:: PDIFF_4 semantic presentation

REAL is V1() V54() V160() V161() V162() V166() set
NAT is V1() epsilon-transitive epsilon-connected ordinal V160() V161() V162() V163() V164() V165() V166() Element of K6(REAL)
K6(REAL) is set
COMPLEX is V1() V54() V160() V166() set
K7(REAL,REAL) is complex-valued ext-real-valued real-valued set
K6(K7(REAL,REAL)) is set
omega is V1() epsilon-transitive epsilon-connected ordinal 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
RAT is V1() V54() V160() V161() V162() V163() V166() set
INT is V1() V54() V160() V161() V162() V163() V164() V166() set
1 is V1() epsilon-transitive epsilon-connected 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() epsilon-transitive epsilon-connected 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
TOP-REAL 2 is V66() V92() V117() V118() V119() V120() V121() V122() V123() V172() V202() V210() L20()
the U1 of (TOP-REAL 2) is set
REAL 1 is V1() functional FinSequence-membered FinSequenceSet of REAL
1 -tuples_on REAL is functional FinSequence-membered FinSequenceSet of REAL
K7((REAL 1),(REAL 1)) is set
K6(K7((REAL 1),(REAL 1))) is set
K418(1) is V66() V129() L15()
the U1 of K418(1) is set
K279(K418(1),K418(1)) is V66() L15()
the U1 of K279(K418(1),K418(1)) is set
REAL 2 is V1() functional FinSequence-membered FinSequenceSet of REAL
2 -tuples_on REAL is functional FinSequence-membered FinSequenceSet of REAL
K7((REAL 2),REAL) is complex-valued ext-real-valued real-valued set
K6(K7((REAL 2),REAL)) is set
3 is V1() epsilon-transitive epsilon-connected ordinal natural V11() real ext-real positive non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
REAL 3 is V1() functional FinSequence-membered FinSequenceSet of REAL
3 -tuples_on REAL is functional FinSequence-membered FinSequenceSet of REAL
K7(REAL,(REAL 3)) is set
K6(K7(REAL,(REAL 3))) 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
K552() is V66() V94() L8()
the U1 of K552() is set
K557() is V66() L8()
K558() is V66() V94() M15(K557())
K559() is V66() V94() V137() V225() M18(K557(),K558())
K561() is V66() V94() V137() V139() V141() L8()
K562() is V66() V94() V137() V225() M15(K561())
0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
the V1() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative functional FinSequence-membered V160() V161() V162() V163() V164() V165() V166() set is V1() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative functional FinSequence-membered V160() V161() V162() V163() V164() V165() V166() set
0c is set
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 ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom (proj (1,3)) is functional FinSequence-membered Element of K6((REAL 3))
K6((REAL 3)) is set
rng (proj (1,3)) is V160() V161() V162() Element of K6(REAL)
f1 is set
the V11() real ext-real Element of REAL is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*f2, the V11() real ext-real Element of REAL , the V11() real ext-real Element of REAL *> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(proj (1,3)) . g1 is V11() real ext-real Element of REAL
g1 . 1 is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
<*f1,f2,f3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (1,3)) . <*f1,f2,f3*> is V11() real ext-real Element of REAL
<*f1,f2,f3*> . 1 is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
<*f1,f2,f3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (1,3)) . <*f1,f2,f3*> is V11() real ext-real Element of REAL
proj (2,3) is V1() V16() V19( REAL 3) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom (proj (2,3)) is functional FinSequence-membered Element of K6((REAL 3))
rng (proj (2,3)) is V160() V161() V162() Element of K6(REAL)
f1 is set
the V11() real ext-real Element of REAL is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<* the V11() real ext-real Element of REAL ,f2, the V11() real ext-real Element of REAL *> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(proj (2,3)) . g1 is V11() real ext-real Element of REAL
g1 . 2 is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
<*f1,f2,f3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (2,3)) . <*f1,f2,f3*> is V11() real ext-real Element of REAL
<*f1,f2,f3*> . 2 is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
<*f1,f2,f3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (2,3)) . <*f1,f2,f3*> is V11() real ext-real Element of REAL
proj (3,3) is V1() V16() V19( REAL 3) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom (proj (3,3)) is functional FinSequence-membered Element of K6((REAL 3))
rng (proj (3,3)) is V160() V161() V162() Element of K6(REAL)
f1 is set
the V11() real ext-real Element of REAL is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<* the V11() real ext-real Element of REAL , the V11() real ext-real Element of REAL ,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(proj (3,3)) . g1 is V11() real ext-real Element of REAL
g1 . 3 is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
<*f1,f2,f3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (3,3)) . <*f1,f2,f3*> is V11() real ext-real Element of REAL
<*f1,f2,f3*> . 3 is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
<*f1,f2,f3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (3,3)) . <*f1,f2,f3*> is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f3 is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f3 is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f3 is V11() real ext-real Element of REAL
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (1,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (1,3)) . f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (2,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (2,3)) . f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (3,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(proj (3,3)) . f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,g1,f3)) is V160() V161() V162() Element of K6(REAL)
(SVF1 (1,g1,f3)) . p is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
<*g2,g3,z*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,g1,f3)) is V160() V161() V162() Element of K6(REAL)
(SVF1 (2,g1,f3)) . f1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
<*g2,g3,z*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,g1,f3)) is V160() V161() V162() Element of K6(REAL)
(SVF1 (3,g1,f3)) . f2 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
<*g2,g3,z*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (1,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,p,f1)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,p,f1)) . f2 is V11() real ext-real Element of REAL
g2 is open V160() V161() V162() Neighbourhood of f2
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g2 is open V160() V161() V162() Neighbourhood of f2
(SVF1 (1,p,f1)) . f2 is V11() real ext-real Element of REAL
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,p,f1)) . f2 is V11() real ext-real Element of REAL
g2 is open V160() V161() V162() Neighbourhood of f2
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g2 is open V160() V161() V162() Neighbourhood of f2
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g3 is open V160() V161() V162() Neighbourhood of f2
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (2,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,p,f1)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,p,f1)) . f3 is V11() real ext-real Element of REAL
g2 is open V160() V161() V162() Neighbourhood of f3
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f3 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g2 is open V160() V161() V162() Neighbourhood of f3
(SVF1 (2,p,f1)) . f3 is V11() real ext-real Element of REAL
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,p,f1)) . f3 is V11() real ext-real Element of REAL
g2 is open V160() V161() V162() Neighbourhood of f3
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g2 is open V160() V161() V162() Neighbourhood of f3
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g3 is open V160() V161() V162() Neighbourhood of f3
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (3,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,p,f1)) is V160() V161() V162() Element of K6(REAL)
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,p,f1)) . g1 is V11() real ext-real Element of REAL
g2 is open V160() V161() V162() Neighbourhood of g1
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g2 is open V160() V161() V162() Neighbourhood of g1
(SVF1 (3,p,f1)) . g1 is V11() real ext-real Element of REAL
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,p,f1)) . g1 is V11() real ext-real Element of REAL
g2 is open V160() V161() V162() Neighbourhood of g1
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g2 is open V160() V161() V162() Neighbourhood of g1
g3 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g3 is open V160() V161() V162() Neighbourhood of g1
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V11() real ext-real Element of REAL
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,g2,g1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (1,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,g2,g1)),p) is V11() real ext-real Element of REAL
dom (SVF1 (1,g2,g1)) is V160() V161() V162() Element of K6(REAL)
(SVF1 (1,g2,g1)) . p is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of p
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 . 1 is V11() real ext-real Element of REAL
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V11() real ext-real Element of REAL
R1 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
<*z,R1,x1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,g2,g1)) . z is V11() real ext-real Element of REAL
y1 is open V160() V161() V162() Neighbourhood of z
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y1 is open V160() V161() V162() Neighbourhood of z
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V11() real ext-real Element of REAL
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,g2,g1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (2,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,g2,g1)),f1) is V11() real ext-real Element of REAL
dom (SVF1 (2,g2,g1)) is V160() V161() V162() Element of K6(REAL)
(SVF1 (2,g2,g1)) . f1 is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of f1
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 . 1 is V11() real ext-real Element of REAL
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V11() real ext-real Element of REAL
R1 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
<*z,R1,x1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,g2,g1)) . R1 is V11() real ext-real Element of REAL
y1 is open V160() V161() V162() Neighbourhood of R1
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y1 is open V160() V161() V162() Neighbourhood of R1
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V11() real ext-real Element of REAL
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,g2,g1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (3,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,g2,g1)),f2) is V11() real ext-real Element of REAL
dom (SVF1 (3,g2,g1)) is V160() V161() V162() Element of K6(REAL)
(SVF1 (3,g2,g1)) . f2 is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of f2
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 . 1 is V11() real ext-real Element of REAL
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V11() real ext-real Element of REAL
R1 is V11() real ext-real Element of REAL
x1 is V11() real ext-real Element of REAL
<*z,R1,x1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,g2,g1)) . x1 is V11() real ext-real Element of REAL
y1 is open V160() V161() V162() Neighbourhood of x1
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y1 is open V160() V161() V162() Neighbourhood of x1
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
z1 . 1 is V11() real ext-real Element of REAL
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V11() real ext-real Element of REAL
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (g2,g1,1) is V11() real ext-real Element of REAL
reproj (1,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (1,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . g1 is V11() real ext-real Element of REAL
diff ((g2 * (reproj (1,g1))),((proj (1,3)) . g1)) is V11() real ext-real Element of REAL
SVF1 (1,g2,g1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,g2,g1)) is V160() V161() V162() Element of K6(REAL)
diff ((SVF1 (1,g2,g1)),p) is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
R1 is V11() real ext-real Element of REAL
<*g3,z,R1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,g2,g1)) . g3 is V11() real ext-real Element of REAL
x1 is open V160() V161() V162() Neighbourhood of g3
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 . 1 is V11() real ext-real Element of REAL
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V11() real ext-real Element of REAL
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (g2,g1,2) is V11() real ext-real Element of REAL
reproj (2,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (2,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . g1 is V11() real ext-real Element of REAL
diff ((g2 * (reproj (2,g1))),((proj (2,3)) . g1)) is V11() real ext-real Element of REAL
SVF1 (2,g2,g1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,g2,g1)) is V160() V161() V162() Element of K6(REAL)
diff ((SVF1 (2,g2,g1)),f1) is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
R1 is V11() real ext-real Element of REAL
<*g3,z,R1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,g2,g1)) . z is V11() real ext-real Element of REAL
x1 is open V160() V161() V162() Neighbourhood of z
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 . 1 is V11() real ext-real Element of REAL
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f3 is V11() real ext-real Element of REAL
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (g2,g1,3) is V11() real ext-real Element of REAL
reproj (3,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (3,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . g1 is V11() real ext-real Element of REAL
diff ((g2 * (reproj (3,g1))),((proj (3,3)) . g1)) is V11() real ext-real Element of REAL
SVF1 (3,g2,g1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,g2,g1)) is V160() V161() V162() Element of K6(REAL)
diff ((SVF1 (3,g2,g1)),f2) is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
R1 is V11() real ext-real Element of REAL
<*g3,z,R1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,g2,g1)) . R1 is V11() real ext-real Element of REAL
x1 is open V160() V161() V162() Neighbourhood of R1
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 . 1 is V11() real ext-real Element of REAL
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (g1,f3,1) is V11() real ext-real Element of REAL
reproj (1,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f3 is V11() real ext-real Element of REAL
diff ((g1 * (reproj (1,f3))),((proj (1,3)) . f3)) is V11() real ext-real Element of REAL
SVF1 (1,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (1,g1,f3)),p) is V11() real ext-real Element of REAL
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (g1,f3,2) is V11() real ext-real Element of REAL
reproj (2,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f3 is V11() real ext-real Element of REAL
diff ((g1 * (reproj (2,f3))),((proj (2,3)) . f3)) is V11() real ext-real Element of REAL
SVF1 (2,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (2,g1,f3)),f1) is V11() real ext-real Element of REAL
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (g1,f3,3) is V11() real ext-real Element of REAL
reproj (3,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g1 * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f3 is V11() real ext-real Element of REAL
diff ((g1 * (reproj (3,f3))),((proj (3,3)) . f3)) is V11() real ext-real Element of REAL
SVF1 (3,g1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((SVF1 (3,g1,f3)),f2) is V11() real ext-real Element of REAL
p is set
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
f1 | p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (1,(f1 | p),f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
(f1 | p) * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(f1 | p),f3)) is V160() V161() V162() Element of K6(REAL)
g1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
<*g1,g2,g3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,(f1 | p),f3)) . g1 is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of g1
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is open V160() V161() V162() Neighbourhood of g1
SVF1 (1,f1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f1 * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,f1,f3)) is V160() V161() V162() Element of K6(REAL)
R1 is V11() real ext-real Element of REAL
dom (reproj (1,f3)) is V160() V161() V162() Element of K6(REAL)
(reproj (1,f3)) . R1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 | p) is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ p is functional FinSequence-membered Element of K6((REAL 3))
R1 is set
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
(SVF1 (1,f1,f3)) . g1 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
(SVF1 (1,f1,f3)) . y1 is V11() real ext-real Element of REAL
((SVF1 (1,f1,f3)) . y1) - ((SVF1 (1,f1,f3)) . g1) is V11() real ext-real Element of REAL
y1 - g1 is V11() real ext-real Element of REAL
R1 . (y1 - g1) is V11() real ext-real Element of REAL
x1 . (y1 - g1) is V11() real ext-real Element of REAL
(R1 . (y1 - g1)) + (x1 . (y1 - g1)) is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
(SVF1 (1,(f1 | p),f3)) . z1 is V11() real ext-real Element of REAL
(SVF1 (1,f1,f3)) . z1 is V11() real ext-real Element of REAL
dom (reproj (1,f3)) is V160() V161() V162() Element of K6(REAL)
(reproj (1,f3)) . z1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 | p) is functional FinSequence-membered Element of K6((REAL 3))
(f1 | p) . ((reproj (1,f3)) . z1) is V11() real ext-real Element of REAL
f1 . ((reproj (1,f3)) . z1) is V11() real ext-real Element of REAL
(SVF1 (1,(f1 | p),f3)) . y1 is V11() real ext-real Element of REAL
((SVF1 (1,(f1 | p),f3)) . y1) - ((SVF1 (1,(f1 | p),f3)) . g1) is V11() real ext-real Element of REAL
((SVF1 (1,f1,f3)) . y1) - ((SVF1 (1,(f1 | p),f3)) . g1) is V11() real ext-real Element of REAL
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y1 is open V160() V161() V162() Neighbourhood of g1
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is set
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
f1 | p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (2,(f1 | p),f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
(f1 | p) * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(f1 | p),f3)) is V160() V161() V162() Element of K6(REAL)
g1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
<*g1,g2,g3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,(f1 | p),f3)) . g2 is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of g2
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is open V160() V161() V162() Neighbourhood of g2
SVF1 (2,f1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f1 * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,f1,f3)) is V160() V161() V162() Element of K6(REAL)
R1 is V11() real ext-real Element of REAL
dom (reproj (2,f3)) is V160() V161() V162() Element of K6(REAL)
(reproj (2,f3)) . R1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 | p) is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ p is functional FinSequence-membered Element of K6((REAL 3))
R1 is set
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
(SVF1 (2,f1,f3)) . g2 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
(SVF1 (2,f1,f3)) . y1 is V11() real ext-real Element of REAL
((SVF1 (2,f1,f3)) . y1) - ((SVF1 (2,f1,f3)) . g2) is V11() real ext-real Element of REAL
y1 - g2 is V11() real ext-real Element of REAL
R1 . (y1 - g2) is V11() real ext-real Element of REAL
x1 . (y1 - g2) is V11() real ext-real Element of REAL
(R1 . (y1 - g2)) + (x1 . (y1 - g2)) is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
(SVF1 (2,(f1 | p),f3)) . z1 is V11() real ext-real Element of REAL
(SVF1 (2,f1,f3)) . z1 is V11() real ext-real Element of REAL
dom (reproj (2,f3)) is V160() V161() V162() Element of K6(REAL)
(reproj (2,f3)) . z1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 | p) is functional FinSequence-membered Element of K6((REAL 3))
(f1 | p) . ((reproj (2,f3)) . z1) is V11() real ext-real Element of REAL
f1 . ((reproj (2,f3)) . z1) is V11() real ext-real Element of REAL
(SVF1 (2,(f1 | p),f3)) . y1 is V11() real ext-real Element of REAL
((SVF1 (2,(f1 | p),f3)) . y1) - ((SVF1 (2,(f1 | p),f3)) . g2) is V11() real ext-real Element of REAL
((SVF1 (2,f1,f3)) . y1) - ((SVF1 (2,(f1 | p),f3)) . g2) is V11() real ext-real Element of REAL
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y1 is open V160() V161() V162() Neighbourhood of g2
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is set
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
f1 | p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (3,(f1 | p),f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
(f1 | p) * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(f1 | p),f3)) is V160() V161() V162() Element of K6(REAL)
g1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
<*g1,g2,g3*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,(f1 | p),f3)) . g3 is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of g3
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is open V160() V161() V162() Neighbourhood of g3
SVF1 (3,f1,f3) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f1 * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,f1,f3)) is V160() V161() V162() Element of K6(REAL)
R1 is V11() real ext-real Element of REAL
dom (reproj (3,f3)) is V160() V161() V162() Element of K6(REAL)
(reproj (3,f3)) . R1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 | p) is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ p is functional FinSequence-membered Element of K6((REAL 3))
R1 is set
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
(SVF1 (3,f1,f3)) . g3 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
(SVF1 (3,f1,f3)) . y1 is V11() real ext-real Element of REAL
((SVF1 (3,f1,f3)) . y1) - ((SVF1 (3,f1,f3)) . g3) is V11() real ext-real Element of REAL
y1 - g3 is V11() real ext-real Element of REAL
R1 . (y1 - g3) is V11() real ext-real Element of REAL
x1 . (y1 - g3) is V11() real ext-real Element of REAL
(R1 . (y1 - g3)) + (x1 . (y1 - g3)) is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
(SVF1 (3,(f1 | p),f3)) . z1 is V11() real ext-real Element of REAL
(SVF1 (3,f1,f3)) . z1 is V11() real ext-real Element of REAL
dom (reproj (3,f3)) is V160() V161() V162() Element of K6(REAL)
(reproj (3,f3)) . z1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 | p) is functional FinSequence-membered Element of K6((REAL 3))
(f1 | p) . ((reproj (3,f3)) . z1) is V11() real ext-real Element of REAL
f1 . ((reproj (3,f3)) . z1) is V11() real ext-real Element of REAL
(SVF1 (3,(f1 | p),f3)) . y1 is V11() real ext-real Element of REAL
((SVF1 (3,(f1 | p),f3)) . y1) - ((SVF1 (3,(f1 | p),f3)) . g3) is V11() real ext-real Element of REAL
((SVF1 (3,f1,f3)) . y1) - ((SVF1 (3,(f1 | p),f3)) . g3) is V11() real ext-real Element of REAL
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
y1 is open V160() V161() V162() Neighbourhood of g3
z1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is set
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
f3 is set
f3 is set
dom p is functional FinSequence-membered Element of K6((REAL 3))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 . f3 is V11() real ext-real Element of REAL
partdiff (p,f3,1) is V11() real ext-real Element of REAL
reproj (1,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f3 is V11() real ext-real Element of REAL
diff ((p * (reproj (1,f3))),((proj (1,3)) . f3)) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f3 is functional FinSequence-membered Element of K6((REAL 3))
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 . g1 is V11() real ext-real Element of REAL
partdiff (p,g1,1) is V11() real ext-real Element of REAL
reproj (1,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . g1 is V11() real ext-real Element of REAL
diff ((p * (reproj (1,g1))),((proj (1,3)) . g1)) is V11() real ext-real Element of REAL
f3 . g1 is V11() real ext-real Element of REAL
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is set
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
f3 is set
f3 is set
dom p is functional FinSequence-membered Element of K6((REAL 3))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 . f3 is V11() real ext-real Element of REAL
partdiff (p,f3,2) is V11() real ext-real Element of REAL
reproj (2,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f3 is V11() real ext-real Element of REAL
diff ((p * (reproj (2,f3))),((proj (2,3)) . f3)) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f3 is functional FinSequence-membered Element of K6((REAL 3))
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 . g1 is V11() real ext-real Element of REAL
partdiff (p,g1,2) is V11() real ext-real Element of REAL
reproj (2,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . g1 is V11() real ext-real Element of REAL
diff ((p * (reproj (2,g1))),((proj (2,3)) . g1)) is V11() real ext-real Element of REAL
f3 . g1 is V11() real ext-real Element of REAL
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is set
