:: PDIFF_5 semantic presentation

REAL is V1() V54() V160() V161() V162() V166() set
NAT is V160() V161() V162() V163() V164() V165() V166() Element of K6(REAL)
K6(REAL) is set
K7(REAL,REAL) is complex-valued ext-real-valued real-valued set
K6(K7(REAL,REAL)) is set
omega is V160() V161() V162() V163() V164() V165() V166() set
K6(omega) is set
K6(NAT) is set
K7(NAT,REAL) is complex-valued ext-real-valued real-valued set
K6(K7(NAT,REAL)) is set
COMPLEX is V1() V54() V160() V166() set
RAT is V1() V54() V160() V161() V162() V163() V166() set
INT is V1() V54() V160() V161() V162() V163() V164() V166() set
1 is V1() ordinal natural V11() real ext-real positive non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
K7(1,1) is V20( RAT ) V20( INT ) complex-valued ext-real-valued real-valued natural-valued set
K6(K7(1,1)) is set
K7(K7(1,1),1) is V20( RAT ) V20( INT ) complex-valued ext-real-valued real-valued natural-valued set
K6(K7(K7(1,1),1)) is set
K7(K7(1,1),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K7(1,1),REAL)) is set
K7(K7(REAL,REAL),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K7(REAL,REAL),REAL)) is set
2 is V1() ordinal natural V11() real ext-real positive non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
K7(2,2) is V20( RAT ) V20( INT ) complex-valued ext-real-valued real-valued natural-valued set
K7(K7(2,2),REAL) is complex-valued ext-real-valued real-valued set
K6(K7(K7(2,2),REAL)) is set
K389(2) is V66() V92() V117() V118() V119() V120() V121() V122() V123() V172() V202() L20()
the U1 of K389(2) is set
REAL 1 is V1() FinSequence-membered M11( REAL )
K7((REAL 1),(REAL 1)) is set
K6(K7((REAL 1),(REAL 1))) is set
K400(1) is V66() V129() L15()
the U1 of K400(1) is set
K261(K400(1),K400(1)) is V66() L15()
the U1 of K261(K400(1),K400(1)) is set
REAL 2 is V1() FinSequence-membered M11( REAL )
K7((REAL 2),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL 2),REAL)) is set
K7(COMPLEX,COMPLEX) is complex-valued set
K6(K7(COMPLEX,COMPLEX)) is set
K7(K7(COMPLEX,COMPLEX),COMPLEX) is complex-valued set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(RAT,RAT) is V20( RAT ) complex-valued ext-real-valued real-valued set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is V20( RAT ) complex-valued ext-real-valued real-valued set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is V20( RAT ) V20( INT ) complex-valued ext-real-valued real-valued set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is V20( RAT ) V20( INT ) complex-valued ext-real-valued real-valued set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is V20( RAT ) V20( INT ) complex-valued ext-real-valued real-valued natural-valued set
K7(K7(NAT,NAT),NAT) is V20( RAT ) V20( INT ) complex-valued ext-real-valued real-valued natural-valued set
K6(K7(K7(NAT,NAT),NAT)) is set
0 is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
the V1() V160() V161() V162() V163() V164() V165() V166() set is V1() V160() V161() V162() V163() V164() V165() V166() set
3 is V1() ordinal natural V11() real ext-real positive non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
0 is set
REAL 3 is V1() FinSequence-membered M11( REAL )
K7((REAL 3),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL 3),REAL)) is set
proj (1,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
proj (2,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
proj (3,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (f,1)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (f,1)),u0)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of f2
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,1)),u0)) . c is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (1,(pdiff1 (f,1)),u0)) . c is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,1)),u0)) . L is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (1,(pdiff1 (f,1)),u0)) . L is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of c
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of L
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,1)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (1,(pdiff1 (f,1)),u0)) . N0) - ((SVF1 (1,(pdiff1 (f,1)),u0)) . c) is V11() real ext-real Element of REAL
N0 - c is V11() real ext-real Element of REAL
z1 . (N0 - c) is V11() real ext-real Element of REAL
N . (N0 - c) is V11() real ext-real Element of REAL
(z1 . (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
L1 . (N0 - c) is V11() real ext-real Element of REAL
R1 . (N0 - c) is V11() real ext-real Element of REAL
(L1 . (N0 - c)) + (R1 . (N0 - c)) is V11() real ext-real Element of REAL
r1 * (N0 - c) is V11() real ext-real Element of REAL
(r1 * (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
f2 * (N0 - c) is V11() real ext-real Element of REAL
(f2 * (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
h * (N0 - c) is V11() real ext-real Element of REAL
(h * (N0 - c)) + (R1 . (N0 - c)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of c
g is V11() real ext-real set
c - g is V11() real ext-real Element of REAL
c + g is V11() real ext-real Element of REAL
].(c - g),(c + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= c - g & not c + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
c + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
c + (- g) is V11() real ext-real Element of REAL
(c + (g / (n + 2))) - c is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative set
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - c is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (f,1)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (f,1)),u0)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of h
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,1)),u0)) . x0 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (2,(pdiff1 (f,1)),u0)) . x0 is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,1)),u0)) . R is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (2,(pdiff1 (f,1)),u0)) . R is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of x0
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of R
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,1)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (2,(pdiff1 (f,1)),u0)) . N0) - ((SVF1 (2,(pdiff1 (f,1)),u0)) . x0) is V11() real ext-real Element of REAL
N0 - x0 is V11() real ext-real Element of REAL
z1 . (N0 - x0) is V11() real ext-real Element of REAL
N . (N0 - x0) is V11() real ext-real Element of REAL
(z1 . (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
L1 . (N0 - x0) is V11() real ext-real Element of REAL
R1 . (N0 - x0) is V11() real ext-real Element of REAL
(L1 . (N0 - x0)) + (R1 . (N0 - x0)) is V11() real ext-real Element of REAL
r1 * (N0 - x0) is V11() real ext-real Element of REAL
(r1 * (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
f2 * (N0 - x0) is V11() real ext-real Element of REAL
(f2 * (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
h * (N0 - x0) is V11() real ext-real Element of REAL
(h * (N0 - x0)) + (R1 . (N0 - x0)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of x0
g is V11() real ext-real set
x0 - g is V11() real ext-real Element of REAL
x0 + g is V11() real ext-real Element of REAL
].(x0 - g),(x0 + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= x0 - g & not x0 + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
x0 + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
x0 + (- g) is V11() real ext-real Element of REAL
