 2)) is V11() real ext-real Element of REAL
(f . (x + (h / 2))) - (f . (x - (h / 2))) is V11() real ext-real Element of REAL
- (h / 2) is V11() real ext-real Element of REAL
(f,(- (h / 2))) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (f,(- (h / 2))) is V57() V58() V59() Element of bool REAL
- (- (h / 2)) is V11() real ext-real Element of REAL
(- (- (h / 2))) ++ (dom f) is V57() V58() V59() Element of bool REAL
(f,(h / 2)) is V13() V16( REAL ) V17( REAL ) Function-like complex-valued ext-real-valued real-valued Element of bool [:REAL,REAL:]
dom (f,(h / 2)) is V57() V58() V59() Element of bool REAL
(- (h / 2)) ++ (dom f) is V57() V58() V59() Element of bool REAL
(- (h / 2)) + (x + (h / 2)) is V11() real ext-real Element of REAL
(f,(h / 2)) . x is V11() real ext-real Element of REAL
(h / 2) + (x - (h / 2)) is V11() real ext-real Element of REAL
(f,(- (h / 2))) . x is V11() real ext-real Element of REAL
x + (- (h / 2)) is V11() real ext-real Element of REAL
f . (x + (- (h / 2))) is V11() real ext-real Element of REAL
(dom (f,(h / 2))) /\ (dom (f,(- (h / 2)))) is V57() V58() V59() Element of bool REAL
dom (f,h) is V57() V58() V59() Element of bool REAL