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
f3 is set
f3 is set
dom p is functional FinSequence-membered Element of K6((REAL 3))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 . f3 is V11() real ext-real Element of REAL
partdiff (p,f3,3) is V11() real ext-real Element of REAL
reproj (3,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f3 is V11() real ext-real Element of REAL
diff ((p * (reproj (3,f3))),((proj (3,3)) . f3)) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
dom f3 is functional FinSequence-membered Element of K6((REAL 3))
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 . g1 is V11() real ext-real Element of REAL
partdiff (p,g1,3) is V11() real ext-real Element of REAL
reproj (3,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . g1 is V11() real ext-real Element of REAL
diff ((p * (reproj (3,g1))),((proj (3,3)) . g1)) is V11() real ext-real Element of REAL
f3 . g1 is V11() real ext-real Element of REAL
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(proj (1,3)) . f1 is V11() real ext-real Element of REAL
SVF1 (1,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,p,f1)) is V160() V161() V162() Element of K6(REAL)
{((proj (1,3)) . f1)} is V160() V161() V162() set
partdiff (p,f1,1) is V11() real ext-real Element of REAL
diff ((p * (reproj (1,f1))),((proj (1,3)) . f1)) is V11() real ext-real Element of REAL
f2 is open V160() V161() V162() Neighbourhood of (proj (1,3)) . f1
f3 is V1() V16() non-empty V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
f3 " is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent Element of K6(K7(NAT,REAL))
rng g1 is V160() V161() V162() Element of K6(REAL)
f3 + g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (f3 + g1) is V160() V161() V162() Element of K6(REAL)
(SVF1 (1,p,f1)) /* (f3 + g1) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (1,p,f1)) /* g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- ((SVF1 (1,p,f1)) /* g1) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
- 1 is V11() real ext-real non positive set
(- 1) * ((SVF1 (1,p,f1)) /* g1) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((SVF1 (1,p,f1)) /* (f3 + g1)) + (- ((SVF1 (1,p,f1)) /* g1)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f3 ") (#) (((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((f3 ") (#) (((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1))) is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
<*g2,g3,z*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,p,f1)) . g2 is V11() real ext-real Element of REAL
R1 is open V160() V161() V162() Neighbourhood of g2
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is open V160() V161() V162() Neighbourhood of g2
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is open V160() V161() V162() Neighbourhood of g2
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is open V160() V161() V162() Neighbourhood of g2
N2 is V11() real ext-real set
g2 - N2 is V11() real ext-real Element of REAL
g2 + N2 is V11() real ext-real Element of REAL
].(g2 - N2),(g2 + N2).[ is open V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= g2 - N2 & not g2 + N2 <= b₁ ) } is set
g2 + 0 is V11() real ext-real Element of REAL
g2 - 0 is V11() real ext-real Element of REAL
lim g1 is V11() real ext-real Element of REAL
lim f3 is V1() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative functional FinSequence-membered V160() V161() V162() V163() V164() V165() V166() Element of REAL
lim (f3 + g1) is V11() real ext-real Element of REAL
0 + g2 is V11() real ext-real Element of REAL
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
{g2} is V160() V161() V162() set
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
R2 is set
R2 is set
N is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
((f3 + g1) ^\ L2) . N is V11() real ext-real Element of REAL
L2 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
L2 + N is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 + g1) . (L2 + N) is V11() real ext-real Element of REAL
((f3 + g1) . (L2 + N)) - g2 is V11() real ext-real Element of REAL
abs (((f3 + g1) . (L2 + N)) - g2) is V11() real ext-real Element of REAL
N + L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 + g1) . (N + L2) is V11() real ext-real Element of REAL
((f3 + g1) . (N + L2)) - g2 is V11() real ext-real Element of REAL
- N2 is V11() real ext-real set
(((f3 + g1) ^\ L2) . N) - g2 is V11() real ext-real Element of REAL
g2 + (- N2) is V11() real ext-real Element of REAL
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
R2 is set
R2 is set
R2 is set
R2 is set
R2 is V11() real ext-real Element of REAL
(SVF1 (1,p,f1)) . R2 is V11() real ext-real Element of REAL
((SVF1 (1,p,f1)) . R2) - ((SVF1 (1,p,f1)) . g2) is V11() real ext-real Element of REAL
R2 - g2 is V11() real ext-real Element of REAL
x1 . (R2 - g2) is V11() real ext-real Element of REAL
y1 . (R2 - g2) is V11() real ext-real Element of REAL
(x1 . (R2 - g2)) + (y1 . (R2 - g2)) is V11() real ext-real Element of REAL
f3 ^\ L2 is V1() V16() non-empty V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent subsequence of f3
R2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
((f3 + g1) ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (1,p,f1)) . (((f3 + g1) ^\ L2) . R2) is V11() real ext-real Element of REAL
(g1 ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (1,p,f1)) . ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (1,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - ((SVF1 (1,p,f1)) . ((g1 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(f3 ^\ L2) . R2 is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
y1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . R2)) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(((f3 + g1) ^\ L2) . R2) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(f3 ^\ L2) + (g1 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((f3 ^\ L2) + (g1 ^\ L2)) . R2 is V11() real ext-real Element of REAL
(((f3 ^\ L2) + (g1 ^\ L2)) . R2) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((f3 ^\ L2) . R2) + ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(((f3 ^\ L2) . R2) + ((g1 ^\ L2) . R2)) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(SVF1 (1,p,f1)) /* ((f3 + g1) ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (1,p,f1)) /* (g1 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (1,p,f1)) /* ((f3 + g1) ^\ L2)) - ((SVF1 (1,p,f1)) /* (g1 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- ((SVF1 (1,p,f1)) /* (g1 ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) * ((SVF1 (1,p,f1)) /* (g1 ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((SVF1 (1,p,f1)) /* ((f3 + g1) ^\ L2)) + (- ((SVF1 (1,p,f1)) /* (g1 ^\ L2))) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
x1 /* (f3 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
y1 /* (f3 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
R2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(((SVF1 (1,p,f1)) /* ((f3 + g1) ^\ L2)) - ((SVF1 (1,p,f1)) /* (g1 ^\ L2))) . R2 is V11() real ext-real Element of REAL
((SVF1 (1,p,f1)) /* ((f3 + g1) ^\ L2)) . R2 is V11() real ext-real Element of REAL
((SVF1 (1,p,f1)) /* (g1 ^\ L2)) . R2 is V11() real ext-real Element of REAL
(((SVF1 (1,p,f1)) /* ((f3 + g1) ^\ L2)) . R2) - (((SVF1 (1,p,f1)) /* (g1 ^\ L2)) . R2) is V11() real ext-real Element of REAL
((f3 + g1) ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (1,p,f1)) . (((f3 + g1) ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (1,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - (((SVF1 (1,p,f1)) /* (g1 ^\ L2)) . R2) is V11() real ext-real Element of REAL
(g1 ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (1,p,f1)) . ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (1,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - ((SVF1 (1,p,f1)) . ((g1 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(f3 ^\ L2) . R2 is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
y1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . R2)) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(x1 /* (f3 ^\ L2)) . R2 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . R2) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) . R2 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . R2) + ((y1 /* (f3 ^\ L2)) . R2) is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . R2 is V11() real ext-real Element of REAL
(f3 ^\ L2) " is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim (((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ")) is V11() real ext-real Element of REAL
x1 . 1 is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
R2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
N is V11() real ext-real Element of REAL
N * 1 is V11() real ext-real Element of REAL
L11 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 ^\ L2) . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ")) . L11 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . L11 is V11() real ext-real Element of REAL
((f3 ^\ L2) ") . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
(x1 /* (f3 ^\ L2)) . L11 is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) . L11 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) + ((y1 /* (f3 ^\ L2)) . L11) is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) + ((y1 /* (f3 ^\ L2)) . L11)) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) + (((y1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
((f3 ^\ L2) . L11) " is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . L11) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
((x1 . ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
N * ((f3 ^\ L2) . L11) is V11() real ext-real Element of REAL
(N * ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
((N * ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
N * (((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) ")) is V11() real ext-real Element of REAL
(N * (((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) "))) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
(N * 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
R2 . L11 is V11() real ext-real Element of REAL
L11 is V11() real ext-real set
((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim (((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) is V11() real ext-real Element of REAL
L12 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
L is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
R11 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
R2 . R11 is V11() real ext-real Element of REAL
(R2 . R11) - (x1 . 1) is V11() real ext-real Element of REAL
abs ((R2 . R11) - (x1 . 1)) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11 is V11() real ext-real Element of REAL
(x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11) is V11() real ext-real Element of REAL
((x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11)) - (x1 . 1) is V11() real ext-real Element of REAL
abs (((x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11)) - (x1 . 1)) is V11() real ext-real Element of REAL
(((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11 is V11() real ext-real Element of REAL
((((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11) - 0 is V11() real ext-real Element of REAL
abs (((((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11) - 0) is V11() real ext-real Element of REAL
((SVF1 (1,p,f1)) /* (f3 + g1)) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (SVF1 (1,p,f1)) /* (f3 + g1)
(((SVF1 (1,p,f1)) /* (f3 + g1)) ^\ L2) - ((SVF1 (1,p,f1)) /* (g1 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (1,p,f1)) /* (f3 + g1)) ^\ L2) + (- ((SVF1 (1,p,f1)) /* (g1 ^\ L2))) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((SVF1 (1,p,f1)) /* (f3 + g1)) ^\ L2) - ((SVF1 (1,p,f1)) /* (g1 ^\ L2))) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (1,p,f1)) /* g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (SVF1 (1,p,f1)) /* g1
(((SVF1 (1,p,f1)) /* (f3 + g1)) ^\ L2) - (((SVF1 (1,p,f1)) /* g1) ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- (((SVF1 (1,p,f1)) /* g1) ^\ L2) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) * (((SVF1 (1,p,f1)) /* g1) ^\ L2) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((SVF1 (1,p,f1)) /* (f3 + g1)) ^\ L2) + (- (((SVF1 (1,p,f1)) /* g1) ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((SVF1 (1,p,f1)) /* (f3 + g1)) ^\ L2) - (((SVF1 (1,p,f1)) /* g1) ^\ L2)) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of ((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)
((((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)) ^\ L2) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(f3 ") ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 "
((((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)) ^\ L2) (#) ((f3 ") ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)) (#) (f3 ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)) (#) (f3 ")) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (((SVF1 (1,p,f1)) /* (f3 + g1)) - ((SVF1 (1,p,f1)) /* g1)) (#) (f3 ")
R2 is open V160() V161() V162() Neighbourhood of g2
N is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(proj (2,3)) . f1 is V11() real ext-real Element of REAL
SVF1 (2,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,p,f1)) is V160() V161() V162() Element of K6(REAL)
{((proj (2,3)) . f1)} is V160() V161() V162() set
partdiff (p,f1,2) is V11() real ext-real Element of REAL
diff ((p * (reproj (2,f1))),((proj (2,3)) . f1)) is V11() real ext-real Element of REAL
f2 is open V160() V161() V162() Neighbourhood of (proj (2,3)) . f1
f3 is V1() V16() non-empty V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
f3 " is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent Element of K6(K7(NAT,REAL))
rng g1 is V160() V161() V162() Element of K6(REAL)
f3 + g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (f3 + g1) is V160() V161() V162() Element of K6(REAL)
(SVF1 (2,p,f1)) /* (f3 + g1) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (2,p,f1)) /* g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- ((SVF1 (2,p,f1)) /* g1) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
- 1 is V11() real ext-real non positive set
(- 1) * ((SVF1 (2,p,f1)) /* g1) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((SVF1 (2,p,f1)) /* (f3 + g1)) + (- ((SVF1 (2,p,f1)) /* g1)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f3 ") (#) (((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((f3 ") (#) (((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1))) is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
<*g2,g3,z*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,p,f1)) . g3 is V11() real ext-real Element of REAL
R1 is open V160() V161() V162() Neighbourhood of g3
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is open V160() V161() V162() Neighbourhood of g3
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is open V160() V161() V162() Neighbourhood of g3
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is open V160() V161() V162() Neighbourhood of g3
N2 is V11() real ext-real set
g3 - N2 is V11() real ext-real Element of REAL
g3 + N2 is V11() real ext-real Element of REAL
].(g3 - N2),(g3 + N2).[ is open V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= g3 - N2 & not g3 + N2 <= b₁ ) } is set
g3 + 0 is V11() real ext-real Element of REAL
g3 - 0 is V11() real ext-real Element of REAL
lim g1 is V11() real ext-real Element of REAL
lim f3 is V1() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative functional FinSequence-membered V160() V161() V162() V163() V164() V165() V166() Element of REAL
lim (f3 + g1) is V11() real ext-real Element of REAL
0 + g3 is V11() real ext-real Element of REAL
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
{g3} is V160() V161() V162() set
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
R2 is set
R2 is set
N is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
((f3 + g1) ^\ L2) . N is V11() real ext-real Element of REAL
L2 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
L2 + N is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 + g1) . (L2 + N) is V11() real ext-real Element of REAL
((f3 + g1) . (L2 + N)) - g3 is V11() real ext-real Element of REAL
abs (((f3 + g1) . (L2 + N)) - g3) is V11() real ext-real Element of REAL
N + L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 + g1) . (N + L2) is V11() real ext-real Element of REAL
((f3 + g1) . (N + L2)) - g3 is V11() real ext-real Element of REAL
- N2 is V11() real ext-real set
(((f3 + g1) ^\ L2) . N) - g3 is V11() real ext-real Element of REAL
g3 + (- N2) is V11() real ext-real Element of REAL
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
R2 is set
R2 is set
R2 is set
R2 is set
R2 is V11() real ext-real Element of REAL
(SVF1 (2,p,f1)) . R2 is V11() real ext-real Element of REAL
((SVF1 (2,p,f1)) . R2) - ((SVF1 (2,p,f1)) . g3) is V11() real ext-real Element of REAL
R2 - g3 is V11() real ext-real Element of REAL
x1 . (R2 - g3) is V11() real ext-real Element of REAL
y1 . (R2 - g3) is V11() real ext-real Element of REAL
(x1 . (R2 - g3)) + (y1 . (R2 - g3)) is V11() real ext-real Element of REAL
f3 ^\ L2 is V1() V16() non-empty V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent subsequence of f3
R2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
((f3 + g1) ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (2,p,f1)) . (((f3 + g1) ^\ L2) . R2) is V11() real ext-real Element of REAL
(g1 ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (2,p,f1)) . ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (2,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - ((SVF1 (2,p,f1)) . ((g1 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(f3 ^\ L2) . R2 is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
y1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . R2)) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(((f3 + g1) ^\ L2) . R2) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(f3 ^\ L2) + (g1 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((f3 ^\ L2) + (g1 ^\ L2)) . R2 is V11() real ext-real Element of REAL
(((f3 ^\ L2) + (g1 ^\ L2)) . R2) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((f3 ^\ L2) . R2) + ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(((f3 ^\ L2) . R2) + ((g1 ^\ L2) . R2)) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(SVF1 (2,p,f1)) /* ((f3 + g1) ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (2,p,f1)) /* (g1 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (2,p,f1)) /* ((f3 + g1) ^\ L2)) - ((SVF1 (2,p,f1)) /* (g1 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- ((SVF1 (2,p,f1)) /* (g1 ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) * ((SVF1 (2,p,f1)) /* (g1 ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((SVF1 (2,p,f1)) /* ((f3 + g1) ^\ L2)) + (- ((SVF1 (2,p,f1)) /* (g1 ^\ L2))) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
x1 /* (f3 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
y1 /* (f3 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
R2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(((SVF1 (2,p,f1)) /* ((f3 + g1) ^\ L2)) - ((SVF1 (2,p,f1)) /* (g1 ^\ L2))) . R2 is V11() real ext-real Element of REAL
((SVF1 (2,p,f1)) /* ((f3 + g1) ^\ L2)) . R2 is V11() real ext-real Element of REAL
((SVF1 (2,p,f1)) /* (g1 ^\ L2)) . R2 is V11() real ext-real Element of REAL
(((SVF1 (2,p,f1)) /* ((f3 + g1) ^\ L2)) . R2) - (((SVF1 (2,p,f1)) /* (g1 ^\ L2)) . R2) is V11() real ext-real Element of REAL
((f3 + g1) ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (2,p,f1)) . (((f3 + g1) ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (2,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - (((SVF1 (2,p,f1)) /* (g1 ^\ L2)) . R2) is V11() real ext-real Element of REAL
(g1 ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (2,p,f1)) . ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (2,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - ((SVF1 (2,p,f1)) . ((g1 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(f3 ^\ L2) . R2 is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
y1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . R2)) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(x1 /* (f3 ^\ L2)) . R2 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . R2) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) . R2 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . R2) + ((y1 /* (f3 ^\ L2)) . R2) is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . R2 is V11() real ext-real Element of REAL
(f3 ^\ L2) " is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim (((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ")) is V11() real ext-real Element of REAL
x1 . 1 is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
R2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
N is V11() real ext-real Element of REAL
N * 1 is V11() real ext-real Element of REAL
L11 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 ^\ L2) . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ")) . L11 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . L11 is V11() real ext-real Element of REAL
((f3 ^\ L2) ") . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
(x1 /* (f3 ^\ L2)) . L11 is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) . L11 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) + ((y1 /* (f3 ^\ L2)) . L11) is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) + ((y1 /* (f3 ^\ L2)) . L11)) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) + (((y1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
((f3 ^\ L2) . L11) " is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . L11) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
((x1 . ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
N * ((f3 ^\ L2) . L11) is V11() real ext-real Element of REAL
(N * ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
((N * ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
N * (((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) ")) is V11() real ext-real Element of REAL
(N * (((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) "))) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
(N * 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
R2 . L11 is V11() real ext-real Element of REAL
L11 is V11() real ext-real set
((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim (((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) is V11() real ext-real Element of REAL
L12 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
L is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
R11 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
R2 . R11 is V11() real ext-real Element of REAL
(R2 . R11) - (x1 . 1) is V11() real ext-real Element of REAL
abs ((R2 . R11) - (x1 . 1)) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11 is V11() real ext-real Element of REAL
(x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11) is V11() real ext-real Element of REAL
((x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11)) - (x1 . 1) is V11() real ext-real Element of REAL
abs (((x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11)) - (x1 . 1)) is V11() real ext-real Element of REAL
(((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11 is V11() real ext-real Element of REAL
((((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11) - 0 is V11() real ext-real Element of REAL
abs (((((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11) - 0) is V11() real ext-real Element of REAL
((SVF1 (2,p,f1)) /* (f3 + g1)) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (SVF1 (2,p,f1)) /* (f3 + g1)
(((SVF1 (2,p,f1)) /* (f3 + g1)) ^\ L2) - ((SVF1 (2,p,f1)) /* (g1 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (2,p,f1)) /* (f3 + g1)) ^\ L2) + (- ((SVF1 (2,p,f1)) /* (g1 ^\ L2))) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((SVF1 (2,p,f1)) /* (f3 + g1)) ^\ L2) - ((SVF1 (2,p,f1)) /* (g1 ^\ L2))) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (2,p,f1)) /* g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (SVF1 (2,p,f1)) /* g1
(((SVF1 (2,p,f1)) /* (f3 + g1)) ^\ L2) - (((SVF1 (2,p,f1)) /* g1) ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- (((SVF1 (2,p,f1)) /* g1) ^\ L2) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) * (((SVF1 (2,p,f1)) /* g1) ^\ L2) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((SVF1 (2,p,f1)) /* (f3 + g1)) ^\ L2) + (- (((SVF1 (2,p,f1)) /* g1) ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((SVF1 (2,p,f1)) /* (f3 + g1)) ^\ L2) - (((SVF1 (2,p,f1)) /* g1) ^\ L2)) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of ((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)
((((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)) ^\ L2) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(f3 ") ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 "
((((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)) ^\ L2) (#) ((f3 ") ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)) (#) (f3 ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)) (#) (f3 ")) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (((SVF1 (2,p,f1)) /* (f3 + g1)) - ((SVF1 (2,p,f1)) /* g1)) (#) (f3 ")
R2 is open V160() V161() V162() Neighbourhood of g3
N is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(proj (3,3)) . f1 is V11() real ext-real Element of REAL
SVF1 (3,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,p,f1)) is V160() V161() V162() Element of K6(REAL)
{((proj (3,3)) . f1)} is V160() V161() V162() set
partdiff (p,f1,3) is V11() real ext-real Element of REAL