(x0 + (g / (n + 2))) - x0 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - x0 is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (f,1)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (f,1)),u0)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of c
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,1)),u0)) . y0 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (3,(pdiff1 (f,1)),u0)) . y0 is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,1)),u0)) . z1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (3,(pdiff1 (f,1)),u0)) . z1 is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of y0
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of z1
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,1)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (3,(pdiff1 (f,1)),u0)) . N0) - ((SVF1 (3,(pdiff1 (f,1)),u0)) . y0) is V11() real ext-real Element of REAL
N0 - y0 is V11() real ext-real Element of REAL
z1 . (N0 - y0) is V11() real ext-real Element of REAL
N . (N0 - y0) is V11() real ext-real Element of REAL
(z1 . (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
L1 . (N0 - y0) is V11() real ext-real Element of REAL
R1 . (N0 - y0) is V11() real ext-real Element of REAL
(L1 . (N0 - y0)) + (R1 . (N0 - y0)) is V11() real ext-real Element of REAL
r1 * (N0 - y0) is V11() real ext-real Element of REAL
(r1 * (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
f2 * (N0 - y0) is V11() real ext-real Element of REAL
(f2 * (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
h * (N0 - y0) is V11() real ext-real Element of REAL
(h * (N0 - y0)) + (R1 . (N0 - y0)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of y0
g is V11() real ext-real set
y0 - g is V11() real ext-real Element of REAL
y0 + g is V11() real ext-real Element of REAL
].(y0 - g),(y0 + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= y0 - g & not y0 + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
y0 + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
y0 + (- g) is V11() real ext-real Element of REAL
(y0 + (g / (n + 2))) - y0 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - y0 is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (f,2)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (f,2)),u0)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of f2
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,2)),u0)) . c is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (1,(pdiff1 (f,2)),u0)) . c is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,2)),u0)) . L is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (1,(pdiff1 (f,2)),u0)) . L is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of c
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of L
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,2)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (1,(pdiff1 (f,2)),u0)) . N0) - ((SVF1 (1,(pdiff1 (f,2)),u0)) . c) is V11() real ext-real Element of REAL
N0 - c is V11() real ext-real Element of REAL
z1 . (N0 - c) is V11() real ext-real Element of REAL
N . (N0 - c) is V11() real ext-real Element of REAL
(z1 . (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
L1 . (N0 - c) is V11() real ext-real Element of REAL
R1 . (N0 - c) is V11() real ext-real Element of REAL
(L1 . (N0 - c)) + (R1 . (N0 - c)) is V11() real ext-real Element of REAL
r1 * (N0 - c) is V11() real ext-real Element of REAL
(r1 * (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
f2 * (N0 - c) is V11() real ext-real Element of REAL
(f2 * (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
h * (N0 - c) is V11() real ext-real Element of REAL
(h * (N0 - c)) + (R1 . (N0 - c)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of c
g is V11() real ext-real set
c - g is V11() real ext-real Element of REAL
c + g is V11() real ext-real Element of REAL
].(c - g),(c + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= c - g & not c + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
c + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
c + (- g) is V11() real ext-real Element of REAL
(c + (g / (n + 2))) - c is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - c is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (f,2)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (f,2)),u0)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of h
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,2)),u0)) . x0 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (2,(pdiff1 (f,2)),u0)) . x0 is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,2)),u0)) . R is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (2,(pdiff1 (f,2)),u0)) . R is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of x0
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of R
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,2)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (2,(pdiff1 (f,2)),u0)) . N0) - ((SVF1 (2,(pdiff1 (f,2)),u0)) . x0) is V11() real ext-real Element of REAL
N0 - x0 is V11() real ext-real Element of REAL
z1 . (N0 - x0) is V11() real ext-real Element of REAL
N . (N0 - x0) is V11() real ext-real Element of REAL
(z1 . (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
L1 . (N0 - x0) is V11() real ext-real Element of REAL
R1 . (N0 - x0) is V11() real ext-real Element of REAL
(L1 . (N0 - x0)) + (R1 . (N0 - x0)) is V11() real ext-real Element of REAL
r1 * (N0 - x0) is V11() real ext-real Element of REAL
(r1 * (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
f2 * (N0 - x0) is V11() real ext-real Element of REAL
(f2 * (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
h * (N0 - x0) is V11() real ext-real Element of REAL
(h * (N0 - x0)) + (R1 . (N0 - x0)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of x0
g is V11() real ext-real set
x0 - g is V11() real ext-real Element of REAL
x0 + g is V11() real ext-real Element of REAL
].(x0 - g),(x0 + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= x0 - g & not x0 + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
x0 + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
x0 + (- g) is V11() real ext-real Element of REAL
(x0 + (g / (n + 2))) - x0 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - x0 is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (f,2)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (f,2)),u0)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of c
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,2)),u0)) . y0 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (3,(pdiff1 (f,2)),u0)) . y0 is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,2)),u0)) . z1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (3,(pdiff1 (f,2)),u0)) . z1 is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of y0
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of z1
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,2)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (3,(pdiff1 (f,2)),u0)) . N0) - ((SVF1 (3,(pdiff1 (f,2)),u0)) . y0) is V11() real ext-real Element of REAL
N0 - y0 is V11() real ext-real Element of REAL
z1 . (N0 - y0) is V11() real ext-real Element of REAL
N . (N0 - y0) is V11() real ext-real Element of REAL
(z1 . (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
L1 . (N0 - y0) is V11() real ext-real Element of REAL
R1 . (N0 - y0) is V11() real ext-real Element of REAL
(L1 . (N0 - y0)) + (R1 . (N0 - y0)) is V11() real ext-real Element of REAL
r1 * (N0 - y0) is V11() real ext-real Element of REAL