diff ((p * (reproj (3,f1))),((proj (3,3)) . f1)) is V11() real ext-real Element of REAL
f2 is open V160() V161() V162() Neighbourhood of (proj (3,3)) . f1
f3 is V1() V16() non-empty V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent Element of K6(K7(NAT,REAL))
f3 " is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent Element of K6(K7(NAT,REAL))
rng g1 is V160() V161() V162() Element of K6(REAL)
f3 + g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
rng (f3 + g1) is V160() V161() V162() Element of K6(REAL)
(SVF1 (3,p,f1)) /* (f3 + g1) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (3,p,f1)) /* g1 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- ((SVF1 (3,p,f1)) /* g1) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
- 1 is V11() real ext-real non positive set
(- 1) * ((SVF1 (3,p,f1)) /* g1) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((SVF1 (3,p,f1)) /* (f3 + g1)) + (- ((SVF1 (3,p,f1)) /* g1)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(f3 ") (#) (((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim ((f3 ") (#) (((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1))) is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
<*g2,g3,z*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,p,f1)) . z is V11() real ext-real Element of REAL
R1 is open V160() V161() V162() Neighbourhood of z
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R1 is open V160() V161() V162() Neighbourhood of z
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
x1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
y1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is open V160() V161() V162() Neighbourhood of z
N2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z1 is open V160() V161() V162() Neighbourhood of z
N2 is V11() real ext-real set
z - N2 is V11() real ext-real Element of REAL
z + N2 is V11() real ext-real Element of REAL
].(z - N2),(z + N2).[ is open V160() V161() V162() Element of K6(REAL)
{ b₁ where b₁ is V11() real ext-real Element of REAL : ( not b₁ <= z - N2 & not z + N2 <= b₁ ) } is set
z + 0 is V11() real ext-real Element of REAL
z - 0 is V11() real ext-real Element of REAL
lim g1 is V11() real ext-real Element of REAL
lim f3 is V1() epsilon-transitive epsilon-connected ordinal T-Sequence-like c=-linear natural V11() real ext-real non positive non negative functional FinSequence-membered V160() V161() V162() V163() V164() V165() V166() Element of REAL
lim (f3 + g1) is V11() real ext-real Element of REAL
0 + z is V11() real ext-real Element of REAL
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
{z} is V160() V161() V162() set
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
R2 is set
R2 is set
N is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
((f3 + g1) ^\ L2) . N is V11() real ext-real Element of REAL
L2 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
L2 + N is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 + g1) . (L2 + N) is V11() real ext-real Element of REAL
((f3 + g1) . (L2 + N)) - z is V11() real ext-real Element of REAL
abs (((f3 + g1) . (L2 + N)) - z) is V11() real ext-real Element of REAL
N + L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 + g1) . (N + L2) is V11() real ext-real Element of REAL
((f3 + g1) . (N + L2)) - z is V11() real ext-real Element of REAL
- N2 is V11() real ext-real set
(((f3 + g1) ^\ L2) . N) - z is V11() real ext-real Element of REAL
z + (- N2) is V11() real ext-real Element of REAL
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
L2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g1 ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like constant total quasi_total complex-valued ext-real-valued real-valued convergent subsequence of g1
rng (g1 ^\ L2) is V160() V161() V162() Element of K6(REAL)
(f3 + g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 + g1
rng ((f3 + g1) ^\ L2) is V160() V161() V162() Element of K6(REAL)
R2 is set
R2 is set
R2 is set
R2 is set
R2 is V11() real ext-real Element of REAL
(SVF1 (3,p,f1)) . R2 is V11() real ext-real Element of REAL
((SVF1 (3,p,f1)) . R2) - ((SVF1 (3,p,f1)) . z) is V11() real ext-real Element of REAL
R2 - z is V11() real ext-real Element of REAL
x1 . (R2 - z) is V11() real ext-real Element of REAL
y1 . (R2 - z) is V11() real ext-real Element of REAL
(x1 . (R2 - z)) + (y1 . (R2 - z)) is V11() real ext-real Element of REAL
f3 ^\ L2 is V1() V16() non-empty V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued 0 -convergent convergent subsequence of f3
R2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
((f3 + g1) ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (3,p,f1)) . (((f3 + g1) ^\ L2) . R2) is V11() real ext-real Element of REAL
(g1 ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (3,p,f1)) . ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (3,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - ((SVF1 (3,p,f1)) . ((g1 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(f3 ^\ L2) . R2 is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
y1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . R2)) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(((f3 + g1) ^\ L2) . R2) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(f3 ^\ L2) + (g1 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((f3 ^\ L2) + (g1 ^\ L2)) . R2 is V11() real ext-real Element of REAL
(((f3 ^\ L2) + (g1 ^\ L2)) . R2) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((f3 ^\ L2) . R2) + ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(((f3 ^\ L2) . R2) + ((g1 ^\ L2) . R2)) - ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
(SVF1 (3,p,f1)) /* ((f3 + g1) ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(SVF1 (3,p,f1)) /* (g1 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (3,p,f1)) /* ((f3 + g1) ^\ L2)) - ((SVF1 (3,p,f1)) /* (g1 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- ((SVF1 (3,p,f1)) /* (g1 ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) * ((SVF1 (3,p,f1)) /* (g1 ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((SVF1 (3,p,f1)) /* ((f3 + g1) ^\ L2)) + (- ((SVF1 (3,p,f1)) /* (g1 ^\ L2))) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
x1 /* (f3 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
y1 /* (f3 ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
R2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(((SVF1 (3,p,f1)) /* ((f3 + g1) ^\ L2)) - ((SVF1 (3,p,f1)) /* (g1 ^\ L2))) . R2 is V11() real ext-real Element of REAL
((SVF1 (3,p,f1)) /* ((f3 + g1) ^\ L2)) . R2 is V11() real ext-real Element of REAL
((SVF1 (3,p,f1)) /* (g1 ^\ L2)) . R2 is V11() real ext-real Element of REAL
(((SVF1 (3,p,f1)) /* ((f3 + g1) ^\ L2)) . R2) - (((SVF1 (3,p,f1)) /* (g1 ^\ L2)) . R2) is V11() real ext-real Element of REAL
((f3 + g1) ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (3,p,f1)) . (((f3 + g1) ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (3,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - (((SVF1 (3,p,f1)) /* (g1 ^\ L2)) . R2) is V11() real ext-real Element of REAL
(g1 ^\ L2) . R2 is V11() real ext-real Element of REAL
(SVF1 (3,p,f1)) . ((g1 ^\ L2) . R2) is V11() real ext-real Element of REAL
((SVF1 (3,p,f1)) . (((f3 + g1) ^\ L2) . R2)) - ((SVF1 (3,p,f1)) . ((g1 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(f3 ^\ L2) . R2 is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
y1 . ((f3 ^\ L2) . R2) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . R2)) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(x1 /* (f3 ^\ L2)) . R2 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . R2) + (y1 . ((f3 ^\ L2) . R2)) is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) . R2 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . R2) + ((y1 /* (f3 ^\ L2)) . R2) is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . R2 is V11() real ext-real Element of REAL
(f3 ^\ L2) " is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim (((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ")) is V11() real ext-real Element of REAL
x1 . 1 is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
R2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
N is V11() real ext-real Element of REAL
N * 1 is V11() real ext-real Element of REAL
L11 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f3 ^\ L2) . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) (#) ((f3 ^\ L2) ")) . L11 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . L11 is V11() real ext-real Element of REAL
((f3 ^\ L2) ") . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) + (y1 /* (f3 ^\ L2))) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
(x1 /* (f3 ^\ L2)) . L11 is V11() real ext-real Element of REAL
(y1 /* (f3 ^\ L2)) . L11 is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) + ((y1 /* (f3 ^\ L2)) . L11) is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) + ((y1 /* (f3 ^\ L2)) . L11)) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11) is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) + (((y1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11 is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) ") . L11)) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
((f3 ^\ L2) . L11) " is V11() real ext-real Element of REAL
((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
(((x1 /* (f3 ^\ L2)) . L11) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
x1 . ((f3 ^\ L2) . L11) is V11() real ext-real Element of REAL
(x1 . ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
((x1 . ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
N * ((f3 ^\ L2) . L11) is V11() real ext-real Element of REAL
(N * ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
((N * ((f3 ^\ L2) . L11)) * (((f3 ^\ L2) . L11) ")) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) ") is V11() real ext-real Element of REAL
N * (((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) ")) is V11() real ext-real Element of REAL
(N * (((f3 ^\ L2) . L11) * (((f3 ^\ L2) . L11) "))) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
(N * 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . L11) is V11() real ext-real Element of REAL
R2 . L11 is V11() real ext-real Element of REAL
L11 is V11() real ext-real set
((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
lim (((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) is V11() real ext-real Element of REAL
L12 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
L is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
R11 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
R2 . R11 is V11() real ext-real Element of REAL
(R2 . R11) - (x1 . 1) is V11() real ext-real Element of REAL
abs ((R2 . R11) - (x1 . 1)) is V11() real ext-real Element of REAL
((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11 is V11() real ext-real Element of REAL
(x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11) is V11() real ext-real Element of REAL
((x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11)) - (x1 . 1) is V11() real ext-real Element of REAL
abs (((x1 . 1) + (((y1 /* (f3 ^\ L2)) (#) ((f3 ^\ L2) ")) . R11)) - (x1 . 1)) is V11() real ext-real Element of REAL
(((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11 is V11() real ext-real Element of REAL
((((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11) - 0 is V11() real ext-real Element of REAL
abs (((((f3 ^\ L2) ") (#) (y1 /* (f3 ^\ L2))) . R11) - 0) is V11() real ext-real Element of REAL
((SVF1 (3,p,f1)) /* (f3 + g1)) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (SVF1 (3,p,f1)) /* (f3 + g1)
(((SVF1 (3,p,f1)) /* (f3 + g1)) ^\ L2) - ((SVF1 (3,p,f1)) /* (g1 ^\ L2)) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (3,p,f1)) /* (f3 + g1)) ^\ L2) + (- ((SVF1 (3,p,f1)) /* (g1 ^\ L2))) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((SVF1 (3,p,f1)) /* (f3 + g1)) ^\ L2) - ((SVF1 (3,p,f1)) /* (g1 ^\ L2))) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((SVF1 (3,p,f1)) /* g1) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (SVF1 (3,p,f1)) /* g1
(((SVF1 (3,p,f1)) /* (f3 + g1)) ^\ L2) - (((SVF1 (3,p,f1)) /* g1) ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
- (((SVF1 (3,p,f1)) /* g1) ^\ L2) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(- 1) * (((SVF1 (3,p,f1)) /* g1) ^\ L2) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
(((SVF1 (3,p,f1)) /* (f3 + g1)) ^\ L2) + (- (((SVF1 (3,p,f1)) /* g1) ^\ L2)) is V16() V19( NAT ) Function-like total complex-valued ext-real-valued real-valued set
((((SVF1 (3,p,f1)) /* (f3 + g1)) ^\ L2) - (((SVF1 (3,p,f1)) /* g1) ^\ L2)) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of ((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)
((((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)) ^\ L2) (#) ((f3 ^\ L2) ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(f3 ") ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of f3 "
((((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)) ^\ L2) (#) ((f3 ") ^\ L2) is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
(((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)) (#) (f3 ") is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(NAT,REAL))
((((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)) (#) (f3 ")) ^\ L2 is V1() V16() V19( NAT ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued subsequence of (((SVF1 (3,p,f1)) /* (f3 + g1)) - ((SVF1 (3,p,f1)) /* g1)) (#) (f3 ")
R2 is open V160() V161() V162() Neighbourhood of z
N is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 (#) f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (1,f1,p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,f1,p)) is V160() V161() V162() Element of K6(REAL)
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
<*f3,g1,g2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,f1,p)) . f3 is V11() real ext-real Element of REAL
g3 is open V160() V161() V162() Neighbourhood of f3
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g3 is open V160() V161() V162() Neighbourhood of f3
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (1,f2,p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f2 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,f2,p)) is V160() V161() V162() Element of K6(REAL)
x1 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*x1,y1,z1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (1,f2,p)) . x1 is V11() real ext-real Element of REAL
N2 is open V160() V161() V162() Neighbourhood of f3
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is open V160() V161() V162() Neighbourhood of x1
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
(SVF1 (1,f2,p)) . f3 is V11() real ext-real Element of REAL
N2 is open V160() V161() V162() Neighbourhood of x1
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N2 is open V160() V161() V162() Neighbourhood of f3
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is open V160() V161() V162() Neighbourhood of f3
((SVF1 (1,f2,p)) . f3) (#) z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (1,f1,p)) . f3) (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L11 + L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (1,f2,p)) . f3) (#) R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (1,f1,p)) . f3) (#) R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R11 + R12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
z (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R13 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R14 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R13 + R14 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R1 (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R2 (#) z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R1 (#) R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R17 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R18 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R17 + R18 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R19 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R16 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R19 + R16 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R15 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R20 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R15 + R20 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (1,(f1 (#) f2),p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(f1 (#) f2) * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (1,(f1 (#) f2),p)) is V160() V161() V162() Element of K6(REAL)
z is V11() real ext-real Element of REAL
dom (reproj (1,p)) is V160() V161() V162() Element of K6(REAL)
(reproj (1,p)) . z is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ (dom f2) is functional FinSequence-membered Element of K6((REAL 3))
dom (f1 (#) f2) is functional FinSequence-membered Element of K6((REAL 3))
z is set
z is V11() real ext-real Element of REAL
(SVF1 (1,f1,p)) . z is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . z) - ((SVF1 (1,f1,p)) . f3) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) - ((SVF1 (1,f1,p)) . f3)) + ((SVF1 (1,f1,p)) . f3) is V11() real ext-real Element of REAL
z - f3 is V11() real ext-real Element of REAL
z . (z - f3) is V11() real ext-real Element of REAL
R1 . (z - f3) is V11() real ext-real Element of REAL
(z . (z - f3)) + (R1 . (z - f3)) is V11() real ext-real Element of REAL
((z . (z - f3)) + (R1 . (z - f3))) + ((SVF1 (1,f1,p)) . f3) is V11() real ext-real Element of REAL
dom ((f1 (#) f2) * (reproj (1,p))) is V160() V161() V162() Element of K6(REAL)
dom (reproj (1,p)) is V160() V161() V162() Element of K6(REAL)
(reproj (1,p)) . z is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 (#) f2) is functional FinSequence-membered Element of K6((REAL 3))
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ (dom f2) is functional FinSequence-membered Element of K6((REAL 3))
dom (f1 * (reproj (1,p))) is V160() V161() V162() Element of K6(REAL)
dom (f2 * (reproj (1,p))) is V160() V161() V162() Element of K6(REAL)
(reproj (1,p)) . f3 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(SVF1 (1,(f1 (#) f2),p)) . z is V11() real ext-real Element of REAL
(SVF1 (1,(f1 (#) f2),p)) . f3 is V11() real ext-real Element of REAL
((SVF1 (1,(f1 (#) f2),p)) . z) - ((SVF1 (1,(f1 (#) f2),p)) . f3) is V11() real ext-real Element of REAL
(f1 (#) f2) . ((reproj (1,p)) . z) is V11() real ext-real Element of REAL
((f1 (#) f2) . ((reproj (1,p)) . z)) - ((SVF1 (1,(f1 (#) f2),p)) . f3) is V11() real ext-real Element of REAL
f1 . ((reproj (1,p)) . z) is V11() real ext-real Element of REAL
f2 . ((reproj (1,p)) . z) is V11() real ext-real Element of REAL
(f1 . ((reproj (1,p)) . z)) * (f2 . ((reproj (1,p)) . z)) is V11() real ext-real Element of REAL
((f1 . ((reproj (1,p)) . z)) * (f2 . ((reproj (1,p)) . z))) - ((SVF1 (1,(f1 (#) f2),p)) . f3) is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . z) * (f2 . ((reproj (1,p)) . z)) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * (f2 . ((reproj (1,p)) . z))) - ((SVF1 (1,(f1 (#) f2),p)) . f3) is V11() real ext-real Element of REAL
(SVF1 (1,f2,p)) . z is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z) is V11() real ext-real Element of REAL
((f1 (#) f2) * (reproj (1,p))) . f3 is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z)) - (((f1 (#) f2) * (reproj (1,p))) . f3) is V11() real ext-real Element of REAL
(f1 (#) f2) . ((reproj (1,p)) . f3) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z)) - ((f1 (#) f2) . ((reproj (1,p)) . f3)) is V11() real ext-real Element of REAL
f1 . ((reproj (1,p)) . f3) is V11() real ext-real Element of REAL
f2 . ((reproj (1,p)) . f3) is V11() real ext-real Element of REAL
(f1 . ((reproj (1,p)) . f3)) * (f2 . ((reproj (1,p)) . f3)) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z)) - ((f1 . ((reproj (1,p)) . f3)) * (f2 . ((reproj (1,p)) . f3))) is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . f3) * (f2 . ((reproj (1,p)) . f3)) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z)) - (((SVF1 (1,f1,p)) . f3) * (f2 . ((reproj (1,p)) . f3))) is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . f3) is V11() real ext-real Element of REAL
- (((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . f3)) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z)) + (- (((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . f3))) is V11() real ext-real Element of REAL
((((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z)) + (- (((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . f3)))) + (((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . f3)) is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . f3) * ((SVF1 (1,f2,p)) . f3) is V11() real ext-real Element of REAL
(((((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . z)) + (- (((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . f3)))) + (((SVF1 (1,f1,p)) . z) * ((SVF1 (1,f2,p)) . f3))) - (((SVF1 (1,f1,p)) . f3) * ((SVF1 (1,f2,p)) . f3)) is V11() real ext-real Element of REAL
((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3) is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . z) * (((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3)) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) - ((SVF1 (1,f1,p)) . f3)) * ((SVF1 (1,f2,p)) . f3) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * (((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3))) + ((((SVF1 (1,f1,p)) . z) - ((SVF1 (1,f1,p)) . f3)) * ((SVF1 (1,f2,p)) . f3)) is V11() real ext-real Element of REAL
((z . (z - f3)) + (R1 . (z - f3))) * ((SVF1 (1,f2,p)) . f3) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * (((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3))) + (((z . (z - f3)) + (R1 . (z - f3))) * ((SVF1 (1,f2,p)) . f3)) is V11() real ext-real Element of REAL
((SVF1 (1,f2,p)) . f3) * (z . (z - f3)) is V11() real ext-real Element of REAL
((SVF1 (1,f2,p)) . f3) * (R1 . (z - f3)) is V11() real ext-real Element of REAL
(((SVF1 (1,f2,p)) . f3) * (z . (z - f3))) + (((SVF1 (1,f2,p)) . f3) * (R1 . (z - f3))) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * (((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3))) + ((((SVF1 (1,f2,p)) . f3) * (z . (z - f3))) + (((SVF1 (1,f2,p)) . f3) * (R1 . (z - f3)))) is V11() real ext-real Element of REAL
L11 . (z - f3) is V11() real ext-real Element of REAL
(L11 . (z - f3)) + (((SVF1 (1,f2,p)) . f3) * (R1 . (z - f3))) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . z) * (((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3))) + ((L11 . (z - f3)) + (((SVF1 (1,f2,p)) . f3) * (R1 . (z - f3)))) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) + ((SVF1 (1,f1,p)) . f3)) * (((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3)) is V11() real ext-real Element of REAL
R11 . (z - f3) is V11() real ext-real Element of REAL
(L11 . (z - f3)) + (R11 . (z - f3)) is V11() real ext-real Element of REAL
((((z . (z - f3)) + (R1 . (z - f3))) + ((SVF1 (1,f1,p)) . f3)) * (((SVF1 (1,f2,p)) . z) - ((SVF1 (1,f2,p)) . f3))) + ((L11 . (z - f3)) + (R11 . (z - f3))) is V11() real ext-real Element of REAL
L2 . (z - f3) is V11() real ext-real Element of REAL
R2 . (z - f3) is V11() real ext-real Element of REAL
(L2 . (z - f3)) + (R2 . (z - f3)) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) + ((SVF1 (1,f1,p)) . f3)) * ((L2 . (z - f3)) + (R2 . (z - f3))) is V11() real ext-real Element of REAL
((((z . (z - f3)) + (R1 . (z - f3))) + ((SVF1 (1,f1,p)) . f3)) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((L11 . (z - f3)) + (R11 . (z - f3))) is V11() real ext-real Element of REAL
((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3))) is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . f3) * (L2 . (z - f3)) is V11() real ext-real Element of REAL
((SVF1 (1,f1,p)) . f3) * (R2 . (z - f3)) is V11() real ext-real Element of REAL
(((SVF1 (1,f1,p)) . f3) * (L2 . (z - f3))) + (((SVF1 (1,f1,p)) . f3) * (R2 . (z - f3))) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((((SVF1 (1,f1,p)) . f3) * (L2 . (z - f3))) + (((SVF1 (1,f1,p)) . f3) * (R2 . (z - f3)))) is V11() real ext-real Element of REAL
((((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((((SVF1 (1,f1,p)) . f3) * (L2 . (z - f3))) + (((SVF1 (1,f1,p)) . f3) * (R2 . (z - f3))))) + ((L11 . (z - f3)) + (R11 . (z - f3))) is V11() real ext-real Element of REAL
L12 . (z - f3) is V11() real ext-real Element of REAL
(L12 . (z - f3)) + (((SVF1 (1,f1,p)) . f3) * (R2 . (z - f3))) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((L12 . (z - f3)) + (((SVF1 (1,f1,p)) . f3) * (R2 . (z - f3)))) is V11() real ext-real Element of REAL
((((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((L12 . (z - f3)) + (((SVF1 (1,f1,p)) . f3) * (R2 . (z - f3))))) + ((L11 . (z - f3)) + (R11 . (z - f3))) is V11() real ext-real Element of REAL
R12 . (z - f3) is V11() real ext-real Element of REAL
(L12 . (z - f3)) + (R12 . (z - f3)) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((L12 . (z - f3)) + (R12 . (z - f3))) is V11() real ext-real Element of REAL
((((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((L12 . (z - f3)) + (R12 . (z - f3)))) + ((L11 . (z - f3)) + (R11 . (z - f3))) is V11() real ext-real Element of REAL
(R11 . (z - f3)) + (R12 . (z - f3)) is V11() real ext-real Element of REAL
(L11 . (z - f3)) + ((R11 . (z - f3)) + (R12 . (z - f3))) is V11() real ext-real Element of REAL
(L12 . (z - f3)) + ((L11 . (z - f3)) + ((R11 . (z - f3)) + (R12 . (z - f3)))) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((L12 . (z - f3)) + ((L11 . (z - f3)) + ((R11 . (z - f3)) + (R12 . (z - f3))))) is V11() real ext-real Element of REAL
R13 . (z - f3) is V11() real ext-real Element of REAL
(L11 . (z - f3)) + (R13 . (z - f3)) is V11() real ext-real Element of REAL
(L12 . (z - f3)) + ((L11 . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + ((L12 . (z - f3)) + ((L11 . (z - f3)) + (R13 . (z - f3)))) is V11() real ext-real Element of REAL
(L11 . (z - f3)) + (L12 . (z - f3)) is V11() real ext-real Element of REAL
((L11 . (z - f3)) + (L12 . (z - f3))) + (R13 . (z - f3)) is V11() real ext-real Element of REAL
(((z . (z - f3)) + (R1 . (z - f3))) * ((L2 . (z - f3)) + (R2 . (z - f3)))) + (((L11 . (z - f3)) + (L12 . (z - f3))) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
(z . (z - f3)) * (L2 . (z - f3)) is V11() real ext-real Element of REAL
(z . (z - f3)) * (R2 . (z - f3)) is V11() real ext-real Element of REAL
((z . (z - f3)) * (L2 . (z - f3))) + ((z . (z - f3)) * (R2 . (z - f3))) is V11() real ext-real Element of REAL
(R1 . (z - f3)) * ((L2 . (z - f3)) + (R2 . (z - f3))) is V11() real ext-real Element of REAL
(((z . (z - f3)) * (L2 . (z - f3))) + ((z . (z - f3)) * (R2 . (z - f3)))) + ((R1 . (z - f3)) * ((L2 . (z - f3)) + (R2 . (z - f3)))) is V11() real ext-real Element of REAL
L is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L . (z - f3) is V11() real ext-real Element of REAL
(L . (z - f3)) + (R13 . (z - f3)) is V11() real ext-real Element of REAL
((((z . (z - f3)) * (L2 . (z - f3))) + ((z . (z - f3)) * (R2 . (z - f3)))) + ((R1 . (z - f3)) * ((L2 . (z - f3)) + (R2 . (z - f3))))) + ((L . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
R14 . (z - f3) is V11() real ext-real Element of REAL
(R2 . (z - f3)) * (z . (z - f3)) is V11() real ext-real Element of REAL
(R14 . (z - f3)) + ((R2 . (z - f3)) * (z . (z - f3))) is V11() real ext-real Element of REAL
((R14 . (z - f3)) + ((R2 . (z - f3)) * (z . (z - f3)))) + ((R1 . (z - f3)) * ((L2 . (z - f3)) + (R2 . (z - f3)))) is V11() real ext-real Element of REAL
(((R14 . (z - f3)) + ((R2 . (z - f3)) * (z . (z - f3)))) + ((R1 . (z - f3)) * ((L2 . (z - f3)) + (R2 . (z - f3))))) + ((L . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
R16 . (z - f3) is V11() real ext-real Element of REAL
(R14 . (z - f3)) + (R16 . (z - f3)) is V11() real ext-real Element of REAL
(R1 . (z - f3)) * (L2 . (z - f3)) is V11() real ext-real Element of REAL
(R1 . (z - f3)) * (R2 . (z - f3)) is V11() real ext-real Element of REAL
((R1 . (z - f3)) * (L2 . (z - f3))) + ((R1 . (z - f3)) * (R2 . (z - f3))) is V11() real ext-real Element of REAL
((R14 . (z - f3)) + (R16 . (z - f3))) + (((R1 . (z - f3)) * (L2 . (z - f3))) + ((R1 . (z - f3)) * (R2 . (z - f3)))) is V11() real ext-real Element of REAL
(((R14 . (z - f3)) + (R16 . (z - f3))) + (((R1 . (z - f3)) * (L2 . (z - f3))) + ((R1 . (z - f3)) * (R2 . (z - f3))))) + ((L . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
R17 . (z - f3) is V11() real ext-real Element of REAL
(R17 . (z - f3)) + ((R1 . (z - f3)) * (R2 . (z - f3))) is V11() real ext-real Element of REAL
((R14 . (z - f3)) + (R16 . (z - f3))) + ((R17 . (z - f3)) + ((R1 . (z - f3)) * (R2 . (z - f3)))) is V11() real ext-real Element of REAL
(((R14 . (z - f3)) + (R16 . (z - f3))) + ((R17 . (z - f3)) + ((R1 . (z - f3)) * (R2 . (z - f3))))) + ((L . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
R18 . (z - f3) is V11() real ext-real Element of REAL
(R17 . (z - f3)) + (R18 . (z - f3)) is V11() real ext-real Element of REAL
((R14 . (z - f3)) + (R16 . (z - f3))) + ((R17 . (z - f3)) + (R18 . (z - f3))) is V11() real ext-real Element of REAL
(((R14 . (z - f3)) + (R16 . (z - f3))) + ((R17 . (z - f3)) + (R18 . (z - f3)))) + ((L . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
R19 . (z - f3) is V11() real ext-real Element of REAL
((R14 . (z - f3)) + (R16 . (z - f3))) + (R19 . (z - f3)) is V11() real ext-real Element of REAL
(((R14 . (z - f3)) + (R16 . (z - f3))) + (R19 . (z - f3))) + ((L . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
(R19 . (z - f3)) + (R16 . (z - f3)) is V11() real ext-real Element of REAL
(R14 . (z - f3)) + ((R19 . (z - f3)) + (R16 . (z - f3))) is V11() real ext-real Element of REAL
((R14 . (z - f3)) + ((R19 . (z - f3)) + (R16 . (z - f3)))) + ((L . (z - f3)) + (R13 . (z - f3))) is V11() real ext-real Element of REAL
R20 . (z - f3) is V11() real ext-real Element of REAL
(R14 . (z - f3)) + (R20 . (z - f3)) is V11() real ext-real Element of REAL
((L . (z - f3)) + (R13 . (z - f3))) + ((R14 . (z - f3)) + (R20 . (z - f3))) is V11() real ext-real Element of REAL
(R13 . (z - f3)) + (R14 . (z - f3)) is V11() real ext-real Element of REAL
((R13 . (z - f3)) + (R14 . (z - f3))) + (R20 . (z - f3)) is V11() real ext-real Element of REAL
(L . (z - f3)) + (((R13 . (z - f3)) + (R14 . (z - f3))) + (R20 . (z - f3))) is V11() real ext-real Element of REAL
R15 . (z - f3) is V11() real ext-real Element of REAL
(R15 . (z - f3)) + (R20 . (z - f3)) is V11() real ext-real Element of REAL
(L . (z - f3)) + ((R15 . (z - f3)) + (R20 . (z - f3))) is V11() real ext-real Element of REAL
R is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R . (z - f3) is V11() real ext-real Element of REAL
(L . (z - f3)) + (R . (z - f3)) is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of f3
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₃ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 (#) f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (2,f1,p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,f1,p)) is V160() V161() V162() Element of K6(REAL)
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
<*f3,g1,g2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,f1,p)) . g1 is V11() real ext-real Element of REAL
g3 is open V160() V161() V162() Neighbourhood of g1
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g3 is open V160() V161() V162() Neighbourhood of g1
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (2,f2,p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f2 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,f2,p)) is V160() V161() V162() Element of K6(REAL)
x1 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*x1,y1,z1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (2,f2,p)) . y1 is V11() real ext-real Element of REAL
N2 is open V160() V161() V162() Neighbourhood of g1
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is open V160() V161() V162() Neighbourhood of y1
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
(SVF1 (2,f2,p)) . g1 is V11() real ext-real Element of REAL
N2 is open V160() V161() V162() Neighbourhood of y1
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N2 is open V160() V161() V162() Neighbourhood of g1
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is open V160() V161() V162() Neighbourhood of g1
((SVF1 (2,f2,p)) . g1) (#) z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (2,f1,p)) . g1) (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L11 + L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (2,f2,p)) . g1) (#) R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (2,f1,p)) . g1) (#) R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R11 + R12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
z (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R13 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R14 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R13 + R14 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R1 (#) R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R1 (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R2 (#) z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R16 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R17 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R16 + R17 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R19 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R18 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R19 + R18 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R15 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R20 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R15 + R20 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (2,(f1 (#) f2),p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(f1 (#) f2) * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (2,(f1 (#) f2),p)) is V160() V161() V162() Element of K6(REAL)
z is V11() real ext-real Element of REAL
dom (reproj (2,p)) is V160() V161() V162() Element of K6(REAL)
(reproj (2,p)) . z is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ (dom f2) is functional FinSequence-membered Element of K6((REAL 3))
dom (f1 (#) f2) is functional FinSequence-membered Element of K6((REAL 3))
z is set
z is V11() real ext-real Element of REAL
(SVF1 (2,f1,p)) . z is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . z) - ((SVF1 (2,f1,p)) . g1) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) - ((SVF1 (2,f1,p)) . g1)) + ((SVF1 (2,f1,p)) . g1) is V11() real ext-real Element of REAL
z - g1 is V11() real ext-real Element of REAL
z . (z - g1) is V11() real ext-real Element of REAL
R1 . (z - g1) is V11() real ext-real Element of REAL
(z . (z - g1)) + (R1 . (z - g1)) is V11() real ext-real Element of REAL
((z . (z - g1)) + (R1 . (z - g1))) + ((SVF1 (2,f1,p)) . g1) is V11() real ext-real Element of REAL
dom ((f1 (#) f2) * (reproj (2,p))) is V160() V161() V162() Element of K6(REAL)
dom (reproj (2,p)) is V160() V161() V162() Element of K6(REAL)
(reproj (2,p)) . z is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 (#) f2) is functional FinSequence-membered Element of K6((REAL 3))
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ (dom f2) is functional FinSequence-membered Element of K6((REAL 3))
dom (f1 * (reproj (2,p))) is V160() V161() V162() Element of K6(REAL)
dom (f2 * (reproj (2,p))) is V160() V161() V162() Element of K6(REAL)
(reproj (2,p)) . g1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(SVF1 (2,(f1 (#) f2),p)) . z is V11() real ext-real Element of REAL
(SVF1 (2,(f1 (#) f2),p)) . g1 is V11() real ext-real Element of REAL
((SVF1 (2,(f1 (#) f2),p)) . z) - ((SVF1 (2,(f1 (#) f2),p)) . g1) is V11() real ext-real Element of REAL
(f1 (#) f2) . ((reproj (2,p)) . z) is V11() real ext-real Element of REAL
((f1 (#) f2) . ((reproj (2,p)) . z)) - ((SVF1 (2,(f1 (#) f2),p)) . g1) is V11() real ext-real Element of REAL
f1 . ((reproj (2,p)) . z) is V11() real ext-real Element of REAL
f2 . ((reproj (2,p)) . z) is V11() real ext-real Element of REAL
(f1 . ((reproj (2,p)) . z)) * (f2 . ((reproj (2,p)) . z)) is V11() real ext-real Element of REAL
((f1 . ((reproj (2,p)) . z)) * (f2 . ((reproj (2,p)) . z))) - ((SVF1 (2,(f1 (#) f2),p)) . g1) is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . z) * (f2 . ((reproj (2,p)) . z)) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * (f2 . ((reproj (2,p)) . z))) - ((SVF1 (2,(f1 (#) f2),p)) . g1) is V11() real ext-real Element of REAL
(SVF1 (2,f2,p)) . z is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z) is V11() real ext-real Element of REAL
((f1 (#) f2) * (reproj (2,p))) . g1 is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z)) - (((f1 (#) f2) * (reproj (2,p))) . g1) is V11() real ext-real Element of REAL
(f1 (#) f2) . ((reproj (2,p)) . g1) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z)) - ((f1 (#) f2) . ((reproj (2,p)) . g1)) is V11() real ext-real Element of REAL
f1 . ((reproj (2,p)) . g1) is V11() real ext-real Element of REAL
f2 . ((reproj (2,p)) . g1) is V11() real ext-real Element of REAL
(f1 . ((reproj (2,p)) . g1)) * (f2 . ((reproj (2,p)) . g1)) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z)) - ((f1 . ((reproj (2,p)) . g1)) * (f2 . ((reproj (2,p)) . g1))) is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . g1) * (f2 . ((reproj (2,p)) . g1)) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z)) - (((SVF1 (2,f1,p)) . g1) * (f2 . ((reproj (2,p)) . g1))) is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . g1) is V11() real ext-real Element of REAL
- (((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . g1)) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z)) + (- (((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . g1))) is V11() real ext-real Element of REAL
((((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z)) + (- (((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . g1)))) + (((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . g1)) is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . g1) * ((SVF1 (2,f2,p)) . g1) is V11() real ext-real Element of REAL
(((((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . z)) + (- (((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . g1)))) + (((SVF1 (2,f1,p)) . z) * ((SVF1 (2,f2,p)) . g1))) - (((SVF1 (2,f1,p)) . g1) * ((SVF1 (2,f2,p)) . g1)) is V11() real ext-real Element of REAL
((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1) is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . z) * (((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1)) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) - ((SVF1 (2,f1,p)) . g1)) * ((SVF1 (2,f2,p)) . g1) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * (((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1))) + ((((SVF1 (2,f1,p)) . z) - ((SVF1 (2,f1,p)) . g1)) * ((SVF1 (2,f2,p)) . g1)) is V11() real ext-real Element of REAL
((z . (z - g1)) + (R1 . (z - g1))) * ((SVF1 (2,f2,p)) . g1) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * (((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1))) + (((z . (z - g1)) + (R1 . (z - g1))) * ((SVF1 (2,f2,p)) . g1)) is V11() real ext-real Element of REAL
((SVF1 (2,f2,p)) . g1) * (z . (z - g1)) is V11() real ext-real Element of REAL
((SVF1 (2,f2,p)) . g1) * (R1 . (z - g1)) is V11() real ext-real Element of REAL
(((SVF1 (2,f2,p)) . g1) * (z . (z - g1))) + (((SVF1 (2,f2,p)) . g1) * (R1 . (z - g1))) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * (((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1))) + ((((SVF1 (2,f2,p)) . g1) * (z . (z - g1))) + (((SVF1 (2,f2,p)) . g1) * (R1 . (z - g1)))) is V11() real ext-real Element of REAL
L11 . (z - g1) is V11() real ext-real Element of REAL
(L11 . (z - g1)) + (((SVF1 (2,f2,p)) . g1) * (R1 . (z - g1))) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . z) * (((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1))) + ((L11 . (z - g1)) + (((SVF1 (2,f2,p)) . g1) * (R1 . (z - g1)))) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) + ((SVF1 (2,f1,p)) . g1)) * (((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1)) is V11() real ext-real Element of REAL
R11 . (z - g1) is V11() real ext-real Element of REAL
(L11 . (z - g1)) + (R11 . (z - g1)) is V11() real ext-real Element of REAL
((((z . (z - g1)) + (R1 . (z - g1))) + ((SVF1 (2,f1,p)) . g1)) * (((SVF1 (2,f2,p)) . z) - ((SVF1 (2,f2,p)) . g1))) + ((L11 . (z - g1)) + (R11 . (z - g1))) is V11() real ext-real Element of REAL
L2 . (z - g1) is V11() real ext-real Element of REAL
R2 . (z - g1) is V11() real ext-real Element of REAL
(L2 . (z - g1)) + (R2 . (z - g1)) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) + ((SVF1 (2,f1,p)) . g1)) * ((L2 . (z - g1)) + (R2 . (z - g1))) is V11() real ext-real Element of REAL
((((z . (z - g1)) + (R1 . (z - g1))) + ((SVF1 (2,f1,p)) . g1)) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((L11 . (z - g1)) + (R11 . (z - g1))) is V11() real ext-real Element of REAL
((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1))) is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . g1) * (L2 . (z - g1)) is V11() real ext-real Element of REAL
((SVF1 (2,f1,p)) . g1) * (R2 . (z - g1)) is V11() real ext-real Element of REAL
(((SVF1 (2,f1,p)) . g1) * (L2 . (z - g1))) + (((SVF1 (2,f1,p)) . g1) * (R2 . (z - g1))) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((((SVF1 (2,f1,p)) . g1) * (L2 . (z - g1))) + (((SVF1 (2,f1,p)) . g1) * (R2 . (z - g1)))) is V11() real ext-real Element of REAL
((((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((((SVF1 (2,f1,p)) . g1) * (L2 . (z - g1))) + (((SVF1 (2,f1,p)) . g1) * (R2 . (z - g1))))) + ((L11 . (z - g1)) + (R11 . (z - g1))) is V11() real ext-real Element of REAL
L12 . (z - g1) is V11() real ext-real Element of REAL
(L12 . (z - g1)) + (((SVF1 (2,f1,p)) . g1) * (R2 . (z - g1))) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((L12 . (z - g1)) + (((SVF1 (2,f1,p)) . g1) * (R2 . (z - g1)))) is V11() real ext-real Element of REAL
((((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((L12 . (z - g1)) + (((SVF1 (2,f1,p)) . g1) * (R2 . (z - g1))))) + ((L11 . (z - g1)) + (R11 . (z - g1))) is V11() real ext-real Element of REAL
R12 . (z - g1) is V11() real ext-real Element of REAL
(L12 . (z - g1)) + (R12 . (z - g1)) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((L12 . (z - g1)) + (R12 . (z - g1))) is V11() real ext-real Element of REAL
((((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((L12 . (z - g1)) + (R12 . (z - g1)))) + ((L11 . (z - g1)) + (R11 . (z - g1))) is V11() real ext-real Element of REAL
(R11 . (z - g1)) + (R12 . (z - g1)) is V11() real ext-real Element of REAL
(L11 . (z - g1)) + ((R11 . (z - g1)) + (R12 . (z - g1))) is V11() real ext-real Element of REAL
(L12 . (z - g1)) + ((L11 . (z - g1)) + ((R11 . (z - g1)) + (R12 . (z - g1)))) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((L12 . (z - g1)) + ((L11 . (z - g1)) + ((R11 . (z - g1)) + (R12 . (z - g1))))) is V11() real ext-real Element of REAL
R13 . (z - g1) is V11() real ext-real Element of REAL
(L11 . (z - g1)) + (R13 . (z - g1)) is V11() real ext-real Element of REAL
(L12 . (z - g1)) + ((L11 . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + ((L12 . (z - g1)) + ((L11 . (z - g1)) + (R13 . (z - g1)))) is V11() real ext-real Element of REAL
(L11 . (z - g1)) + (L12 . (z - g1)) is V11() real ext-real Element of REAL
((L11 . (z - g1)) + (L12 . (z - g1))) + (R13 . (z - g1)) is V11() real ext-real Element of REAL
(((z . (z - g1)) + (R1 . (z - g1))) * ((L2 . (z - g1)) + (R2 . (z - g1)))) + (((L11 . (z - g1)) + (L12 . (z - g1))) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
(z . (z - g1)) * (L2 . (z - g1)) is V11() real ext-real Element of REAL
(z . (z - g1)) * (R2 . (z - g1)) is V11() real ext-real Element of REAL
((z . (z - g1)) * (L2 . (z - g1))) + ((z . (z - g1)) * (R2 . (z - g1))) is V11() real ext-real Element of REAL
(R1 . (z - g1)) * ((L2 . (z - g1)) + (R2 . (z - g1))) is V11() real ext-real Element of REAL
(((z . (z - g1)) * (L2 . (z - g1))) + ((z . (z - g1)) * (R2 . (z - g1)))) + ((R1 . (z - g1)) * ((L2 . (z - g1)) + (R2 . (z - g1)))) is V11() real ext-real Element of REAL
L is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L . (z - g1) is V11() real ext-real Element of REAL
(L . (z - g1)) + (R13 . (z - g1)) is V11() real ext-real Element of REAL
((((z . (z - g1)) * (L2 . (z - g1))) + ((z . (z - g1)) * (R2 . (z - g1)))) + ((R1 . (z - g1)) * ((L2 . (z - g1)) + (R2 . (z - g1))))) + ((L . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
R14 . (z - g1) is V11() real ext-real Element of REAL
(R2 . (z - g1)) * (z . (z - g1)) is V11() real ext-real Element of REAL
(R14 . (z - g1)) + ((R2 . (z - g1)) * (z . (z - g1))) is V11() real ext-real Element of REAL
((R14 . (z - g1)) + ((R2 . (z - g1)) * (z . (z - g1)))) + ((R1 . (z - g1)) * ((L2 . (z - g1)) + (R2 . (z - g1)))) is V11() real ext-real Element of REAL
(((R14 . (z - g1)) + ((R2 . (z - g1)) * (z . (z - g1)))) + ((R1 . (z - g1)) * ((L2 . (z - g1)) + (R2 . (z - g1))))) + ((L . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
R18 . (z - g1) is V11() real ext-real Element of REAL
(R14 . (z - g1)) + (R18 . (z - g1)) is V11() real ext-real Element of REAL
(R1 . (z - g1)) * (L2 . (z - g1)) is V11() real ext-real Element of REAL
(R1 . (z - g1)) * (R2 . (z - g1)) is V11() real ext-real Element of REAL
((R1 . (z - g1)) * (L2 . (z - g1))) + ((R1 . (z - g1)) * (R2 . (z - g1))) is V11() real ext-real Element of REAL
((R14 . (z - g1)) + (R18 . (z - g1))) + (((R1 . (z - g1)) * (L2 . (z - g1))) + ((R1 . (z - g1)) * (R2 . (z - g1)))) is V11() real ext-real Element of REAL
(((R14 . (z - g1)) + (R18 . (z - g1))) + (((R1 . (z - g1)) * (L2 . (z - g1))) + ((R1 . (z - g1)) * (R2 . (z - g1))))) + ((L . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
R16 . (z - g1) is V11() real ext-real Element of REAL
(R16 . (z - g1)) + ((R1 . (z - g1)) * (R2 . (z - g1))) is V11() real ext-real Element of REAL
((R14 . (z - g1)) + (R18 . (z - g1))) + ((R16 . (z - g1)) + ((R1 . (z - g1)) * (R2 . (z - g1)))) is V11() real ext-real Element of REAL
(((R14 . (z - g1)) + (R18 . (z - g1))) + ((R16 . (z - g1)) + ((R1 . (z - g1)) * (R2 . (z - g1))))) + ((L . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
R17 . (z - g1) is V11() real ext-real Element of REAL
(R16 . (z - g1)) + (R17 . (z - g1)) is V11() real ext-real Element of REAL
((R14 . (z - g1)) + (R18 . (z - g1))) + ((R16 . (z - g1)) + (R17 . (z - g1))) is V11() real ext-real Element of REAL
(((R14 . (z - g1)) + (R18 . (z - g1))) + ((R16 . (z - g1)) + (R17 . (z - g1)))) + ((L . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
R19 . (z - g1) is V11() real ext-real Element of REAL
((R14 . (z - g1)) + (R18 . (z - g1))) + (R19 . (z - g1)) is V11() real ext-real Element of REAL
(((R14 . (z - g1)) + (R18 . (z - g1))) + (R19 . (z - g1))) + ((L . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
(R19 . (z - g1)) + (R18 . (z - g1)) is V11() real ext-real Element of REAL
(R14 . (z - g1)) + ((R19 . (z - g1)) + (R18 . (z - g1))) is V11() real ext-real Element of REAL
((R14 . (z - g1)) + ((R19 . (z - g1)) + (R18 . (z - g1)))) + ((L . (z - g1)) + (R13 . (z - g1))) is V11() real ext-real Element of REAL
R20 . (z - g1) is V11() real ext-real Element of REAL
(R14 . (z - g1)) + (R20 . (z - g1)) is V11() real ext-real Element of REAL
((L . (z - g1)) + (R13 . (z - g1))) + ((R14 . (z - g1)) + (R20 . (z - g1))) is V11() real ext-real Element of REAL
(R13 . (z - g1)) + (R14 . (z - g1)) is V11() real ext-real Element of REAL
((R13 . (z - g1)) + (R14 . (z - g1))) + (R20 . (z - g1)) is V11() real ext-real Element of REAL
(L . (z - g1)) + (((R13 . (z - g1)) + (R14 . (z - g1))) + (R20 . (z - g1))) is V11() real ext-real Element of REAL
R15 . (z - g1) is V11() real ext-real Element of REAL
(R15 . (z - g1)) + (R20 . (z - g1)) is V11() real ext-real Element of REAL
(L . (z - g1)) + ((R15 . (z - g1)) + (R20 . (z - g1))) is V11() real ext-real Element of REAL
R is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R . (z - g1) is V11() real ext-real Element of REAL
(L . (z - g1)) + (R . (z - g1)) is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of g1
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₃ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 (#) f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
SVF1 (3,f1,p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,f1,p)) is V160() V161() V162() Element of K6(REAL)
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
<*f3,g1,g2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,f1,p)) . g2 is V11() real ext-real Element of REAL
g3 is open V160() V161() V162() Neighbourhood of g2
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
g3 is open V160() V161() V162() Neighbourhood of g2
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (3,f2,p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
f2 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,f2,p)) is V160() V161() V162() Element of K6(REAL)
x1 is V11() real ext-real Element of REAL
y1 is V11() real ext-real Element of REAL
z1 is V11() real ext-real Element of REAL
<*x1,y1,z1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
(SVF1 (3,f2,p)) . z1 is V11() real ext-real Element of REAL
N2 is open V160() V161() V162() Neighbourhood of g2
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is open V160() V161() V162() Neighbourhood of z1
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
(SVF1 (3,f2,p)) . g2 is V11() real ext-real Element of REAL
N2 is open V160() V161() V162() Neighbourhood of z1
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N2 is open V160() V161() V162() Neighbourhood of g2
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
N is open V160() V161() V162() Neighbourhood of g2
((SVF1 (3,f2,p)) . g2) (#) z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (3,f1,p)) . g2) (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
L11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L11 + L12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (3,f2,p)) . g2) (#) R1 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((SVF1 (3,f1,p)) . g2) (#) R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R11 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R11 + R12 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
z (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R13 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R14 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R13 + R14 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R1 (#) R2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R1 (#) L2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R2 (#) z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R16 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R17 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R16 + R17 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R19 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R18 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R19 + R18 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
R15 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R20 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R15 + R20 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
z is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
SVF1 (3,(f1 (#) f2),p) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(f1 (#) f2) * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