(r1 * (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
f2 * (N0 - y0) is V11() real ext-real Element of REAL
(f2 * (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
h * (N0 - y0) is V11() real ext-real Element of REAL
(h * (N0 - y0)) + (R1 . (N0 - y0)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of y0
g is V11() real ext-real set
y0 - g is V11() real ext-real Element of REAL
y0 + g is V11() real ext-real Element of REAL
].(y0 - g),(y0 + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= y0 - g & not y0 + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
y0 + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
y0 + (- g) is V11() real ext-real Element of REAL
(y0 + (g / (n + 2))) - y0 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - y0 is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (f,3)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (f,3)),u0)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of f2
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,3)),u0)) . c is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (1,(pdiff1 (f,3)),u0)) . c is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of c
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,3)),u0)) . L is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (1,(pdiff1 (f,3)),u0)) . L is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of L
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of c
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of L
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (1,(pdiff1 (f,3)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (1,(pdiff1 (f,3)),u0)) . N0) - ((SVF1 (1,(pdiff1 (f,3)),u0)) . c) is V11() real ext-real Element of REAL
N0 - c is V11() real ext-real Element of REAL
z1 . (N0 - c) is V11() real ext-real Element of REAL
N . (N0 - c) is V11() real ext-real Element of REAL
(z1 . (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
L1 . (N0 - c) is V11() real ext-real Element of REAL
R1 . (N0 - c) is V11() real ext-real Element of REAL
(L1 . (N0 - c)) + (R1 . (N0 - c)) is V11() real ext-real Element of REAL
r1 * (N0 - c) is V11() real ext-real Element of REAL
(r1 * (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
f2 * (N0 - c) is V11() real ext-real Element of REAL
(f2 * (N0 - c)) + (N . (N0 - c)) is V11() real ext-real Element of REAL
h * (N0 - c) is V11() real ext-real Element of REAL
(h * (N0 - c)) + (R1 . (N0 - c)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of c
g is V11() real ext-real set
c - g is V11() real ext-real Element of REAL
c + g is V11() real ext-real Element of REAL
].(c - g),(c + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= c - g & not c + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
c + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
c + (- g) is V11() real ext-real Element of REAL
(c + (g / (n + 2))) - c is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - c is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (f,3)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (f,3)),u0)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of h
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,3)),u0)) . x0 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (2,(pdiff1 (f,3)),u0)) . x0 is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of x0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,3)),u0)) . R is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (2,(pdiff1 (f,3)),u0)) . R is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of R
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of x0
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of R
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (2,(pdiff1 (f,3)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (2,(pdiff1 (f,3)),u0)) . N0) - ((SVF1 (2,(pdiff1 (f,3)),u0)) . x0) is V11() real ext-real Element of REAL
N0 - x0 is V11() real ext-real Element of REAL
z1 . (N0 - x0) is V11() real ext-real Element of REAL
N . (N0 - x0) is V11() real ext-real Element of REAL
(z1 . (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
L1 . (N0 - x0) is V11() real ext-real Element of REAL
R1 . (N0 - x0) is V11() real ext-real Element of REAL
(L1 . (N0 - x0)) + (R1 . (N0 - x0)) is V11() real ext-real Element of REAL
r1 * (N0 - x0) is V11() real ext-real Element of REAL
(r1 * (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
f2 * (N0 - x0) is V11() real ext-real Element of REAL
(f2 * (N0 - x0)) + (N . (N0 - x0)) is V11() real ext-real Element of REAL
h * (N0 - x0) is V11() real ext-real Element of REAL
(h * (N0 - x0)) + (R1 . (N0 - x0)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of x0
g is V11() real ext-real set
x0 - g is V11() real ext-real Element of REAL
x0 + g is V11() real ext-real Element of REAL
].(x0 - g),(x0 + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= x0 - g & not x0 + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
x0 + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
x0 + (- g) is V11() real ext-real Element of REAL
(x0 + (g / (n + 2))) - x0 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - x0 is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (f,3)),u0)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (f,3)),u0)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
y0 . 1 is V11() real ext-real Element of REAL
z1 * 1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of c
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,3)),u0)) . y0 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
c is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
<*c,x0,y0*> is set
(SVF1 (3,(pdiff1 (f,3)),u0)) . y0 is V11() real ext-real Element of REAL
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z0 is V160() V161() V162() Neighbourhood of y0
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V11() real ext-real Element of REAL
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
<*L,R,z1*> is set
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,3)),u0)) . z1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V11() real ext-real Element of REAL
R is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*L,R,z1*> is set
(SVF1 (3,(pdiff1 (f,3)),u0)) . z1 is V11() real ext-real Element of REAL
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N1 is V160() V161() V162() Neighbourhood of z1
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 . 1 is V11() real ext-real Element of REAL
R1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
r1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real Element of REAL
r1 * 1 is V11() real ext-real Element of REAL
p1 * 1 is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of y0
g is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
g . 1 is V11() real ext-real Element of REAL
s1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
h is V160() V161() V162() Neighbourhood of z1
n is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
n . 1 is V11() real ext-real Element of REAL
c₂₄ is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N0 is V11() real ext-real Element of REAL
(SVF1 (3,(pdiff1 (f,3)),u0)) . N0 is V11() real ext-real Element of REAL
((SVF1 (3,(pdiff1 (f,3)),u0)) . N0) - ((SVF1 (3,(pdiff1 (f,3)),u0)) . y0) is V11() real ext-real Element of REAL
N0 - y0 is V11() real ext-real Element of REAL
z1 . (N0 - y0) is V11() real ext-real Element of REAL
N . (N0 - y0) is V11() real ext-real Element of REAL