dom (SVF1 (3,(f1 (#) f2),p)) is V160() V161() V162() Element of K6(REAL)
z is V11() real ext-real Element of REAL
dom (reproj (3,p)) is V160() V161() V162() Element of K6(REAL)
(reproj (3,p)) . z is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ (dom f2) is functional FinSequence-membered Element of K6((REAL 3))
dom (f1 (#) f2) is functional FinSequence-membered Element of K6((REAL 3))
z is set
z is V11() real ext-real Element of REAL
(SVF1 (3,f1,p)) . z is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . z) - ((SVF1 (3,f1,p)) . g2) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) - ((SVF1 (3,f1,p)) . g2)) + ((SVF1 (3,f1,p)) . g2) is V11() real ext-real Element of REAL
z - g2 is V11() real ext-real Element of REAL
z . (z - g2) is V11() real ext-real Element of REAL
R1 . (z - g2) is V11() real ext-real Element of REAL
(z . (z - g2)) + (R1 . (z - g2)) is V11() real ext-real Element of REAL
((z . (z - g2)) + (R1 . (z - g2))) + ((SVF1 (3,f1,p)) . g2) is V11() real ext-real Element of REAL
dom ((f1 (#) f2) * (reproj (3,p))) is V160() V161() V162() Element of K6(REAL)
dom (reproj (3,p)) is V160() V161() V162() Element of K6(REAL)
(reproj (3,p)) . z is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
dom (f1 (#) f2) is functional FinSequence-membered Element of K6((REAL 3))
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
dom f2 is functional FinSequence-membered Element of K6((REAL 3))
(dom f1) /\ (dom f2) is functional FinSequence-membered Element of K6((REAL 3))
dom (f1 * (reproj (3,p))) is V160() V161() V162() Element of K6(REAL)
dom (f2 * (reproj (3,p))) is V160() V161() V162() Element of K6(REAL)
(reproj (3,p)) . g2 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(SVF1 (3,(f1 (#) f2),p)) . z is V11() real ext-real Element of REAL
(SVF1 (3,(f1 (#) f2),p)) . g2 is V11() real ext-real Element of REAL
((SVF1 (3,(f1 (#) f2),p)) . z) - ((SVF1 (3,(f1 (#) f2),p)) . g2) is V11() real ext-real Element of REAL
(f1 (#) f2) . ((reproj (3,p)) . z) is V11() real ext-real Element of REAL
((f1 (#) f2) . ((reproj (3,p)) . z)) - ((SVF1 (3,(f1 (#) f2),p)) . g2) is V11() real ext-real Element of REAL
f1 . ((reproj (3,p)) . z) is V11() real ext-real Element of REAL
f2 . ((reproj (3,p)) . z) is V11() real ext-real Element of REAL
(f1 . ((reproj (3,p)) . z)) * (f2 . ((reproj (3,p)) . z)) is V11() real ext-real Element of REAL
((f1 . ((reproj (3,p)) . z)) * (f2 . ((reproj (3,p)) . z))) - ((SVF1 (3,(f1 (#) f2),p)) . g2) is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . z) * (f2 . ((reproj (3,p)) . z)) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * (f2 . ((reproj (3,p)) . z))) - ((SVF1 (3,(f1 (#) f2),p)) . g2) is V11() real ext-real Element of REAL
(SVF1 (3,f2,p)) . z is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z) is V11() real ext-real Element of REAL
((f1 (#) f2) * (reproj (3,p))) . g2 is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z)) - (((f1 (#) f2) * (reproj (3,p))) . g2) is V11() real ext-real Element of REAL
(f1 (#) f2) . ((reproj (3,p)) . g2) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z)) - ((f1 (#) f2) . ((reproj (3,p)) . g2)) is V11() real ext-real Element of REAL
f1 . ((reproj (3,p)) . g2) is V11() real ext-real Element of REAL
f2 . ((reproj (3,p)) . g2) is V11() real ext-real Element of REAL
(f1 . ((reproj (3,p)) . g2)) * (f2 . ((reproj (3,p)) . g2)) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z)) - ((f1 . ((reproj (3,p)) . g2)) * (f2 . ((reproj (3,p)) . g2))) is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . g2) * (f2 . ((reproj (3,p)) . g2)) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z)) - (((SVF1 (3,f1,p)) . g2) * (f2 . ((reproj (3,p)) . g2))) is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . g2) is V11() real ext-real Element of REAL
- (((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . g2)) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z)) + (- (((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . g2))) is V11() real ext-real Element of REAL
((((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z)) + (- (((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . g2)))) + (((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . g2)) is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . g2) * ((SVF1 (3,f2,p)) . g2) is V11() real ext-real Element of REAL
(((((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . z)) + (- (((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . g2)))) + (((SVF1 (3,f1,p)) . z) * ((SVF1 (3,f2,p)) . g2))) - (((SVF1 (3,f1,p)) . g2) * ((SVF1 (3,f2,p)) . g2)) is V11() real ext-real Element of REAL
((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2) is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . z) * (((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2)) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) - ((SVF1 (3,f1,p)) . g2)) * ((SVF1 (3,f2,p)) . g2) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * (((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2))) + ((((SVF1 (3,f1,p)) . z) - ((SVF1 (3,f1,p)) . g2)) * ((SVF1 (3,f2,p)) . g2)) is V11() real ext-real Element of REAL
((z . (z - g2)) + (R1 . (z - g2))) * ((SVF1 (3,f2,p)) . g2) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * (((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2))) + (((z . (z - g2)) + (R1 . (z - g2))) * ((SVF1 (3,f2,p)) . g2)) is V11() real ext-real Element of REAL
((SVF1 (3,f2,p)) . g2) * (z . (z - g2)) is V11() real ext-real Element of REAL
((SVF1 (3,f2,p)) . g2) * (R1 . (z - g2)) is V11() real ext-real Element of REAL
(((SVF1 (3,f2,p)) . g2) * (z . (z - g2))) + (((SVF1 (3,f2,p)) . g2) * (R1 . (z - g2))) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * (((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2))) + ((((SVF1 (3,f2,p)) . g2) * (z . (z - g2))) + (((SVF1 (3,f2,p)) . g2) * (R1 . (z - g2)))) is V11() real ext-real Element of REAL
L11 . (z - g2) is V11() real ext-real Element of REAL
(L11 . (z - g2)) + (((SVF1 (3,f2,p)) . g2) * (R1 . (z - g2))) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . z) * (((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2))) + ((L11 . (z - g2)) + (((SVF1 (3,f2,p)) . g2) * (R1 . (z - g2)))) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) + ((SVF1 (3,f1,p)) . g2)) * (((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2)) is V11() real ext-real Element of REAL
R11 . (z - g2) is V11() real ext-real Element of REAL
(L11 . (z - g2)) + (R11 . (z - g2)) is V11() real ext-real Element of REAL
((((z . (z - g2)) + (R1 . (z - g2))) + ((SVF1 (3,f1,p)) . g2)) * (((SVF1 (3,f2,p)) . z) - ((SVF1 (3,f2,p)) . g2))) + ((L11 . (z - g2)) + (R11 . (z - g2))) is V11() real ext-real Element of REAL
L2 . (z - g2) is V11() real ext-real Element of REAL
R2 . (z - g2) is V11() real ext-real Element of REAL
(L2 . (z - g2)) + (R2 . (z - g2)) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) + ((SVF1 (3,f1,p)) . g2)) * ((L2 . (z - g2)) + (R2 . (z - g2))) is V11() real ext-real Element of REAL
((((z . (z - g2)) + (R1 . (z - g2))) + ((SVF1 (3,f1,p)) . g2)) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((L11 . (z - g2)) + (R11 . (z - g2))) is V11() real ext-real Element of REAL
((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2))) is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . g2) * (L2 . (z - g2)) is V11() real ext-real Element of REAL
((SVF1 (3,f1,p)) . g2) * (R2 . (z - g2)) is V11() real ext-real Element of REAL
(((SVF1 (3,f1,p)) . g2) * (L2 . (z - g2))) + (((SVF1 (3,f1,p)) . g2) * (R2 . (z - g2))) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((((SVF1 (3,f1,p)) . g2) * (L2 . (z - g2))) + (((SVF1 (3,f1,p)) . g2) * (R2 . (z - g2)))) is V11() real ext-real Element of REAL
((((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((((SVF1 (3,f1,p)) . g2) * (L2 . (z - g2))) + (((SVF1 (3,f1,p)) . g2) * (R2 . (z - g2))))) + ((L11 . (z - g2)) + (R11 . (z - g2))) is V11() real ext-real Element of REAL
L12 . (z - g2) is V11() real ext-real Element of REAL
(L12 . (z - g2)) + (((SVF1 (3,f1,p)) . g2) * (R2 . (z - g2))) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((L12 . (z - g2)) + (((SVF1 (3,f1,p)) . g2) * (R2 . (z - g2)))) is V11() real ext-real Element of REAL
((((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((L12 . (z - g2)) + (((SVF1 (3,f1,p)) . g2) * (R2 . (z - g2))))) + ((L11 . (z - g2)) + (R11 . (z - g2))) is V11() real ext-real Element of REAL
R12 . (z - g2) is V11() real ext-real Element of REAL
(L12 . (z - g2)) + (R12 . (z - g2)) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((L12 . (z - g2)) + (R12 . (z - g2))) is V11() real ext-real Element of REAL
((((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((L12 . (z - g2)) + (R12 . (z - g2)))) + ((L11 . (z - g2)) + (R11 . (z - g2))) is V11() real ext-real Element of REAL
(R11 . (z - g2)) + (R12 . (z - g2)) is V11() real ext-real Element of REAL
(L11 . (z - g2)) + ((R11 . (z - g2)) + (R12 . (z - g2))) is V11() real ext-real Element of REAL
(L12 . (z - g2)) + ((L11 . (z - g2)) + ((R11 . (z - g2)) + (R12 . (z - g2)))) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((L12 . (z - g2)) + ((L11 . (z - g2)) + ((R11 . (z - g2)) + (R12 . (z - g2))))) is V11() real ext-real Element of REAL
R13 . (z - g2) is V11() real ext-real Element of REAL
(L11 . (z - g2)) + (R13 . (z - g2)) is V11() real ext-real Element of REAL
(L12 . (z - g2)) + ((L11 . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + ((L12 . (z - g2)) + ((L11 . (z - g2)) + (R13 . (z - g2)))) is V11() real ext-real Element of REAL
(L11 . (z - g2)) + (L12 . (z - g2)) is V11() real ext-real Element of REAL
((L11 . (z - g2)) + (L12 . (z - g2))) + (R13 . (z - g2)) is V11() real ext-real Element of REAL
(((z . (z - g2)) + (R1 . (z - g2))) * ((L2 . (z - g2)) + (R2 . (z - g2)))) + (((L11 . (z - g2)) + (L12 . (z - g2))) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
(z . (z - g2)) * (L2 . (z - g2)) is V11() real ext-real Element of REAL
(z . (z - g2)) * (R2 . (z - g2)) is V11() real ext-real Element of REAL
((z . (z - g2)) * (L2 . (z - g2))) + ((z . (z - g2)) * (R2 . (z - g2))) is V11() real ext-real Element of REAL
(R1 . (z - g2)) * ((L2 . (z - g2)) + (R2 . (z - g2))) is V11() real ext-real Element of REAL
(((z . (z - g2)) * (L2 . (z - g2))) + ((z . (z - g2)) * (R2 . (z - g2)))) + ((R1 . (z - g2)) * ((L2 . (z - g2)) + (R2 . (z - g2)))) is V11() real ext-real Element of REAL
L is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
L . (z - g2) is V11() real ext-real Element of REAL
(L . (z - g2)) + (R13 . (z - g2)) is V11() real ext-real Element of REAL
((((z . (z - g2)) * (L2 . (z - g2))) + ((z . (z - g2)) * (R2 . (z - g2)))) + ((R1 . (z - g2)) * ((L2 . (z - g2)) + (R2 . (z - g2))))) + ((L . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
R14 . (z - g2) is V11() real ext-real Element of REAL
(R2 . (z - g2)) * (z . (z - g2)) is V11() real ext-real Element of REAL
(R14 . (z - g2)) + ((R2 . (z - g2)) * (z . (z - g2))) is V11() real ext-real Element of REAL
((R14 . (z - g2)) + ((R2 . (z - g2)) * (z . (z - g2)))) + ((R1 . (z - g2)) * ((L2 . (z - g2)) + (R2 . (z - g2)))) is V11() real ext-real Element of REAL
(((R14 . (z - g2)) + ((R2 . (z - g2)) * (z . (z - g2)))) + ((R1 . (z - g2)) * ((L2 . (z - g2)) + (R2 . (z - g2))))) + ((L . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
R18 . (z - g2) is V11() real ext-real Element of REAL
(R14 . (z - g2)) + (R18 . (z - g2)) is V11() real ext-real Element of REAL
(R1 . (z - g2)) * (L2 . (z - g2)) is V11() real ext-real Element of REAL
(R1 . (z - g2)) * (R2 . (z - g2)) is V11() real ext-real Element of REAL
((R1 . (z - g2)) * (L2 . (z - g2))) + ((R1 . (z - g2)) * (R2 . (z - g2))) is V11() real ext-real Element of REAL
((R14 . (z - g2)) + (R18 . (z - g2))) + (((R1 . (z - g2)) * (L2 . (z - g2))) + ((R1 . (z - g2)) * (R2 . (z - g2)))) is V11() real ext-real Element of REAL
(((R14 . (z - g2)) + (R18 . (z - g2))) + (((R1 . (z - g2)) * (L2 . (z - g2))) + ((R1 . (z - g2)) * (R2 . (z - g2))))) + ((L . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
R16 . (z - g2) is V11() real ext-real Element of REAL
(R16 . (z - g2)) + ((R1 . (z - g2)) * (R2 . (z - g2))) is V11() real ext-real Element of REAL
((R14 . (z - g2)) + (R18 . (z - g2))) + ((R16 . (z - g2)) + ((R1 . (z - g2)) * (R2 . (z - g2)))) is V11() real ext-real Element of REAL
(((R14 . (z - g2)) + (R18 . (z - g2))) + ((R16 . (z - g2)) + ((R1 . (z - g2)) * (R2 . (z - g2))))) + ((L . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
R17 . (z - g2) is V11() real ext-real Element of REAL
(R16 . (z - g2)) + (R17 . (z - g2)) is V11() real ext-real Element of REAL
((R14 . (z - g2)) + (R18 . (z - g2))) + ((R16 . (z - g2)) + (R17 . (z - g2))) is V11() real ext-real Element of REAL
(((R14 . (z - g2)) + (R18 . (z - g2))) + ((R16 . (z - g2)) + (R17 . (z - g2)))) + ((L . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
R19 . (z - g2) is V11() real ext-real Element of REAL
((R14 . (z - g2)) + (R18 . (z - g2))) + (R19 . (z - g2)) is V11() real ext-real Element of REAL
(((R14 . (z - g2)) + (R18 . (z - g2))) + (R19 . (z - g2))) + ((L . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
(R19 . (z - g2)) + (R18 . (z - g2)) is V11() real ext-real Element of REAL
(R14 . (z - g2)) + ((R19 . (z - g2)) + (R18 . (z - g2))) is V11() real ext-real Element of REAL
((R14 . (z - g2)) + ((R19 . (z - g2)) + (R18 . (z - g2)))) + ((L . (z - g2)) + (R13 . (z - g2))) is V11() real ext-real Element of REAL
R20 . (z - g2) is V11() real ext-real Element of REAL
(R14 . (z - g2)) + (R20 . (z - g2)) is V11() real ext-real Element of REAL
((L . (z - g2)) + (R13 . (z - g2))) + ((R14 . (z - g2)) + (R20 . (z - g2))) is V11() real ext-real Element of REAL
(R13 . (z - g2)) + (R14 . (z - g2)) is V11() real ext-real Element of REAL
((R13 . (z - g2)) + (R14 . (z - g2))) + (R20 . (z - g2)) is V11() real ext-real Element of REAL
(L . (z - g2)) + (((R13 . (z - g2)) + (R14 . (z - g2))) + (R20 . (z - g2))) is V11() real ext-real Element of REAL
R15 . (z - g2) is V11() real ext-real Element of REAL
(R15 . (z - g2)) + (R20 . (z - g2)) is V11() real ext-real Element of REAL
(L . (z - g2)) + ((R15 . (z - g2)) + (R20 . (z - g2))) is V11() real ext-real Element of REAL
R is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
R . (z - g2) is V11() real ext-real Element of REAL
(L . (z - g2)) + (R . (z - g2)) is V11() real ext-real Element of REAL
z is open V160() V161() V162() Neighbourhood of g2
c₃₂ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued linear Element of K6(K7(REAL,REAL))
c₃₃ is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued RestFunc-like Element of K6(K7(REAL,REAL))
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (1,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (1,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (2,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (2,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
SVF1 (3,p,f1) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
reproj (3,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
<*f2,f3,g1*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
|[p,f1,f2]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f3 is V11() real ext-real Element of REAL
p + f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
f1 + g1 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
|[f3,g1,g2]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[p,f1,f2]| + |[f3,g1,g2]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K495() is V16() V19(K7(REAL,REAL)) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(K7(REAL,REAL),REAL))
K229(K495(),|[p,f1,f2]|,|[f3,g1,g2]|) is V16() Function-like set
f2 + g2 is V11() real ext-real Element of REAL
|[(p + f3),(f1 + g1),(f2 + g2)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[f3,g1,g2]| . 1 is V11() real ext-real Element of REAL
|[f3,g1,g2]| . 2 is V11() real ext-real Element of REAL
|[f3,g1,g2]| . 3 is V11() real ext-real Element of REAL
|[p,f1,f2]| . 1 is V11() real ext-real Element of REAL
(|[p,f1,f2]| . 1) + (|[f3,g1,g2]| . 1) is V11() real ext-real Element of REAL
|[p,f1,f2]| . 2 is V11() real ext-real Element of REAL
(|[p,f1,f2]| . 2) + (|[f3,g1,g2]| . 2) is V11() real ext-real Element of REAL
|[p,f1,f2]| . 3 is V11() real ext-real Element of REAL
(|[p,f1,f2]| . 3) + (|[f3,g1,g2]| . 3) is V11() real ext-real Element of REAL
<e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[1,0,0]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (p,f1,1) is V11() real ext-real Element of REAL
reproj (1,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f1 is V11() real ext-real Element of REAL
diff ((p * (reproj (1,f1))),((proj (1,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff (p,f1,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (p,f1,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K497() is V16() V19(K7(REAL,REAL)) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(K7(REAL,REAL),REAL))
id REAL is V1() V16() V19( REAL ) V20( REAL ) total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (p,f1,1)),(id REAL)) is set
K530((partdiff (p,f1,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
<e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[0,1,0]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (p,f1,2) is V11() real ext-real Element of REAL
reproj (2,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f1 is V11() real ext-real Element of REAL
diff ((p * (reproj (2,f1))),((proj (2,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff (p,f1,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (p,f1,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (p,f1,2)),(id REAL)) is set
K530((partdiff (p,f1,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (p,f1,1)) * <e1>) + ((partdiff (p,f1,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K495() is V16() V19(K7(REAL,REAL)) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(K7(REAL,REAL),REAL))
K229(K495(),((partdiff (p,f1,1)) * <e1>),((partdiff (p,f1,2)) * <e2>)) is V16() Function-like set
<e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[0,0,1]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (p,f1,3) is V11() real ext-real Element of REAL
reproj (3,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f1 is V11() real ext-real Element of REAL
diff ((p * (reproj (3,f1))),((proj (3,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff (p,f1,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (p,f1,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (p,f1,3)),(id REAL)) is set
K530((partdiff (p,f1,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (p,f1,1)) * <e1>) + ((partdiff (p,f1,2)) * <e2>)) + ((partdiff (p,f1,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (p,f1,1)) * <e1>) + ((partdiff (p,f1,2)) * <e2>)),((partdiff (p,f1,3)) * <e3>)) is V16() Function-like set
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f1,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f1,p,1) is V11() real ext-real Element of REAL
reproj (1,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,1)),(id REAL)) is set
K530((partdiff (f1,p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f1,p,2) is V11() real ext-real Element of REAL
reproj (2,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,2)),(id REAL)) is set
K530((partdiff (f1,p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f1,p,1)) * <e1>),((partdiff (f1,p,2)) * <e2>)) is V16() Function-like set
partdiff (f1,p,3) is V11() real ext-real Element of REAL
reproj (3,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,3)),(id REAL)) is set
K530((partdiff (f1,p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)) + ((partdiff (f1,p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)),((partdiff (f1,p,3)) * <e3>)) is V16() Function-like set
|[(partdiff (f1,p,1)),(partdiff (f1,p,2)),(partdiff (f1,p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,1)) * 1 is V11() real ext-real Element of REAL
(partdiff (f1,p,1)) * 0 is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) * 1),((partdiff (f1,p,1)) * 0),((partdiff (f1,p,1)) * 0)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,2)) * |[0,1,0]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,2))) * |[0,1,0]| is V16() complex-valued ext-real-valued real-valued FinSequence-like set
|[((partdiff (f1,p,1)) * 1),((partdiff (f1,p,1)) * 0),((partdiff (f1,p,1)) * 0)]| + ((partdiff (f1,p,2)) * |[0,1,0]|) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[((partdiff (f1,p,1)) * 1),((partdiff (f1,p,1)) * 0),((partdiff (f1,p,1)) * 0)]|,((partdiff (f1,p,2)) * |[0,1,0]|)) is V16() Function-like set
(partdiff (f1,p,3)) * |[0,0,1]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,3))) * |[0,0,1]| is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(|[((partdiff (f1,p,1)) * 1),((partdiff (f1,p,1)) * 0),((partdiff (f1,p,1)) * 0)]| + ((partdiff (f1,p,2)) * |[0,1,0]|)) + ((partdiff (f1,p,3)) * |[0,0,1]|) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(|[((partdiff (f1,p,1)) * 1),((partdiff (f1,p,1)) * 0),((partdiff (f1,p,1)) * 0)]| + ((partdiff (f1,p,2)) * |[0,1,0]|)),((partdiff (f1,p,3)) * |[0,0,1]|)) is V16() Function-like set
|[(partdiff (f1,p,1)),0,0]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,2)) * 0 is V11() real ext-real Element of REAL
(partdiff (f1,p,2)) * 1 is V11() real ext-real Element of REAL
|[((partdiff (f1,p,2)) * 0),((partdiff (f1,p,2)) * 1),((partdiff (f1,p,2)) * 0)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f1,p,1)),0,0]| + |[((partdiff (f1,p,2)) * 0),((partdiff (f1,p,2)) * 1),((partdiff (f1,p,2)) * 0)]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[(partdiff (f1,p,1)),0,0]|,|[((partdiff (f1,p,2)) * 0),((partdiff (f1,p,2)) * 1),((partdiff (f1,p,2)) * 0)]|) is V16() Function-like set
(|[(partdiff (f1,p,1)),0,0]| + |[((partdiff (f1,p,2)) * 0),((partdiff (f1,p,2)) * 1),((partdiff (f1,p,2)) * 0)]|) + ((partdiff (f1,p,3)) * |[0,0,1]|) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(|[(partdiff (f1,p,1)),0,0]| + |[((partdiff (f1,p,2)) * 0),((partdiff (f1,p,2)) * 1),((partdiff (f1,p,2)) * 0)]|),((partdiff (f1,p,3)) * |[0,0,1]|)) is V16() Function-like set
|[0,(partdiff (f1,p,2)),0]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f1,p,1)),0,0]| + |[0,(partdiff (f1,p,2)),0]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[(partdiff (f1,p,1)),0,0]|,|[0,(partdiff (f1,p,2)),0]|) is V16() Function-like set
(partdiff (f1,p,3)) * 0 is V11() real ext-real Element of REAL
(partdiff (f1,p,3)) * 1 is V11() real ext-real Element of REAL
|[((partdiff (f1,p,3)) * 0),((partdiff (f1,p,3)) * 0),((partdiff (f1,p,3)) * 1)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(|[(partdiff (f1,p,1)),0,0]| + |[0,(partdiff (f1,p,2)),0]|) + |[((partdiff (f1,p,3)) * 0),((partdiff (f1,p,3)) * 0),((partdiff (f1,p,3)) * 1)]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(|[(partdiff (f1,p,1)),0,0]| + |[0,(partdiff (f1,p,2)),0]|),|[((partdiff (f1,p,3)) * 0),((partdiff (f1,p,3)) * 0),((partdiff (f1,p,3)) * 1)]|) is V16() Function-like set
(partdiff (f1,p,1)) + 0 is V11() real ext-real Element of REAL
0 + (partdiff (f1,p,2)) is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
|[((partdiff (f1,p,1)) + 0),(0 + (partdiff (f1,p,2))),(0 + 0)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[0,0,(partdiff (f1,p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[((partdiff (f1,p,1)) + 0),(0 + (partdiff (f1,p,2))),(0 + 0)]| + |[0,0,(partdiff (f1,p,3))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[((partdiff (f1,p,1)) + 0),(0 + (partdiff (f1,p,2))),(0 + 0)]|,|[0,0,(partdiff (f1,p,3))]|) is V16() Function-like set
(partdiff (f1,p,2)) + 0 is V11() real ext-real Element of REAL
0 + (partdiff (f1,p,3)) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) + 0),((partdiff (f1,p,2)) + 0),(0 + (partdiff (f1,p,3)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f1,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f1,p,1) is V11() real ext-real Element of REAL
reproj (1,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,1)),(id REAL)) is set
K530((partdiff (f1,p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f1,p,2) is V11() real ext-real Element of REAL
reproj (2,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,2)),(id REAL)) is set
K530((partdiff (f1,p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f1,p,1)) * <e1>),((partdiff (f1,p,2)) * <e2>)) is V16() Function-like set
partdiff (f1,p,3) is V11() real ext-real Element of REAL
reproj (3,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,3)),(id REAL)) is set
K530((partdiff (f1,p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)) + ((partdiff (f1,p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)),((partdiff (f1,p,3)) * <e3>)) is V16() Function-like set
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 + f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
((f1 + f2),p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff ((f1 + f2),p,1) is V11() real ext-real Element of REAL
(f1 + f2) * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 + f2) * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff ((f1 + f2),p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 + f2),p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 + f2),p,1)),(id REAL)) is set
K530((partdiff ((f1 + f2),p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff ((f1 + f2),p,2) is V11() real ext-real Element of REAL
(f1 + f2) * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 + f2) * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff ((f1 + f2),p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 + f2),p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 + f2),p,2)),(id REAL)) is set