(z1 . (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
L1 . (N0 - y0) is V11() real ext-real Element of REAL
R1 . (N0 - y0) is V11() real ext-real Element of REAL
(L1 . (N0 - y0)) + (R1 . (N0 - y0)) is V11() real ext-real Element of REAL
r1 * (N0 - y0) is V11() real ext-real Element of REAL
(r1 * (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
f2 * (N0 - y0) is V11() real ext-real Element of REAL
(f2 * (N0 - y0)) + (N . (N0 - y0)) is V11() real ext-real Element of REAL
h * (N0 - y0) is V11() real ext-real Element of REAL
(h * (N0 - y0)) + (R1 . (N0 - y0)) is V11() real ext-real Element of REAL
N0 is V160() V161() V162() Neighbourhood of y0
g is V11() real ext-real set
y0 - g is V11() real ext-real Element of REAL
y0 + g is V11() real ext-real Element of REAL
].(y0 - g),(y0 + g).[ is V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= y0 - g & not y0 + g <= b₁ ) } is set
s1 is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
h is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (h + 2) is V11() real ext-real Element of REAL
s1 . h is V11() real ext-real Element of REAL
lim s1 is V11() real ext-real Element of REAL
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
n is ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
h . n is V11() real ext-real Element of REAL
n + 2 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / (n + 2) is V11() real ext-real Element of REAL
n + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
(n + 1) + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
0 + 1 is V1() ordinal natural V11() real ext-real positive non negative Element of REAL
g / 1 is V11() real ext-real Element of REAL
y0 + (g / (n + 2)) is V11() real ext-real Element of REAL
- g is V11() real ext-real set
y0 + (- g) is V11() real ext-real Element of REAL
(y0 + (g / (n + 2))) - y0 is V11() real ext-real Element of REAL
n is ordinal natural V11() real ext-real non negative set
h . n is V11() real ext-real Element of REAL
f2 * (h . n) is V11() real ext-real Element of REAL
N . (h . n) is V11() real ext-real Element of REAL
(f2 * (h . n)) + (N . (h . n)) is V11() real ext-real Element of REAL
h * (h . n) is V11() real ext-real Element of REAL
R1 . (h . n) is V11() real ext-real Element of REAL
(h * (h . n)) + (R1 . (h . n)) is V11() real ext-real Element of REAL
c₂₄ is V11() real ext-real Element of REAL
c₂₄ - y0 is V11() real ext-real Element of REAL
(f2 * (h . n)) / (h . n) is V11() real ext-real Element of REAL
(N . (h . n)) / (h . n) is V11() real ext-real Element of REAL
((f2 * (h . n)) / (h . n)) + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
((h * (h . n)) + (R1 . (h . n))) / (h . n) is V11() real ext-real Element of REAL
(h . n) / (h . n) is V11() real ext-real Element of REAL
f2 * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
f2 * 1 is V11() real ext-real Element of REAL
(h * (h . n)) / (h . n) is V11() real ext-real Element of REAL
h * ((h . n) / (h . n)) is V11() real ext-real Element of REAL
h * 1 is V11() real ext-real Element of REAL
f2 + ((N . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
(R1 . (h . n)) / (h . n) is V11() real ext-real Element of REAL
h + ((R1 . (h . n)) / (h . n)) is V11() real ext-real Element of REAL
dom N is V160() V161() V162() Element of K6(REAL)
rng h is V160() V161() V162() Element of K6(REAL)
dom R1 is V160() V161() V162() Element of K6(REAL)
(h . n) " is V11() real ext-real Element of REAL
(N . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") . n is V11() real ext-real Element of REAL
(N . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
N /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(N /* h) . n is V11() real ext-real Element of REAL
((N /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (N /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (N /* h)) . n is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h . n) ") is V11() real ext-real Element of REAL
(R1 . (h . n)) * ((h ") . n) is V11() real ext-real Element of REAL
R1 /* h is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(R1 /* h) . n is V11() real ext-real Element of REAL
((R1 /* h) . n) * ((h ") . n) is V11() real ext-real Element of REAL
(h ") (#) (R1 /* h) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((h ") (#) (R1 /* h)) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n) is V11() real ext-real Element of REAL
h + ((((h ") (#) (R1 /* h)) . n) - (((h ") (#) (N /* h)) . n)) is V11() real ext-real Element of REAL
f2 - h is V11() real ext-real Element of REAL
((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . n is V11() real ext-real Element of REAL
(((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) . 1 is V11() real ext-real Element of REAL
lim (((h ") (#) (R1 /* h)) - ((h ") (#) (N /* h))) is V11() real ext-real Element of REAL
lim ((h ") (#) (N /* h)) is V11() real ext-real Element of REAL
lim ((h ") (#) (R1 /* h)) is V11() real ext-real Element of REAL
0 - 0 is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (c,1)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (c,1)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (1,(pdiff1 (c,1)),h)) . x0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of x0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of x0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (c,1)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (c,1)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (2,(pdiff1 (c,1)),h)) . y0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of y0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of y0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (c,1)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (c,1)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (3,(pdiff1 (c,1)),h)) . z0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (c,2)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (c,2)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (1,(pdiff1 (c,2)),h)) . x0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of x0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of x0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (c,2)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (c,2)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (2,(pdiff1 (c,2)),h)) . y0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of y0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of y0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (c,2)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (c,2)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (3,(pdiff1 (c,2)),h)) . z0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (c,3)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (c,3)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (1,(pdiff1 (c,3)),h)) . x0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of x0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of x0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (c,3)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (c,3)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (2,(pdiff1 (c,3)),h)) . y0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of y0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of y0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (c,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (c,3)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (c,3)),h)) is V160() V161() V162() Element of K6(REAL)
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
(SVF1 (3,(pdiff1 (c,3)),h)) . z0 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z0
N is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (c,1)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,(pdiff1 (c,1)),h)),f) is V11() real ext-real Element of REAL
dom (SVF1 (1,(pdiff1 (c,1)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (1,(pdiff1 (c,1)),h)) . y0 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of y0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of y0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of y0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of y0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (c,1)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,(pdiff1 (c,1)),h)),u0) is V11() real ext-real Element of REAL
dom (SVF1 (2,(pdiff1 (c,1)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (2,(pdiff1 (c,1)),h)) . z0 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of z0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of z0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (c,1)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,(pdiff1 (c,1)),h)),f2) is V11() real ext-real Element of REAL
dom (SVF1 (3,(pdiff1 (c,1)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (3,(pdiff1 (c,1)),h)) . z1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of z1
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of z1
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z1
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z1
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (c,2)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,(pdiff1 (c,2)),h)),f) is V11() real ext-real Element of REAL
dom (SVF1 (1,(pdiff1 (c,2)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (1,(pdiff1 (c,2)),h)) . y0 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of y0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of y0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of y0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of y0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (c,2)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,(pdiff1 (c,2)),h)),u0) is V11() real ext-real Element of REAL
dom (SVF1 (2,(pdiff1 (c,2)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (2,(pdiff1 (c,2)),h)) . z0 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of z0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of z0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (c,2)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,(pdiff1 (c,2)),h)),f2) is V11() real ext-real Element of REAL
dom (SVF1 (3,(pdiff1 (c,2)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (3,(pdiff1 (c,2)),h)) . z1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of z1
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of z1
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z1
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z1
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (c,3)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,(pdiff1 (c,3)),h)),f) is V11() real ext-real Element of REAL
dom (SVF1 (1,(pdiff1 (c,3)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (1,(pdiff1 (c,3)),h)) . y0 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of y0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of y0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of y0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of y0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (c,3)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,(pdiff1 (c,3)),h)),u0) is V11() real ext-real Element of REAL
dom (SVF1 (2,(pdiff1 (c,3)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (2,(pdiff1 (c,3)),h)) . z0 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of z0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of z0
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z0
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V11() real ext-real Element of REAL
u0 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f,u0,f2*> is set
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
c is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(c,h) is V11() real ext-real Element of REAL
pdiff1 (c,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (c,3)),h) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,(pdiff1 (c,3)),h)),f2) is V11() real ext-real Element of REAL
dom (SVF1 (3,(pdiff1 (c,3)),h)) is V160() V161() V162() Element of K6(REAL)
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*y0,z0,z1*> is set
(SVF1 (3,(pdiff1 (c,3)),h)) . z1 is V11() real ext-real Element of REAL
N is V160() V161() V162() Neighbourhood of z1
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is V160() V161() V162() Neighbourhood of z1
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V160() V161() V162() Neighbourhood of z1
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L . 1 is V11() real ext-real Element of REAL
z1 is V160() V161() V162() Neighbourhood of z1
N1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
r1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N1 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is set
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is set
h is set
dom f is Element of K6((REAL 3))
h is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . h is V11() real ext-real Element of REAL
(f,h) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is Element of K6((REAL 3))
K6((REAL 3)) is set
h is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom h is Element of K6((REAL 3))
c is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 . c is V11() real ext-real Element of REAL
(f,c) is V11() real ext-real Element of REAL
h . c is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (u0,1)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (u0,1)),f)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (1,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (u0,1)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (u0,1)),f)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (u0,1)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (u0,1)),f)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (2,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (u0,1)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (u0,1)),f)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (u0,1)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (u0,1)),f)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (3,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (u0,1)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (u0,1)),f)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (u0,2)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (u0,2)),f)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (1,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (u0,2)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (u0,2)),f)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (u0,2)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (u0,2)),f)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (2,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (u0,2)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (u0,2)),f)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (u0,2)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (u0,2)),f)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (3,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (u0,2)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (u0,2)),f)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (u0,3)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (u0,3)),f)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (1,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (u0,3)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (1,(pdiff1 (u0,3)),f)) . f2 is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of f2