K530((partdiff ((f1 + f2),p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff ((f1 + f2),p,1)) * <e1>) + ((partdiff ((f1 + f2),p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff ((f1 + f2),p,1)) * <e1>),((partdiff ((f1 + f2),p,2)) * <e2>)) is V16() Function-like set
partdiff ((f1 + f2),p,3) is V11() real ext-real Element of REAL
(f1 + f2) * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 + f2) * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff ((f1 + f2),p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 + f2),p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 + f2),p,3)),(id REAL)) is set
K530((partdiff ((f1 + f2),p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff ((f1 + f2),p,1)) * <e1>) + ((partdiff ((f1 + f2),p,2)) * <e2>)) + ((partdiff ((f1 + f2),p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff ((f1 + f2),p,1)) * <e1>) + ((partdiff ((f1 + f2),p,2)) * <e2>)),((partdiff ((f1 + f2),p,3)) * <e3>)) is V16() Function-like set
(f2,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f2,p,1) is V11() real ext-real Element of REAL
f2 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f2,p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,1)),(id REAL)) is set
K530((partdiff (f2,p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f2,p,2) is V11() real ext-real Element of REAL
f2 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f2,p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,2)),(id REAL)) is set
K530((partdiff (f2,p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f2,p,1)) * <e1>),((partdiff (f2,p,2)) * <e2>)) is V16() Function-like set
partdiff (f2,p,3) is V11() real ext-real Element of REAL
f2 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f2,p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,3)),(id REAL)) is set
K530((partdiff (f2,p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>)) + ((partdiff (f2,p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>)),((partdiff (f2,p,3)) * <e3>)) is V16() Function-like set
(f1,p) + (f2,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(f1,p),(f2,p)) is V16() Function-like set
|[(partdiff ((f1 + f2),p,1)),(partdiff ((f1 + f2),p,2)),(partdiff ((f1 + f2),p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,1)) + (partdiff (f2,p,1)) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) + (partdiff (f2,p,1))),(partdiff ((f1 + f2),p,2)),(partdiff ((f1 + f2),p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,2)) + (partdiff (f2,p,2)) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) + (partdiff (f2,p,1))),((partdiff (f1,p,2)) + (partdiff (f2,p,2))),(partdiff ((f1 + f2),p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,3)) + (partdiff (f2,p,3)) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) + (partdiff (f2,p,1))),((partdiff (f1,p,2)) + (partdiff (f2,p,2))),((partdiff (f1,p,3)) + (partdiff (f2,p,3)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f1,p,1)),(partdiff (f1,p,2)),(partdiff (f1,p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f1,p,1)),(partdiff (f1,p,2)),(partdiff (f1,p,3))]| + |[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[(partdiff (f1,p,1)),(partdiff (f1,p,2)),(partdiff (f1,p,3))]|,|[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]|) is V16() Function-like set
(f1,p) + |[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(f1,p),|[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]|) is V16() Function-like set
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f1,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f1,p,1) is V11() real ext-real Element of REAL
reproj (1,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,1)),(id REAL)) is set
K530((partdiff (f1,p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f1,p,2) is V11() real ext-real Element of REAL
reproj (2,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,2)),(id REAL)) is set
K530((partdiff (f1,p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f1,p,1)) * <e1>),((partdiff (f1,p,2)) * <e2>)) is V16() Function-like set
partdiff (f1,p,3) is V11() real ext-real Element of REAL
reproj (3,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,3)),(id REAL)) is set
K530((partdiff (f1,p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)) + ((partdiff (f1,p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)),((partdiff (f1,p,3)) * <e3>)) is V16() Function-like set
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 - f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
- f2 is V16() V19( REAL 3) Function-like complex-valued ext-real-valued real-valued set
- 1 is V11() real ext-real non positive set
(- 1) * f2 is V16() V19( REAL 3) Function-like complex-valued ext-real-valued real-valued set
f1 + (- f2) is V16() V19( REAL 3) Function-like complex-valued ext-real-valued real-valued set
((f1 - f2),p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff ((f1 - f2),p,1) is V11() real ext-real Element of REAL
(f1 - f2) * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 - f2) * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff ((f1 - f2),p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 - f2),p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 - f2),p,1)),(id REAL)) is set
K530((partdiff ((f1 - f2),p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff ((f1 - f2),p,2) is V11() real ext-real Element of REAL
(f1 - f2) * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 - f2) * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff ((f1 - f2),p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 - f2),p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 - f2),p,2)),(id REAL)) is set
K530((partdiff ((f1 - f2),p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff ((f1 - f2),p,1)) * <e1>) + ((partdiff ((f1 - f2),p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff ((f1 - f2),p,1)) * <e1>),((partdiff ((f1 - f2),p,2)) * <e2>)) is V16() Function-like set
partdiff ((f1 - f2),p,3) is V11() real ext-real Element of REAL
(f1 - f2) * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 - f2) * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff ((f1 - f2),p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 - f2),p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 - f2),p,3)),(id REAL)) is set
K530((partdiff ((f1 - f2),p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff ((f1 - f2),p,1)) * <e1>) + ((partdiff ((f1 - f2),p,2)) * <e2>)) + ((partdiff ((f1 - f2),p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff ((f1 - f2),p,1)) * <e1>) + ((partdiff ((f1 - f2),p,2)) * <e2>)),((partdiff ((f1 - f2),p,3)) * <e3>)) is V16() Function-like set
(f2,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f2,p,1) is V11() real ext-real Element of REAL
f2 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f2,p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,1)),(id REAL)) is set
K530((partdiff (f2,p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f2,p,2) is V11() real ext-real Element of REAL
f2 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f2,p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,2)),(id REAL)) is set
K530((partdiff (f2,p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f2,p,1)) * <e1>),((partdiff (f2,p,2)) * <e2>)) is V16() Function-like set
partdiff (f2,p,3) is V11() real ext-real Element of REAL
f2 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f2,p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,3)),(id REAL)) is set
K530((partdiff (f2,p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>)) + ((partdiff (f2,p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>)),((partdiff (f2,p,3)) * <e3>)) is V16() Function-like set
(f1,p) - (f2,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
- (f2,p) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
(- 1) * (f2,p) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
K530((- 1)) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(- 1),(id REAL)) is set
K530((- 1)) * (f2,p) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
K493() is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K493() * (f2,p) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(f1,p) + (- (f2,p)) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
K229(K495(),(f1,p),(- (f2,p))) is V16() Function-like set
K496() is V16() V19(K7(REAL,REAL)) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(K7(REAL,REAL),REAL))
K517(REAL,K495(),(id REAL),K493()) is V16() V19(K7(REAL,REAL)) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(K7(REAL,REAL),REAL))
K229(K496(),(f1,p),(f2,p)) is V16() Function-like set
|[(partdiff ((f1 - f2),p,1)),(partdiff ((f1 - f2),p,2)),(partdiff ((f1 - f2),p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,1)) - (partdiff (f2,p,1)) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) - (partdiff (f2,p,1))),(partdiff ((f1 - f2),p,2)),(partdiff ((f1 - f2),p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,2)) - (partdiff (f2,p,2)) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) - (partdiff (f2,p,1))),((partdiff (f1,p,2)) - (partdiff (f2,p,2))),(partdiff ((f1 - f2),p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f1,p,3)) - (partdiff (f2,p,3)) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) - (partdiff (f2,p,1))),((partdiff (f1,p,2)) - (partdiff (f2,p,2))),((partdiff (f1,p,3)) - (partdiff (f2,p,3)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
- (partdiff (f2,p,1)) is V11() real ext-real Element of REAL
(partdiff (f1,p,1)) + (- (partdiff (f2,p,1))) is V11() real ext-real Element of REAL
- (partdiff (f2,p,2)) is V11() real ext-real Element of REAL
(partdiff (f1,p,2)) + (- (partdiff (f2,p,2))) is V11() real ext-real Element of REAL
- (partdiff (f2,p,3)) is V11() real ext-real Element of REAL
(partdiff (f1,p,3)) + (- (partdiff (f2,p,3))) is V11() real ext-real Element of REAL
|[((partdiff (f1,p,1)) + (- (partdiff (f2,p,1)))),((partdiff (f1,p,2)) + (- (partdiff (f2,p,2)))),((partdiff (f1,p,3)) + (- (partdiff (f2,p,3))))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f1,p,1)),(partdiff (f1,p,2)),(partdiff (f1,p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(- (partdiff (f2,p,1))),(- (partdiff (f2,p,2))),(- (partdiff (f2,p,3)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f1,p,1)),(partdiff (f1,p,2)),(partdiff (f1,p,3))]| + |[(- (partdiff (f2,p,1))),(- (partdiff (f2,p,2))),(- (partdiff (f2,p,3)))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[(partdiff (f1,p,1)),(partdiff (f1,p,2)),(partdiff (f1,p,3))]|,|[(- (partdiff (f2,p,1))),(- (partdiff (f2,p,2))),(- (partdiff (f2,p,3)))]|) is V16() Function-like set
- 1 is V11() real ext-real non positive Element of REAL
(- 1) * (partdiff (f2,p,1)) is V11() real ext-real Element of REAL
(- 1) * (partdiff (f2,p,2)) is V11() real ext-real Element of REAL
(- 1) * (partdiff (f2,p,3)) is V11() real ext-real Element of REAL
|[((- 1) * (partdiff (f2,p,1))),((- 1) * (partdiff (f2,p,2))),((- 1) * (partdiff (f2,p,3)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(f1,p) + |[((- 1) * (partdiff (f2,p,1))),((- 1) * (partdiff (f2,p,2))),((- 1) * (partdiff (f2,p,3)))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(f1,p),|[((- 1) * (partdiff (f2,p,1))),((- 1) * (partdiff (f2,p,2))),((- 1) * (partdiff (f2,p,3)))]|) is V16() Function-like set
|[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(- 1) * |[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((- 1)) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(- 1),(id REAL)) is set
K530((- 1)) * |[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]| is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(f1,p) + ((- 1) * |[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]|) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(f1,p),((- 1) * |[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]|)) is V16() Function-like set
p is V11() real ext-real Element of REAL
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
p (#) f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
((p (#) f2),f1) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff ((p (#) f2),f1,1) is V11() real ext-real Element of REAL
reproj (1,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
(p (#) f2) * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f1 is V11() real ext-real Element of REAL
diff (((p (#) f2) * (reproj (1,f1))),((proj (1,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f2),f1,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f2),f1,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f2),f1,1)),(id REAL)) is set
K530((partdiff ((p (#) f2),f1,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff ((p (#) f2),f1,2) is V11() real ext-real Element of REAL
reproj (2,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
(p (#) f2) * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f1 is V11() real ext-real Element of REAL
diff (((p (#) f2) * (reproj (2,f1))),((proj (2,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f2),f1,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f2),f1,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f2),f1,2)),(id REAL)) is set
K530((partdiff ((p (#) f2),f1,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff ((p (#) f2),f1,1)) * <e1>) + ((partdiff ((p (#) f2),f1,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff ((p (#) f2),f1,1)) * <e1>),((partdiff ((p (#) f2),f1,2)) * <e2>)) is V16() Function-like set
partdiff ((p (#) f2),f1,3) is V11() real ext-real Element of REAL
reproj (3,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
(p (#) f2) * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f1 is V11() real ext-real Element of REAL
diff (((p (#) f2) * (reproj (3,f1))),((proj (3,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f2),f1,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f2),f1,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f2),f1,3)),(id REAL)) is set
K530((partdiff ((p (#) f2),f1,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff ((p (#) f2),f1,1)) * <e1>) + ((partdiff ((p (#) f2),f1,2)) * <e2>)) + ((partdiff ((p (#) f2),f1,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff ((p (#) f2),f1,1)) * <e1>) + ((partdiff ((p (#) f2),f1,2)) * <e2>)),((partdiff ((p (#) f2),f1,3)) * <e3>)) is V16() Function-like set
(f2,f1) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f2,f1,1) is V11() real ext-real Element of REAL
f2 * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (1,f1))),((proj (1,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff (f2,f1,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,f1,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,f1,1)),(id REAL)) is set
K530((partdiff (f2,f1,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f2,f1,2) is V11() real ext-real Element of REAL
f2 * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (2,f1))),((proj (2,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff (f2,f1,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,f1,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,f1,2)),(id REAL)) is set
K530((partdiff (f2,f1,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f2,f1,1)) * <e1>) + ((partdiff (f2,f1,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f2,f1,1)) * <e1>),((partdiff (f2,f1,2)) * <e2>)) is V16() Function-like set
partdiff (f2,f1,3) is V11() real ext-real Element of REAL
f2 * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (3,f1))),((proj (3,3)) . f1)) is V11() real ext-real Element of REAL
(partdiff (f2,f1,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,f1,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,f1,3)),(id REAL)) is set
K530((partdiff (f2,f1,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f2,f1,1)) * <e1>) + ((partdiff (f2,f1,2)) * <e2>)) + ((partdiff (f2,f1,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f2,f1,1)) * <e1>) + ((partdiff (f2,f1,2)) * <e2>)),((partdiff (f2,f1,3)) * <e3>)) is V16() Function-like set
p * (f2,f1) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(p) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),p,(id REAL)) is set
K530(p) * (f2,f1) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
|[(partdiff ((p (#) f2),f1,1)),(partdiff ((p (#) f2),f1,2)),(partdiff ((p (#) f2),f1,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p * (partdiff (f2,f1,1)) is V11() real ext-real Element of REAL
|[(p * (partdiff (f2,f1,1))),(partdiff ((p (#) f2),f1,2)),(partdiff ((p (#) f2),f1,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p * (partdiff (f2,f1,2)) is V11() real ext-real Element of REAL
|[(p * (partdiff (f2,f1,1))),(p * (partdiff (f2,f1,2))),(partdiff ((p (#) f2),f1,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p * (partdiff (f2,f1,3)) is V11() real ext-real Element of REAL
|[(p * (partdiff (f2,f1,1))),(p * (partdiff (f2,f1,2))),(p * (partdiff (f2,f1,3)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(partdiff (f2,f1,1)),(partdiff (f2,f1,2)),(partdiff (f2,f1,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p * |[(partdiff (f2,f1,1)),(partdiff (f2,f1,2)),(partdiff (f2,f1,3))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(p) * |[(partdiff (f2,f1,1)),(partdiff (f2,f1,2)),(partdiff (f2,f1,3))]| is V16() complex-valued ext-real-valued real-valued FinSequence-like set
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
p (#) f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f3,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f3,f2,1) is V11() real ext-real Element of REAL
reproj (1,f2) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f3 * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f2 is V11() real ext-real Element of REAL
diff ((f3 * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (f3,f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f3,f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f3,f2,1)),(id REAL)) is set
K530((partdiff (f3,f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f3,f2,2) is V11() real ext-real Element of REAL
reproj (2,f2) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f3 * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f2 is V11() real ext-real Element of REAL
diff ((f3 * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (f3,f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f3,f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f3,f2,2)),(id REAL)) is set
K530((partdiff (f3,f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f3,f2,1)) * <e1>) + ((partdiff (f3,f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f3,f2,1)) * <e1>),((partdiff (f3,f2,2)) * <e2>)) is V16() Function-like set
partdiff (f3,f2,3) is V11() real ext-real Element of REAL
reproj (3,f2) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f3 * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f2 is V11() real ext-real Element of REAL
diff ((f3 * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (f3,f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f3,f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f3,f2,3)),(id REAL)) is set
K530((partdiff (f3,f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f3,f2,1)) * <e1>) + ((partdiff (f3,f2,2)) * <e2>)) + ((partdiff (f3,f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f3,f2,1)) * <e1>) + ((partdiff (f3,f2,2)) * <e2>)),((partdiff (f3,f2,3)) * <e3>)) is V16() Function-like set
p * (f3,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(p) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),p,(id REAL)) is set
K530(p) * (f3,f2) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 (#) g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(p (#) f3) + (f1 (#) g1) is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(((p (#) f3) + (f1 (#) g1)),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (((p (#) f3) + (f1 (#) g1)),f2,1) is V11() real ext-real Element of REAL
((p (#) f3) + (f1 (#) g1)) * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((((p (#) f3) + (f1 (#) g1)) * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (((p (#) f3) + (f1 (#) g1)),f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (((p (#) f3) + (f1 (#) g1)),f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (((p (#) f3) + (f1 (#) g1)),f2,1)),(id REAL)) is set
K530((partdiff (((p (#) f3) + (f1 (#) g1)),f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (((p (#) f3) + (f1 (#) g1)),f2,2) is V11() real ext-real Element of REAL
((p (#) f3) + (f1 (#) g1)) * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((((p (#) f3) + (f1 (#) g1)) * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (((p (#) f3) + (f1 (#) g1)),f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (((p (#) f3) + (f1 (#) g1)),f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (((p (#) f3) + (f1 (#) g1)),f2,2)),(id REAL)) is set
K530((partdiff (((p (#) f3) + (f1 (#) g1)),f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (((p (#) f3) + (f1 (#) g1)),f2,1)) * <e1>) + ((partdiff (((p (#) f3) + (f1 (#) g1)),f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (((p (#) f3) + (f1 (#) g1)),f2,1)) * <e1>),((partdiff (((p (#) f3) + (f1 (#) g1)),f2,2)) * <e2>)) is V16() Function-like set
partdiff (((p (#) f3) + (f1 (#) g1)),f2,3) is V11() real ext-real Element of REAL
((p (#) f3) + (f1 (#) g1)) * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((((p (#) f3) + (f1 (#) g1)) * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (((p (#) f3) + (f1 (#) g1)),f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (((p (#) f3) + (f1 (#) g1)),f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (((p (#) f3) + (f1 (#) g1)),f2,3)),(id REAL)) is set
K530((partdiff (((p (#) f3) + (f1 (#) g1)),f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (((p (#) f3) + (f1 (#) g1)),f2,1)) * <e1>) + ((partdiff (((p (#) f3) + (f1 (#) g1)),f2,2)) * <e2>)) + ((partdiff (((p (#) f3) + (f1 (#) g1)),f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (((p (#) f3) + (f1 (#) g1)),f2,1)) * <e1>) + ((partdiff (((p (#) f3) + (f1 (#) g1)),f2,2)) * <e2>)),((partdiff (((p (#) f3) + (f1 (#) g1)),f2,3)) * <e3>)) is V16() Function-like set
(g1,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (g1,f2,1) is V11() real ext-real Element of REAL
g1 * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g1 * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (g1,f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (g1,f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (g1,f2,1)),(id REAL)) is set
K530((partdiff (g1,f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (g1,f2,2) is V11() real ext-real Element of REAL
g1 * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g1 * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (g1,f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (g1,f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (g1,f2,2)),(id REAL)) is set
K530((partdiff (g1,f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (g1,f2,1)) * <e1>) + ((partdiff (g1,f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (g1,f2,1)) * <e1>),((partdiff (g1,f2,2)) * <e2>)) is V16() Function-like set
partdiff (g1,f2,3) is V11() real ext-real Element of REAL
g1 * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g1 * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (g1,f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (g1,f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (g1,f2,3)),(id REAL)) is set
K530((partdiff (g1,f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (g1,f2,1)) * <e1>) + ((partdiff (g1,f2,2)) * <e2>)) + ((partdiff (g1,f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (g1,f2,1)) * <e1>) + ((partdiff (g1,f2,2)) * <e2>)),((partdiff (g1,f2,3)) * <e3>)) is V16() Function-like set
f1 * (g1,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(f1) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),f1,(id REAL)) is set
K530(f1) * (g1,f2) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(p * (f3,f2)) + (f1 * (g1,f2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(p * (f3,f2)),(f1 * (g1,f2))) is V16() Function-like set
((p (#) f3),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff ((p (#) f3),f2,1) is V11() real ext-real Element of REAL
(p (#) f3) * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((p (#) f3) * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f3),f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f3),f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f3),f2,1)),(id REAL)) is set
K530((partdiff ((p (#) f3),f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff ((p (#) f3),f2,2) is V11() real ext-real Element of REAL
(p (#) f3) * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((p (#) f3) * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f3),f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f3),f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f3),f2,2)),(id REAL)) is set
K530((partdiff ((p (#) f3),f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff ((p (#) f3),f2,1)) * <e1>) + ((partdiff ((p (#) f3),f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff ((p (#) f3),f2,1)) * <e1>),((partdiff ((p (#) f3),f2,2)) * <e2>)) is V16() Function-like set
partdiff ((p (#) f3),f2,3) is V11() real ext-real Element of REAL
(p (#) f3) * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((p (#) f3) * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f3),f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f3),f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f3),f2,3)),(id REAL)) is set
K530((partdiff ((p (#) f3),f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff ((p (#) f3),f2,1)) * <e1>) + ((partdiff ((p (#) f3),f2,2)) * <e2>)) + ((partdiff ((p (#) f3),f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff ((p (#) f3),f2,1)) * <e1>) + ((partdiff ((p (#) f3),f2,2)) * <e2>)),((partdiff ((p (#) f3),f2,3)) * <e3>)) is V16() Function-like set
((f1 (#) g1),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff ((f1 (#) g1),f2,1) is V11() real ext-real Element of REAL
(f1 (#) g1) * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 (#) g1) * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((f1 (#) g1),f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 (#) g1),f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 (#) g1),f2,1)),(id REAL)) is set
K530((partdiff ((f1 (#) g1),f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff ((f1 (#) g1),f2,2) is V11() real ext-real Element of REAL
(f1 (#) g1) * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 (#) g1) * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((f1 (#) g1),f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 (#) g1),f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 (#) g1),f2,2)),(id REAL)) is set
K530((partdiff ((f1 (#) g1),f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff ((f1 (#) g1),f2,1)) * <e1>) + ((partdiff ((f1 (#) g1),f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff ((f1 (#) g1),f2,1)) * <e1>),((partdiff ((f1 (#) g1),f2,2)) * <e2>)) is V16() Function-like set
partdiff ((f1 (#) g1),f2,3) is V11() real ext-real Element of REAL
(f1 (#) g1) * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 (#) g1) * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((f1 (#) g1),f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 (#) g1),f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 (#) g1),f2,3)),(id REAL)) is set
K530((partdiff ((f1 (#) g1),f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff ((f1 (#) g1),f2,1)) * <e1>) + ((partdiff ((f1 (#) g1),f2,2)) * <e2>)) + ((partdiff ((f1 (#) g1),f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff ((f1 (#) g1),f2,1)) * <e1>) + ((partdiff ((f1 (#) g1),f2,2)) * <e2>)),((partdiff ((f1 (#) g1),f2,3)) * <e3>)) is V16() Function-like set
((p (#) f3),f2) + ((f1 (#) g1),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((p (#) f3),f2),((f1 (#) g1),f2)) is V16() Function-like set
(p * (f3,f2)) + ((f1 (#) g1),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(p * (f3,f2)),((f1 (#) g1),f2)) is V16() Function-like set
p is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f2 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
p (#) f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f3,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f3,f2,1) is V11() real ext-real Element of REAL
reproj (1,f2) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f3 * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f2 is V11() real ext-real Element of REAL
diff ((f3 * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (f3,f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f3,f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f3,f2,1)),(id REAL)) is set
K530((partdiff (f3,f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f3,f2,2) is V11() real ext-real Element of REAL
reproj (2,f2) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f3 * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f2 is V11() real ext-real Element of REAL
diff ((f3 * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (f3,f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f3,f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f3,f2,2)),(id REAL)) is set
K530((partdiff (f3,f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f3,f2,1)) * <e1>) + ((partdiff (f3,f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f3,f2,1)) * <e1>),((partdiff (f3,f2,2)) * <e2>)) is V16() Function-like set
partdiff (f3,f2,3) is V11() real ext-real Element of REAL
reproj (3,f2) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f3 * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f2 is V11() real ext-real Element of REAL
diff ((f3 * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (f3,f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f3,f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f3,f2,3)),(id REAL)) is set
K530((partdiff (f3,f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f3,f2,1)) * <e1>) + ((partdiff (f3,f2,2)) * <e2>)) + ((partdiff (f3,f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f3,f2,1)) * <e1>) + ((partdiff (f3,f2,2)) * <e2>)),((partdiff (f3,f2,3)) * <e3>)) is V16() Function-like set
p * (f3,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(p) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),p,(id REAL)) is set
K530(p) * (f3,f2) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 (#) g1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(p (#) f3) - (f1 (#) g1) is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
- (f1 (#) g1) is V16() V19( REAL 3) Function-like complex-valued ext-real-valued real-valued set
- 1 is V11() real ext-real non positive set
(- 1) * (f1 (#) g1) is V16() V19( REAL 3) Function-like complex-valued ext-real-valued real-valued set
(p (#) f3) + (- (f1 (#) g1)) is V16() V19( REAL 3) Function-like complex-valued ext-real-valued real-valued set
(((p (#) f3) - (f1 (#) g1)),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (((p (#) f3) - (f1 (#) g1)),f2,1) is V11() real ext-real Element of REAL
((p (#) f3) - (f1 (#) g1)) * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((((p (#) f3) - (f1 (#) g1)) * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (((p (#) f3) - (f1 (#) g1)),f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (((p (#) f3) - (f1 (#) g1)),f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (((p (#) f3) - (f1 (#) g1)),f2,1)),(id REAL)) is set
K530((partdiff (((p (#) f3) - (f1 (#) g1)),f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (((p (#) f3) - (f1 (#) g1)),f2,2) is V11() real ext-real Element of REAL
((p (#) f3) - (f1 (#) g1)) * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((((p (#) f3) - (f1 (#) g1)) * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (((p (#) f3) - (f1 (#) g1)),f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (((p (#) f3) - (f1 (#) g1)),f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (((p (#) f3) - (f1 (#) g1)),f2,2)),(id REAL)) is set
K530((partdiff (((p (#) f3) - (f1 (#) g1)),f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (((p (#) f3) - (f1 (#) g1)),f2,1)) * <e1>) + ((partdiff (((p (#) f3) - (f1 (#) g1)),f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (((p (#) f3) - (f1 (#) g1)),f2,1)) * <e1>),((partdiff (((p (#) f3) - (f1 (#) g1)),f2,2)) * <e2>)) is V16() Function-like set
partdiff (((p (#) f3) - (f1 (#) g1)),f2,3) is V11() real ext-real Element of REAL
((p (#) f3) - (f1 (#) g1)) * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((((p (#) f3) - (f1 (#) g1)) * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (((p (#) f3) - (f1 (#) g1)),f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (((p (#) f3) - (f1 (#) g1)),f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (((p (#) f3) - (f1 (#) g1)),f2,3)),(id REAL)) is set
K530((partdiff (((p (#) f3) - (f1 (#) g1)),f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (((p (#) f3) - (f1 (#) g1)),f2,1)) * <e1>) + ((partdiff (((p (#) f3) - (f1 (#) g1)),f2,2)) * <e2>)) + ((partdiff (((p (#) f3) - (f1 (#) g1)),f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (((p (#) f3) - (f1 (#) g1)),f2,1)) * <e1>) + ((partdiff (((p (#) f3) - (f1 (#) g1)),f2,2)) * <e2>)),((partdiff (((p (#) f3) - (f1 (#) g1)),f2,3)) * <e3>)) is V16() Function-like set
(g1,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (g1,f2,1) is V11() real ext-real Element of REAL
g1 * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g1 * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (g1,f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (g1,f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (g1,f2,1)),(id REAL)) is set
K530((partdiff (g1,f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (g1,f2,2) is V11() real ext-real Element of REAL
g1 * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g1 * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (g1,f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (g1,f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (g1,f2,2)),(id REAL)) is set
K530((partdiff (g1,f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (g1,f2,1)) * <e1>) + ((partdiff (g1,f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (g1,f2,1)) * <e1>),((partdiff (g1,f2,2)) * <e2>)) is V16() Function-like set
partdiff (g1,f2,3) is V11() real ext-real Element of REAL
g1 * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((g1 * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff (g1,f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (g1,f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (g1,f2,3)),(id REAL)) is set
K530((partdiff (g1,f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (g1,f2,1)) * <e1>) + ((partdiff (g1,f2,2)) * <e2>)) + ((partdiff (g1,f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (g1,f2,1)) * <e1>) + ((partdiff (g1,f2,2)) * <e2>)),((partdiff (g1,f2,3)) * <e3>)) is V16() Function-like set
f1 * (g1,f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(f1) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),f1,(id REAL)) is set
K530(f1) * (g1,f2) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(p * (f3,f2)) - (f1 * (g1,f2)) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
- (f1 * (g1,f2)) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
(- 1) * (f1 * (g1,f2)) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
K530((- 1)) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(- 1),(id REAL)) is set
K530((- 1)) * (f1 * (g1,f2)) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
K493() is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K493() * (f1 * (g1,f2)) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(p * (f3,f2)) + (- (f1 * (g1,f2))) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
K229(K495(),(p * (f3,f2)),(- (f1 * (g1,f2)))) is V16() Function-like set
K496() is V16() V19(K7(REAL,REAL)) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(K7(REAL,REAL),REAL))
K517(REAL,K495(),(id REAL),K493()) is V16() V19(K7(REAL,REAL)) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(K7(REAL,REAL),REAL))
K229(K496(),(p * (f3,f2)),(f1 * (g1,f2))) is V16() Function-like set
((p (#) f3),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff ((p (#) f3),f2,1) is V11() real ext-real Element of REAL
(p (#) f3) * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((p (#) f3) * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f3),f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f3),f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f3),f2,1)),(id REAL)) is set
K530((partdiff ((p (#) f3),f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff ((p (#) f3),f2,2) is V11() real ext-real Element of REAL
(p (#) f3) * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((p (#) f3) * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f3),f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f3),f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f3),f2,2)),(id REAL)) is set
K530((partdiff ((p (#) f3),f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff ((p (#) f3),f2,1)) * <e1>) + ((partdiff ((p (#) f3),f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff ((p (#) f3),f2,1)) * <e1>),((partdiff ((p (#) f3),f2,2)) * <e2>)) is V16() Function-like set
partdiff ((p (#) f3),f2,3) is V11() real ext-real Element of REAL
(p (#) f3) * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((p (#) f3) * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((p (#) f3),f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((p (#) f3),f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((p (#) f3),f2,3)),(id REAL)) is set
K530((partdiff ((p (#) f3),f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff ((p (#) f3),f2,1)) * <e1>) + ((partdiff ((p (#) f3),f2,2)) * <e2>)) + ((partdiff ((p (#) f3),f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff ((p (#) f3),f2,1)) * <e1>) + ((partdiff ((p (#) f3),f2,2)) * <e2>)),((partdiff ((p (#) f3),f2,3)) * <e3>)) is V16() Function-like set
((f1 (#) g1),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff ((f1 (#) g1),f2,1) is V11() real ext-real Element of REAL
(f1 (#) g1) * (reproj (1,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 (#) g1) * (reproj (1,f2))),((proj (1,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((f1 (#) g1),f2,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 (#) g1),f2,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 (#) g1),f2,1)),(id REAL)) is set
K530((partdiff ((f1 (#) g1),f2,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff ((f1 (#) g1),f2,2) is V11() real ext-real Element of REAL
(f1 (#) g1) * (reproj (2,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 (#) g1) * (reproj (2,f2))),((proj (2,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((f1 (#) g1),f2,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 (#) g1),f2,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 (#) g1),f2,2)),(id REAL)) is set
K530((partdiff ((f1 (#) g1),f2,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff ((f1 (#) g1),f2,1)) * <e1>) + ((partdiff ((f1 (#) g1),f2,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff ((f1 (#) g1),f2,1)) * <e1>),((partdiff ((f1 (#) g1),f2,2)) * <e2>)) is V16() Function-like set
partdiff ((f1 (#) g1),f2,3) is V11() real ext-real Element of REAL
(f1 (#) g1) * (reproj (3,f2)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff (((f1 (#) g1) * (reproj (3,f2))),((proj (3,3)) . f2)) is V11() real ext-real Element of REAL
(partdiff ((f1 (#) g1),f2,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff ((f1 (#) g1),f2,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff ((f1 (#) g1),f2,3)),(id REAL)) is set
K530((partdiff ((f1 (#) g1),f2,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff ((f1 (#) g1),f2,1)) * <e1>) + ((partdiff ((f1 (#) g1),f2,2)) * <e2>)) + ((partdiff ((f1 (#) g1),f2,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff ((f1 (#) g1),f2,1)) * <e1>) + ((partdiff ((f1 (#) g1),f2,2)) * <e2>)),((partdiff ((f1 (#) g1),f2,3)) * <e3>)) is V16() Function-like set
((p (#) f3),f2) - ((f1 (#) g1),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
- ((f1 (#) g1),f2) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
(- 1) * ((f1 (#) g1),f2) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
K530((- 1)) * ((f1 (#) g1),f2) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
K493() * ((f1 (#) g1),f2) is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((p (#) f3),f2) + (- ((f1 (#) g1),f2)) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
K229(K495(),((p (#) f3),f2),(- ((f1 (#) g1),f2))) is V16() Function-like set
K229(K496(),((p (#) f3),f2),((f1 (#) g1),f2)) is V16() Function-like set
(p * (f3,f2)) - ((f1 (#) g1),f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(p * (f3,f2)) + (- ((f1 (#) g1),f2)) is V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like set
K229(K495(),(p * (f3,f2)),(- ((f1 (#) g1),f2))) is V16() Function-like set
K229(K496(),(p * (f3,f2)),((f1 (#) g1),f2)) is V16() Function-like set
0.REAL 3 is real-valued V61(3) FinSequence-like Element of the U1 of (TOP-REAL 3)
TOP-REAL 3 is V66() V92() V117() V118() V119() V120() V121() V122() V123() V172() V202() V210() L20()
the U1 of (TOP-REAL 3) is set
3 |-> 0 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like Element of 3 -tuples_on REAL
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f1,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f1,p,1) is V11() real ext-real Element of REAL
reproj (1,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,1)),(id REAL)) is set
K530((partdiff (f1,p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f1,p,2) is V11() real ext-real Element of REAL
reproj (2,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,2)),(id REAL)) is set
K530((partdiff (f1,p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f1,p,1)) * <e1>),((partdiff (f1,p,2)) * <e2>)) is V16() Function-like set
partdiff (f1,p,3) is V11() real ext-real Element of REAL
reproj (3,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f1,p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f1,p,3)),(id REAL)) is set
K530((partdiff (f1,p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)) + ((partdiff (f1,p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f1,p,1)) * <e1>) + ((partdiff (f1,p,2)) * <e2>)),((partdiff (f1,p,3)) * <e3>)) is V16() Function-like set
dom f1 is functional FinSequence-membered Element of K6((REAL 3))
[#] REAL is closed open V160() V161() V162() Element of K6(REAL)
f3 is V11() real ext-real Element of REAL
g1 is V11() real ext-real Element of REAL
dom (f1 * (reproj (1,p))) is V160() V161() V162() Element of K6(REAL)
(f1 * (reproj (1,p))) . g1 is V11() real ext-real Element of REAL
(reproj (1,p)) . g1 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 . ((reproj (1,p)) . g1) is V11() real ext-real Element of REAL
f2 is open V160() V161() V162() Element of K6(REAL)
(f1 * (reproj (1,p))) | f2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
g2 is V11() real ext-real Element of REAL
diff ((f1 * (reproj (1,p))),g2) is V11() real ext-real Element of REAL
(f1 * (reproj (1,p))) `| f2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
((f1 * (reproj (1,p))) `| f2) . g2 is V11() real ext-real Element of REAL
g2 is V11() real ext-real Element of REAL
dom (f1 * (reproj (2,p))) is V160() V161() V162() Element of K6(REAL)
(f1 * (reproj (2,p))) . g2 is V11() real ext-real Element of REAL
(reproj (2,p)) . g2 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 . ((reproj (2,p)) . g2) is V11() real ext-real Element of REAL
(f1 * (reproj (2,p))) | f2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(f1 * (reproj (2,p))) `| f2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
g3 is V11() real ext-real Element of REAL
((f1 * (reproj (2,p))) `| f2) . g3 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
diff ((f1 * (reproj (2,p))),g3) is V11() real ext-real Element of REAL
((f1 * (reproj (2,p))) `| f2) . g3 is V11() real ext-real Element of REAL
g3 is V11() real ext-real Element of REAL
dom (f1 * (reproj (3,p))) is V160() V161() V162() Element of K6(REAL)
(f1 * (reproj (3,p))) . g3 is V11() real ext-real Element of REAL
(reproj (3,p)) . g3 is V16() V19( NAT ) Function-like V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 . ((reproj (3,p)) . g3) is V11() real ext-real Element of REAL
(f1 * (reproj (3,p))) | f2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(f1 * (reproj (3,p))) `| f2 is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
z is V11() real ext-real Element of REAL
((f1 * (reproj (3,p))) `| f2) . z is V11() real ext-real Element of REAL
z is V11() real ext-real Element of REAL
diff ((f1 * (reproj (3,p))),z) is V11() real ext-real Element of REAL
((f1 * (reproj (3,p))) `| f2) . z is V11() real ext-real Element of REAL
|[0,0,0]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p . 1 is V11() real ext-real Element of REAL
(p . 1) ^2 is V11() real ext-real Element of REAL
p . 2 is V11() real ext-real Element of REAL
(p . 2) ^2 is V11() real ext-real Element of REAL
((p . 1) ^2) + ((p . 2) ^2) is V11() real ext-real Element of REAL
p . 3 is V11() real ext-real Element of REAL
(p . 3) ^2 is V11() real ext-real Element of REAL
(((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2) is V11() real ext-real Element of REAL
sqrt ((((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2)) is V11() real ext-real Element of REAL
(p . 1) / (sqrt ((((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2))) is V11() real ext-real Element of REAL
(p . 2) / (sqrt ((((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2))) is V11() real ext-real Element of REAL
(p . 3) / (sqrt ((((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2))) is V11() real ext-real Element of REAL
|[((p . 1) / (sqrt ((((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2)))),((p . 2) / (sqrt ((((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2)))),((p . 3) / (sqrt ((((p . 1) ^2) + ((p . 2) ^2)) + ((p . 3) ^2))))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (p,f1,1) is V11() real ext-real Element of REAL
reproj (1,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (1,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f1 is V11() real ext-real Element of REAL
diff ((p * (reproj (1,f1))),((proj (1,3)) . f1)) is V11() real ext-real Element of REAL
f2 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(f2) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 . 1 is V11() real ext-real Element of REAL
(f2 . 1) ^2 is V11() real ext-real Element of REAL
f2 . 2 is V11() real ext-real Element of REAL
(f2 . 2) ^2 is V11() real ext-real Element of REAL
((f2 . 1) ^2) + ((f2 . 2) ^2) is V11() real ext-real Element of REAL
f2 . 3 is V11() real ext-real Element of REAL
(f2 . 3) ^2 is V11() real ext-real Element of REAL
(((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2) is V11() real ext-real Element of REAL
sqrt ((((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2)) is V11() real ext-real Element of REAL
(f2 . 1) / (sqrt ((((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2))) is V11() real ext-real Element of REAL
(f2 . 2) / (sqrt ((((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2))) is V11() real ext-real Element of REAL
(f2 . 3) / (sqrt ((((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2))) is V11() real ext-real Element of REAL
|[((f2 . 1) / (sqrt ((((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2)))),((f2 . 2) / (sqrt ((((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2)))),((f2 . 3) / (sqrt ((((f2 . 1) ^2) + ((f2 . 2) ^2)) + ((f2 . 3) ^2))))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(f2) . 1 is V11() real ext-real Element of REAL
(partdiff (p,f1,1)) * ((f2) . 1) is V11() real ext-real Element of REAL
partdiff (p,f1,2) is V11() real ext-real Element of REAL
reproj (2,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (2,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f1 is V11() real ext-real Element of REAL
diff ((p * (reproj (2,f1))),((proj (2,3)) . f1)) is V11() real ext-real Element of REAL
(f2) . 2 is V11() real ext-real Element of REAL
(partdiff (p,f1,2)) * ((f2) . 2) is V11() real ext-real Element of REAL
((partdiff (p,f1,1)) * ((f2) . 1)) + ((partdiff (p,f1,2)) * ((f2) . 2)) is V11() real ext-real Element of REAL
partdiff (p,f1,3) is V11() real ext-real Element of REAL
reproj (3,f1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
p * (reproj (3,f1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f1 is V11() real ext-real Element of REAL
diff ((p * (reproj (3,f1))),((proj (3,3)) . f1)) is V11() real ext-real Element of REAL
(f2) . 3 is V11() real ext-real Element of REAL
(partdiff (p,f1,3)) * ((f2) . 3) is V11() real ext-real Element of REAL
(((partdiff (p,f1,1)) * ((f2) . 1)) + ((partdiff (p,f1,2)) * ((f2) . 2))) + ((partdiff (p,f1,3)) * ((f2) . 3)) is V11() real ext-real Element of REAL
p is V11() real ext-real Element of REAL
p ^2 is V11() real ext-real Element of REAL
f1 is V11() real ext-real Element of REAL
f1 ^2 is V11() real ext-real Element of REAL
(p ^2) + (f1 ^2) is V11() real ext-real Element of REAL
f2 is V11() real ext-real Element of REAL
<*p,f1,f2*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
f2 ^2 is V11() real ext-real Element of REAL
((p ^2) + (f1 ^2)) + (f2 ^2) is V11() real ext-real Element of REAL
sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)) is V11() real ext-real Element of REAL
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(g2,g1,f3) is V11() real ext-real Element of REAL
partdiff (g2,g1,1) is V11() real ext-real Element of REAL
reproj (1,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (1,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . g1 is V11() real ext-real Element of REAL
diff ((g2 * (reproj (1,g1))),((proj (1,3)) . g1)) is V11() real ext-real Element of REAL
(f3) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f3 . 1 is V11() real ext-real Element of REAL
(f3 . 1) ^2 is V11() real ext-real Element of REAL
f3 . 2 is V11() real ext-real Element of REAL
(f3 . 2) ^2 is V11() real ext-real Element of REAL
((f3 . 1) ^2) + ((f3 . 2) ^2) is V11() real ext-real Element of REAL
f3 . 3 is V11() real ext-real Element of REAL
(f3 . 3) ^2 is V11() real ext-real Element of REAL
(((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2) is V11() real ext-real Element of REAL
sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)) is V11() real ext-real Element of REAL
(f3 . 1) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))) is V11() real ext-real Element of REAL
(f3 . 2) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))) is V11() real ext-real Element of REAL
(f3 . 3) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))) is V11() real ext-real Element of REAL
|[((f3 . 1) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))),((f3 . 2) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))),((f3 . 3) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(f3) . 1 is V11() real ext-real Element of REAL
(partdiff (g2,g1,1)) * ((f3) . 1) is V11() real ext-real Element of REAL
partdiff (g2,g1,2) is V11() real ext-real Element of REAL
reproj (2,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (2,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . g1 is V11() real ext-real Element of REAL
diff ((g2 * (reproj (2,g1))),((proj (2,3)) . g1)) is V11() real ext-real Element of REAL