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (u0,3)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (u0,3)),f)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (2,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (u0,3)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (2,(pdiff1 (u0,3)),f)) . h is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of h
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (u0,3)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (u0,3)),f)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (3,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (u0,3)),f)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
(SVF1 (3,(pdiff1 (u0,3)),f)) . c is V11() real ext-real Element of REAL
x0 is V160() V161() V162() Neighbourhood of c
y0 is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z0 is V1() V16() V19( REAL ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,1)),f,1) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (1,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,(pdiff1 (u0,1)),f)),f2) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,1)),f,2) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (2,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,(pdiff1 (u0,1)),f)),h) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,1)),f,3) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (3,(pdiff1 (u0,1)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,(pdiff1 (u0,1)),f)),c) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,2)),f,1) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (1,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,(pdiff1 (u0,2)),f)),f2) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,2)),f,2) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (2,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,(pdiff1 (u0,2)),f)),h) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,2)),f,3) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (3,(pdiff1 (u0,2)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,(pdiff1 (u0,2)),f)),c) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,3)),f,1) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (1,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,(pdiff1 (u0,3)),f)),f2) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,3)),f,2) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (2,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,(pdiff1 (u0,3)),f)),h) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((pdiff1 (u0,3)),f,3) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
h is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
<*f2,h,c*> is set
SVF1 (3,(pdiff1 (u0,3)),f) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,(pdiff1 (u0,3)),f)),c) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (1,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (1,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (f,1)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (1,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (1,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (1,(pdiff1 (f,1)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (1,(pdiff1 (f,1)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (1,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,1)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (1,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,1)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (1,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,1)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,1)),u0,1) is V11() real ext-real Element of REAL
diff ((SVF1 (1,(pdiff1 (f,1)),u0)),x0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (2,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (2,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (f,1)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (2,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (2,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (2,(pdiff1 (f,1)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (2,(pdiff1 (f,1)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (2,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,1)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (2,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,1)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (2,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,1)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,1)),u0,2) is V11() real ext-real Element of REAL
diff ((SVF1 (2,(pdiff1 (f,1)),u0)),y0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (3,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (3,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (f,1)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (3,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (3,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (3,(pdiff1 (f,1)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (3,(pdiff1 (f,1)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (3,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,1)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (3,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,1)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (3,(pdiff1 (f,1)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,1)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,1)),u0,3) is V11() real ext-real Element of REAL
diff ((SVF1 (3,(pdiff1 (f,1)),u0)),z0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (1,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (1,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (f,2)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (1,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (1,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (1,(pdiff1 (f,2)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (1,(pdiff1 (f,2)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (1,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,2)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (1,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,2)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (1,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,2)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,2)),u0,1) is V11() real ext-real Element of REAL
diff ((SVF1 (1,(pdiff1 (f,2)),u0)),x0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (2,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (2,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (f,2)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (2,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (2,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (2,(pdiff1 (f,2)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (2,(pdiff1 (f,2)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (2,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,2)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (2,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,2)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (2,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,2)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,2)),u0,2) is V11() real ext-real Element of REAL
diff ((SVF1 (2,(pdiff1 (f,2)),u0)),y0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (3,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (3,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (f,2)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (3,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (3,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (3,(pdiff1 (f,2)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (3,(pdiff1 (f,2)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (3,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,2)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (3,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,2)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (3,(pdiff1 (f,2)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,2)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,2)),u0,3) is V11() real ext-real Element of REAL
diff ((SVF1 (3,(pdiff1 (f,2)),u0)),z0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (1,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (1,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(pdiff1 (f,3)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (1,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (1,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (1,(pdiff1 (f,3)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (1,(pdiff1 (f,3)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (1,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,3)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (1,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,3)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (1,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (1,(pdiff1 (f,3)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,3)),u0,1) is V11() real ext-real Element of REAL
diff ((SVF1 (1,(pdiff1 (f,3)),u0)),x0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (2,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (2,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(pdiff1 (f,3)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (2,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (2,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (2,(pdiff1 (f,3)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (2,(pdiff1 (f,3)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (2,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,3)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (2,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,3)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (2,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (2,(pdiff1 (f,3)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,3)),u0,2) is V11() real ext-real Element of REAL
diff ((SVF1 (2,(pdiff1 (f,3)),u0)),y0) is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
(proj (3,3)) . u0 is V11() real ext-real Element of REAL
SVF1 (3,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(pdiff1 (f,3)),u0)) is V160() V161() V162() Element of K6(REAL)
{((proj (3,3)) . u0)} is V160() V161() V162() set
(f,u0) is V11() real ext-real Element of REAL
f2 is V160() V161() V162() Neighbourhood of (proj (3,3)) . u0
h is V16() non-zero V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
h " is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
c is V16() V19( NAT ) V20( REAL ) V21() constant total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng c is V160() V161() V162() Element of K6(REAL)
h + c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (h + c) is V160() V161() V162() Element of K6(REAL)
(SVF1 (3,(pdiff1 (f,3)),u0)) /* (h + c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (3,(pdiff1 (f,3)),u0)) /* c is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (3,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,3)),u0)) /* c) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(h ") (#) (((SVF1 (3,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,3)),u0)) /* c)) is V16() V19( NAT ) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((h ") (#) (((SVF1 (3,(pdiff1 (f,3)),u0)) /* (h + c)) - ((SVF1 (3,(pdiff1 (f,3)),u0)) /* c))) is V11() real ext-real Element of REAL
x0 is V11() real ext-real Element of REAL
y0 is V11() real ext-real Element of REAL
z0 is V11() real ext-real Element of REAL
<*x0,y0,z0*> is set
partdiff ((pdiff1 (f,3)),u0,3) is V11() real ext-real Element of REAL
diff ((SVF1 (3,(pdiff1 (f,3)),u0)),z0) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) + (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,1)) + (pdiff1 (f2,1))),f,1) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) + (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,1)),f,1) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),f,1) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,1)),f,1)) + (partdiff ((pdiff1 (f2,1)),f,1)) is V11() real ext-real Element of REAL
(u0,f) + (partdiff ((pdiff1 (f2,1)),f,1)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) + (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,1)) + (pdiff1 (f2,1))),f,2) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) + (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,1)),f,2) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),f,2) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,1)),f,2)) + (partdiff ((pdiff1 (f2,1)),f,2)) is V11() real ext-real Element of REAL
(u0,f) + (partdiff ((pdiff1 (f2,1)),f,2)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) + (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,1)) + (pdiff1 (f2,1))),f,3) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) + (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,1)),f,3) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),f,3) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,1)),f,3)) + (partdiff ((pdiff1 (f2,1)),f,3)) is V11() real ext-real Element of REAL
(u0,f) + (partdiff ((pdiff1 (f2,1)),f,3)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) + (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,2)) + (pdiff1 (f2,2))),f,1) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) + (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,2)),f,1) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),f,1) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,2)),f,1)) + (partdiff ((pdiff1 (f2,2)),f,1)) is V11() real ext-real Element of REAL
(u0,f) + (partdiff ((pdiff1 (f2,2)),f,1)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) + (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,2)) + (pdiff1 (f2,2))),f,2) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) + (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,2)),f,2) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),f,2) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,2)),f,2)) + (partdiff ((pdiff1 (f2,2)),f,2)) is V11() real ext-real Element of REAL
(u0,f) + (partdiff ((pdiff1 (f2,2)),f,2)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) + (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,2)) + (pdiff1 (f2,2))),f,3) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) + (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,2)),f,3) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),f,3) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,2)),f,3)) + (partdiff ((pdiff1 (f2,2)),f,3)) is V11() real ext-real Element of REAL