(f3) . 2 is V11() real ext-real Element of REAL
(partdiff (g2,g1,2)) * ((f3) . 2) is V11() real ext-real Element of REAL
((partdiff (g2,g1,1)) * ((f3) . 1)) + ((partdiff (g2,g1,2)) * ((f3) . 2)) is V11() real ext-real Element of REAL
partdiff (g2,g1,3) is V11() real ext-real Element of REAL
reproj (3,g1) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
g2 * (reproj (3,g1)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . g1 is V11() real ext-real Element of REAL
diff ((g2 * (reproj (3,g1))),((proj (3,3)) . g1)) is V11() real ext-real Element of REAL
(f3) . 3 is V11() real ext-real Element of REAL
(partdiff (g2,g1,3)) * ((f3) . 3) is V11() real ext-real Element of REAL
(((partdiff (g2,g1,1)) * ((f3) . 1)) + ((partdiff (g2,g1,2)) * ((f3) . 2))) + ((partdiff (g2,g1,3)) * ((f3) . 3)) is V11() real ext-real Element of REAL
(partdiff (g2,g1,1)) * p is V11() real ext-real Element of REAL
((partdiff (g2,g1,1)) * p) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2))) is V11() real ext-real Element of REAL
(partdiff (g2,g1,2)) * f1 is V11() real ext-real Element of REAL
((partdiff (g2,g1,2)) * f1) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2))) is V11() real ext-real Element of REAL
(((partdiff (g2,g1,1)) * p) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)))) + (((partdiff (g2,g1,2)) * f1) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)))) is V11() real ext-real Element of REAL
(partdiff (g2,g1,3)) * f2 is V11() real ext-real Element of REAL
((partdiff (g2,g1,3)) * f2) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2))) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * p) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)))) + (((partdiff (g2,g1,2)) * f1) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2))))) + (((partdiff (g2,g1,3)) * f2) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)))) is V11() real ext-real Element of REAL
(p ^2) + ((f3 . 2) ^2) is V11() real ext-real Element of REAL
((p ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2) is V11() real ext-real Element of REAL
sqrt (((p ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)) is V11() real ext-real Element of REAL
((p ^2) + (f1 ^2)) + ((f3 . 3) ^2) is V11() real ext-real Element of REAL
sqrt (((p ^2) + (f1 ^2)) + ((f3 . 3) ^2)) is V11() real ext-real Element of REAL
(partdiff (g2,g1,1)) * ((f3 . 1) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
((partdiff (g2,g1,1)) * ((f3 . 1) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) + ((partdiff (g2,g1,2)) * ((f3) . 2)) is V11() real ext-real Element of REAL
(((partdiff (g2,g1,1)) * ((f3 . 1) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) + ((partdiff (g2,g1,2)) * ((f3) . 2))) + ((partdiff (g2,g1,3)) * ((f3) . 3)) is V11() real ext-real Element of REAL
(partdiff (g2,g1,1)) * (f3 . 1) is V11() real ext-real Element of REAL
((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))) is V11() real ext-real Element of REAL
(((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + ((partdiff (g2,g1,2)) * ((f3) . 2)) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + ((partdiff (g2,g1,2)) * ((f3) . 2))) + ((partdiff (g2,g1,3)) * ((f3) . 3)) is V11() real ext-real Element of REAL
(partdiff (g2,g1,2)) * ((f3 . 2) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
(((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + ((partdiff (g2,g1,2)) * ((f3 . 2) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + ((partdiff (g2,g1,2)) * ((f3 . 2) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))))) + ((partdiff (g2,g1,3)) * ((f3) . 3)) is V11() real ext-real Element of REAL
(partdiff (g2,g1,2)) * (f3 . 2) is V11() real ext-real Element of REAL
((partdiff (g2,g1,2)) * (f3 . 2)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))) is V11() real ext-real Element of REAL
(((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + (((partdiff (g2,g1,2)) * (f3 . 2)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + (((partdiff (g2,g1,2)) * (f3 . 2)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) + ((partdiff (g2,g1,3)) * ((f3) . 3)) is V11() real ext-real Element of REAL
(partdiff (g2,g1,3)) * ((f3 . 3) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + (((partdiff (g2,g1,2)) * (f3 . 2)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) + ((partdiff (g2,g1,3)) * ((f3 . 3) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) is V11() real ext-real Element of REAL
(partdiff (g2,g1,3)) * (f3 . 3) is V11() real ext-real Element of REAL
((partdiff (g2,g1,3)) * (f3 . 3)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * (f3 . 1)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) + (((partdiff (g2,g1,2)) * (f3 . 2)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) + (((partdiff (g2,g1,3)) * (f3 . 3)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
(((partdiff (g2,g1,1)) * p) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)))) + (((partdiff (g2,g1,2)) * (f3 . 2)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * p) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)))) + (((partdiff (g2,g1,2)) * (f3 . 2)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2))))) + (((partdiff (g2,g1,3)) * (f3 . 3)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
((((partdiff (g2,g1,1)) * p) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2)))) + (((partdiff (g2,g1,2)) * f1) / (sqrt (((p ^2) + (f1 ^2)) + (f2 ^2))))) + (((partdiff (g2,g1,3)) * (f3 . 3)) / (sqrt ((((f3 . 1) ^2) + ((f3 . 2) ^2)) + ((f3 . 3) ^2)))) is V11() real ext-real Element of REAL
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(f1) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 . 1 is V11() real ext-real Element of REAL
(f1 . 1) ^2 is V11() real ext-real Element of REAL
f1 . 2 is V11() real ext-real Element of REAL
(f1 . 2) ^2 is V11() real ext-real Element of REAL
((f1 . 1) ^2) + ((f1 . 2) ^2) is V11() real ext-real Element of REAL
f1 . 3 is V11() real ext-real Element of REAL
(f1 . 3) ^2 is V11() real ext-real Element of REAL
(((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2) is V11() real ext-real Element of REAL
sqrt ((((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2)) is V11() real ext-real Element of REAL
(f1 . 1) / (sqrt ((((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2))) is V11() real ext-real Element of REAL
(f1 . 2) / (sqrt ((((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2))) is V11() real ext-real Element of REAL
(f1 . 3) / (sqrt ((((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2))) is V11() real ext-real Element of REAL
|[((f1 . 1) / (sqrt ((((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2)))),((f1 . 2) / (sqrt ((((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2)))),((f1 . 3) / (sqrt ((((f1 . 1) ^2) + ((f1 . 2) ^2)) + ((f1 . 3) ^2))))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f2,p,f1) is V11() real ext-real Element of REAL
partdiff (f2,p,1) is V11() real ext-real Element of REAL
reproj (1,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f2 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . p is V11() real ext-real Element of REAL
diff ((f2 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(f1) . 1 is V11() real ext-real Element of REAL
(partdiff (f2,p,1)) * ((f1) . 1) is V11() real ext-real Element of REAL
partdiff (f2,p,2) is V11() real ext-real Element of REAL
reproj (2,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f2 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . p is V11() real ext-real Element of REAL
diff ((f2 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(f1) . 2 is V11() real ext-real Element of REAL
(partdiff (f2,p,2)) * ((f1) . 2) is V11() real ext-real Element of REAL
((partdiff (f2,p,1)) * ((f1) . 1)) + ((partdiff (f2,p,2)) * ((f1) . 2)) is V11() real ext-real Element of REAL
partdiff (f2,p,3) is V11() real ext-real Element of REAL
reproj (3,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f2 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . p is V11() real ext-real Element of REAL
diff ((f2 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
(f1) . 3 is V11() real ext-real Element of REAL
(partdiff (f2,p,3)) * ((f1) . 3) is V11() real ext-real Element of REAL
(((partdiff (f2,p,1)) * ((f1) . 1)) + ((partdiff (f2,p,2)) * ((f1) . 2))) + ((partdiff (f2,p,3)) * ((f1) . 3)) is V11() real ext-real Element of REAL
(f2,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(partdiff (f2,p,1)) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,1))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,1)),(id REAL)) is set
K530((partdiff (f2,p,1))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(partdiff (f2,p,2)) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,2))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,2)),(id REAL)) is set
K530((partdiff (f2,p,2))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((partdiff (f2,p,1)) * <e1>),((partdiff (f2,p,2)) * <e2>)) is V16() Function-like set
(partdiff (f2,p,3)) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530((partdiff (f2,p,3))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),(partdiff (f2,p,3)),(id REAL)) is set
K530((partdiff (f2,p,3))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>)) + ((partdiff (f2,p,3)) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f2,p,1)) * <e1>) + ((partdiff (f2,p,2)) * <e2>)),((partdiff (f2,p,3)) * <e3>)) is V16() Function-like set
|((f2,p),(f1))| is V11() real ext-real Element of REAL
mlt ((f2,p),(f1)) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like FinSequence of REAL
K229(K497(),(f2,p),(f1)) is V16() Function-like set
Sum (mlt ((f2,p),(f1))) is V11() real ext-real Element of REAL
g1 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like FinSequence of REAL
len g1 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
(f2,p) . 1 is V11() real ext-real Element of REAL
(f2,p) . 2 is V11() real ext-real Element of REAL
(f2,p) . 3 is V11() real ext-real Element of REAL
<*((f2,p) . 1),((f2,p) . 2),((f2,p) . 3)*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
len <*((f2,p) . 1),((f2,p) . 2),((f2,p) . 3)*> is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
g2 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() FinSequence-like FinSubsequence-like FinSequence of REAL
len g2 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
|[(partdiff (f2,p,1)),(partdiff (f2,p,2)),(partdiff (f2,p,3))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
g1 . 1 is V11() real ext-real Element of REAL
g2 . 1 is V11() real ext-real Element of REAL
(g1 . 1) * (g2 . 1) is V11() real ext-real Element of REAL
g1 . 2 is V11() real ext-real Element of REAL
g2 . 2 is V11() real ext-real Element of REAL
(g1 . 2) * (g2 . 2) is V11() real ext-real Element of REAL
g1 . 3 is V11() real ext-real Element of REAL
g2 . 3 is V11() real ext-real Element of REAL
(g1 . 3) * (g2 . 3) is V11() real ext-real Element of REAL
<*((g1 . 1) * (g2 . 1)),((g1 . 2) * (g2 . 2)),((g1 . 3) * (g2 . 3))*> is V1() V16() V19( NAT ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like set
Sum <*((g1 . 1) * (g2 . 1)),((g1 . 2) * (g2 . 2)),((g1 . 3) * (g2 . 3))*> is V11() real ext-real set
((f2,p) . 1) * (g2 . 1) is V11() real ext-real Element of REAL
((f2,p) . 2) * (g2 . 2) is V11() real ext-real Element of REAL
(((f2,p) . 1) * (g2 . 1)) + (((f2,p) . 2) * (g2 . 2)) is V11() real ext-real Element of REAL
((f2,p) . 3) * (g2 . 3) is V11() real ext-real Element of REAL
((((f2,p) . 1) * (g2 . 1)) + (((f2,p) . 2) * (g2 . 2))) + (((f2,p) . 3) * (g2 . 3)) is V11() real ext-real Element of REAL
(partdiff (f2,p,1)) * (g2 . 1) is V11() real ext-real Element of REAL
((partdiff (f2,p,1)) * (g2 . 1)) + (((f2,p) . 2) * (g2 . 2)) is V11() real ext-real Element of REAL
(((partdiff (f2,p,1)) * (g2 . 1)) + (((f2,p) . 2) * (g2 . 2))) + (((f2,p) . 3) * (g2 . 3)) is V11() real ext-real Element of REAL
(partdiff (f2,p,2)) * (g2 . 2) is V11() real ext-real Element of REAL
((partdiff (f2,p,1)) * (g2 . 1)) + ((partdiff (f2,p,2)) * (g2 . 2)) is V11() real ext-real Element of REAL
(((partdiff (f2,p,1)) * (g2 . 1)) + ((partdiff (f2,p,2)) * (g2 . 2))) + (((f2,p) . 3) * (g2 . 3)) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
f3 is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f2,f3,2) is V11() real ext-real Element of REAL
reproj (2,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f2 * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . f3 is V11() real ext-real Element of REAL
diff ((f2 * (reproj (2,f3))),((proj (2,3)) . f3)) is V11() real ext-real Element of REAL
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (f1,f3,3) is V11() real ext-real Element of REAL
reproj (3,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . f3 is V11() real ext-real Element of REAL
diff ((f1 * (reproj (3,f3))),((proj (3,3)) . f3)) is V11() real ext-real Element of REAL
(partdiff (f2,f3,2)) - (partdiff (f1,f3,3)) is V11() real ext-real Element of REAL
((partdiff (f2,f3,2)) - (partdiff (f1,f3,3))) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (f2,f3,2)) - (partdiff (f1,f3,3)))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),((partdiff (f2,f3,2)) - (partdiff (f1,f3,3))),(id REAL)) is set
K530(((partdiff (f2,f3,2)) - (partdiff (f1,f3,3)))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
p is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (p,f3,3) is V11() real ext-real Element of REAL
p * (reproj (3,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((p * (reproj (3,f3))),((proj (3,3)) . f3)) is V11() real ext-real Element of REAL
partdiff (f2,f3,1) is V11() real ext-real Element of REAL
reproj (1,f3) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f2 * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . f3 is V11() real ext-real Element of REAL
diff ((f2 * (reproj (1,f3))),((proj (1,3)) . f3)) is V11() real ext-real Element of REAL
(partdiff (p,f3,3)) - (partdiff (f2,f3,1)) is V11() real ext-real Element of REAL
((partdiff (p,f3,3)) - (partdiff (f2,f3,1))) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (p,f3,3)) - (partdiff (f2,f3,1)))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),((partdiff (p,f3,3)) - (partdiff (f2,f3,1))),(id REAL)) is set
K530(((partdiff (p,f3,3)) - (partdiff (f2,f3,1)))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f2,f3,2)) - (partdiff (f1,f3,3))) * <e1>) + (((partdiff (p,f3,3)) - (partdiff (f2,f3,1))) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f2,f3,2)) - (partdiff (f1,f3,3))) * <e1>),(((partdiff (p,f3,3)) - (partdiff (f2,f3,1))) * <e2>)) is V16() Function-like set
partdiff (f1,f3,1) is V11() real ext-real Element of REAL
f1 * (reproj (1,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f1 * (reproj (1,f3))),((proj (1,3)) . f3)) is V11() real ext-real Element of REAL
partdiff (p,f3,2) is V11() real ext-real Element of REAL
p * (reproj (2,f3)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((p * (reproj (2,f3))),((proj (2,3)) . f3)) is V11() real ext-real Element of REAL
(partdiff (f1,f3,1)) - (partdiff (p,f3,2)) is V11() real ext-real Element of REAL
((partdiff (f1,f3,1)) - (partdiff (p,f3,2))) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (f1,f3,1)) - (partdiff (p,f3,2)))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),((partdiff (f1,f3,1)) - (partdiff (p,f3,2))),(id REAL)) is set
K530(((partdiff (f1,f3,1)) - (partdiff (p,f3,2)))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((((partdiff (f2,f3,2)) - (partdiff (f1,f3,3))) * <e1>) + (((partdiff (p,f3,3)) - (partdiff (f2,f3,1))) * <e2>)) + (((partdiff (f1,f3,1)) - (partdiff (p,f3,2))) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((((partdiff (f2,f3,2)) - (partdiff (f1,f3,3))) * <e1>) + (((partdiff (p,f3,3)) - (partdiff (f2,f3,1))) * <e2>)),(((partdiff (f1,f3,1)) - (partdiff (p,f3,2))) * <e3>)) is V16() Function-like set
p is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
f1 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (f1,p,3) is V11() real ext-real Element of REAL
reproj (3,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (3,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
partdiff (f1,p,2) is V11() real ext-real Element of REAL
reproj (2,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f1 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (2,3)) . p is V11() real ext-real Element of REAL
diff ((f1 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
f2 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
partdiff (f2,p,3) is V11() real ext-real Element of REAL
f2 * (reproj (3,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f2 * (reproj (3,p))),((proj (3,3)) . p)) is V11() real ext-real Element of REAL
partdiff (f2,p,1) is V11() real ext-real Element of REAL
reproj (1,p) is V1() V16() V19( REAL ) V20( REAL 3) Function-like total quasi_total V134() V135() Element of K6(K7(REAL,(REAL 3)))
f2 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
(proj (1,3)) . p is V11() real ext-real Element of REAL
diff ((f2 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f2,p,1)) - (partdiff (f1,p,2)) is V11() real ext-real Element of REAL
f3 is V16() V19( REAL 3) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7((REAL 3),REAL))
(f1,f2,f3,p) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
partdiff (f3,p,2) is V11() real ext-real Element of REAL
f3 * (reproj (2,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f3 * (reproj (2,p))),((proj (2,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f3,p,2)) - (partdiff (f2,p,3)) is V11() real ext-real Element of REAL
((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * <e1> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (f3,p,2)) - (partdiff (f2,p,3)))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),((partdiff (f3,p,2)) - (partdiff (f2,p,3))),(id REAL)) is set
K530(((partdiff (f3,p,2)) - (partdiff (f2,p,3)))) * <e1> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
partdiff (f3,p,1) is V11() real ext-real Element of REAL
f3 * (reproj (1,p)) is V16() V19( REAL ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
diff ((f3 * (reproj (1,p))),((proj (1,3)) . p)) is V11() real ext-real Element of REAL
(partdiff (f1,p,3)) - (partdiff (f3,p,1)) is V11() real ext-real Element of REAL
((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * <e2> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (f1,p,3)) - (partdiff (f3,p,1)))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),((partdiff (f1,p,3)) - (partdiff (f3,p,1))),(id REAL)) is set
K530(((partdiff (f1,p,3)) - (partdiff (f3,p,1)))) * <e2> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * <e1>) + (((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * <e2>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * <e1>),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * <e2>)) is V16() Function-like set
((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * <e3> is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (f2,p,1)) - (partdiff (f1,p,2)))) is V1() V16() V19( REAL ) V20( REAL ) Function-like total quasi_total complex-valued ext-real-valued real-valued Element of K6(K7(REAL,REAL))
K231(K497(),((partdiff (f2,p,1)) - (partdiff (f1,p,2))),(id REAL)) is set
K530(((partdiff (f2,p,1)) - (partdiff (f1,p,2)))) * <e3> is V16() complex-valued ext-real-valued real-valued FinSequence-like set
((((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * <e1>) + (((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * <e2>)) + (((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * <e3>) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),((((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * <e1>) + (((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * <e2>)),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * <e3>)) is V16() Function-like set
|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),((partdiff (f1,p,3)) - (partdiff (f3,p,1))),((partdiff (f2,p,1)) - (partdiff (f1,p,2)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 1 is V11() real ext-real Element of REAL
((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0 is V11() real ext-real Element of REAL
|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 1),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * |[0,1,0]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (f1,p,3)) - (partdiff (f3,p,1)))) * |[0,1,0]| is V16() complex-valued ext-real-valued real-valued FinSequence-like set
|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 1),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0)]| + (((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * |[0,1,0]|) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 1),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0)]|,(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * |[0,1,0]|)) is V16() Function-like set
((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * |[0,0,1]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K530(((partdiff (f2,p,1)) - (partdiff (f1,p,2)))) * |[0,0,1]| is V16() complex-valued ext-real-valued real-valued FinSequence-like set
(|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 1),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0)]| + (((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * |[0,1,0]|)) + (((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * |[0,0,1]|) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 1),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0),(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) * 0)]| + (((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * |[0,1,0]|)),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * |[0,0,1]|)) is V16() Function-like set
|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0 is V11() real ext-real Element of REAL
((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 1 is V11() real ext-real Element of REAL
|[(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 1),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]| + |[(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 1),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0)]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]|,|[(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 1),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0)]|) is V16() Function-like set
(|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]| + |[(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 1),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0)]|) + (((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * |[0,0,1]|) is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]| + |[(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 1),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) * 0)]|),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * |[0,0,1]|)) is V16() Function-like set
|[0,((partdiff (f1,p,3)) - (partdiff (f3,p,1))),0]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]| + |[0,((partdiff (f1,p,3)) - (partdiff (f3,p,1))),0]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]|,|[0,((partdiff (f1,p,3)) - (partdiff (f3,p,1))),0]|) is V16() Function-like set
((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 0 is V11() real ext-real Element of REAL
((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 1 is V11() real ext-real Element of REAL
|[(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 0),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 0),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 1)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
(|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]| + |[0,((partdiff (f1,p,3)) - (partdiff (f3,p,1))),0]|) + |[(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 0),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 0),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 1)]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),(|[((partdiff (f3,p,2)) - (partdiff (f2,p,3))),0,0]| + |[0,((partdiff (f1,p,3)) - (partdiff (f3,p,1))),0]|),|[(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 0),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 0),(((partdiff (f2,p,1)) - (partdiff (f1,p,2))) * 1)]|) is V16() Function-like set
((partdiff (f3,p,2)) - (partdiff (f2,p,3))) + 0 is V11() real ext-real Element of REAL
0 + ((partdiff (f1,p,3)) - (partdiff (f3,p,1))) is V11() real ext-real Element of REAL
0 + 0 is epsilon-transitive epsilon-connected ordinal natural V11() real ext-real non negative V136() V159() V160() V161() V162() V163() V164() V165() Element of NAT
|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) + 0),(0 + ((partdiff (f1,p,3)) - (partdiff (f3,p,1)))),(0 + 0)]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[0,0,((partdiff (f2,p,1)) - (partdiff (f1,p,2)))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) + 0),(0 + ((partdiff (f1,p,3)) - (partdiff (f3,p,1)))),(0 + 0)]| + |[0,0,((partdiff (f2,p,1)) - (partdiff (f1,p,2)))]| is V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3
K229(K495(),|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) + 0),(0 + ((partdiff (f1,p,3)) - (partdiff (f3,p,1)))),(0 + 0)]|,|[0,0,((partdiff (f2,p,1)) - (partdiff (f1,p,2)))]|) is V16() Function-like set
((partdiff (f1,p,3)) - (partdiff (f3,p,1))) + 0 is V11() real ext-real Element of REAL
0 + ((partdiff (f2,p,1)) - (partdiff (f1,p,2))) is V11() real ext-real Element of REAL
|[(((partdiff (f3,p,2)) - (partdiff (f2,p,3))) + 0),(((partdiff (f1,p,3)) - (partdiff (f3,p,1))) + 0),(0 + ((partdiff (f2,p,1)) - (partdiff (f1,p,2))))]| is V1() V16() V19( NAT ) V20( REAL ) Function-like complex-valued ext-real-valued real-valued V54() V61(3) FinSequence-like FinSubsequence-like Element of REAL 3