(u0,f) + (partdiff ((pdiff1 (f2,2)),f,3)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) - (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,1)) - (pdiff1 (f2,1))),f,1) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) - (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,1)),f,1) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),f,1) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,1)),f,1)) - (partdiff ((pdiff1 (f2,1)),f,1)) is V11() real ext-real Element of REAL
(u0,f) - (partdiff ((pdiff1 (f2,1)),f,1)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) - (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,1)) - (pdiff1 (f2,1))),f,2) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) - (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,1)),f,2) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),f,2) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,1)),f,2)) - (partdiff ((pdiff1 (f2,1)),f,2)) is V11() real ext-real Element of REAL
(u0,f) - (partdiff ((pdiff1 (f2,1)),f,2)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) - (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,1)) - (pdiff1 (f2,1))),f,3) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) - (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,1)),f,3) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),f,3) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,1)),f,3)) - (partdiff ((pdiff1 (f2,1)),f,3)) is V11() real ext-real Element of REAL
(u0,f) - (partdiff ((pdiff1 (f2,1)),f,3)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) - (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,2)) - (pdiff1 (f2,2))),f,1) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) - (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,2)),f,1) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),f,1) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,2)),f,1)) - (partdiff ((pdiff1 (f2,2)),f,1)) is V11() real ext-real Element of REAL
(u0,f) - (partdiff ((pdiff1 (f2,2)),f,1)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) - (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,2)) - (pdiff1 (f2,2))),f,2) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) - (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,2)),f,2) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),f,2) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,2)),f,2)) - (partdiff ((pdiff1 (f2,2)),f,2)) is V11() real ext-real Element of REAL
(u0,f) - (partdiff ((pdiff1 (f2,2)),f,2)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(u0,f) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) - (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (((pdiff1 (u0,2)) - (pdiff1 (f2,2))),f,3) is V11() real ext-real Element of REAL
(f2,f) is V11() real ext-real Element of REAL
(u0,f) - (f2,f) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (u0,2)),f,3) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),f,3) is V11() real ext-real Element of REAL
(partdiff ((pdiff1 (u0,2)),f,3)) - (partdiff ((pdiff1 (f2,2)),f,3)) is V11() real ext-real Element of REAL
(u0,f) - (partdiff ((pdiff1 (f2,2)),f,3)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,1))),u0,1) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),u0,1) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,1)),u0,1)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,1))),u0,2) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),u0,2) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,1)),u0,2)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,1))),u0,3) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,1)),u0,3) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,1)),u0,3)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,2))),u0,1) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),u0,1) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,2)),u0,1)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,2))),u0,2) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),u0,2) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,2)),u0,2)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,2))),u0,3) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,2)),u0,3) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,2)),u0,3)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,3)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,3))),u0,1) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,3)),u0,1) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,3)),u0,1)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,3)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,3))),u0,2) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,3)),u0,2) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,3)),u0,2)) is V11() real ext-real Element of REAL
f is V11() real ext-real Element of REAL
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f (#) (pdiff1 (f2,3)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff ((f (#) (pdiff1 (f2,3))),u0,3) is V11() real ext-real Element of REAL
(f2,u0) is V11() real ext-real Element of REAL
f * (f2,u0) is V11() real ext-real Element of REAL
partdiff ((pdiff1 (f2,3)),u0,3) is V11() real ext-real Element of REAL
f * (partdiff ((pdiff1 (f2,3)),u0,3)) is V11() real ext-real Element of REAL
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) (#) (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) (#) (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,1)) (#) (pdiff1 (f2,1)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) (#) (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) (#) (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,2)) (#) (pdiff1 (f2,2)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,3)) (#) (pdiff1 (f2,3)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,3)) (#) (pdiff1 (f2,3)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
u0 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (u0,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f2,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(pdiff1 (u0,3)) (#) (pdiff1 (f2,3)) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (1,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (2,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,1) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (3,(pdiff1 (f,1)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (1,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (2,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,2) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (3,(pdiff1 (f,2)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (1,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (2,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . u0 is V11() real ext-real Element of REAL
f is V16() V19( REAL 3) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
pdiff1 (f,3) is V1() V16() V19( REAL 3) V20( REAL ) V21() total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
u0 is V16() V19( NAT ) V20( REAL ) V21() complex-valued ext-real-valued real-valued V61(3) FinSequence-like Element of REAL 3
SVF1 (3,(pdiff1 (f,3)),u0) is V16() V19( REAL ) V20( REAL ) V21() complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . u0 is V11() real ext-real Element of REAL