:: HFDIFF_1 semantic presentation

REAL is non empty V57() V84() V85() V86() V90() set
NAT is non empty V4() V5() V6() V84() V85() V86() V87() V88() V89() V90() Element of K6(REAL)
K6(REAL) is set
K7(NAT,REAL) is V74() V75() V76() set
K6(K7(NAT,REAL)) is set
K7(REAL,REAL) is V74() V75() V76() set
K6(K7(REAL,REAL)) is set
COMPLEX is non empty V57() V84() V90() set
K7(NAT,COMPLEX) is V74() set
K6(K7(NAT,COMPLEX)) is set
K7(COMPLEX,COMPLEX) is V74() set
K6(K7(COMPLEX,COMPLEX)) is set
NAT is non empty V4() V5() V6() V84() V85() V86() V87() V88() V89() V90() set
K6(NAT) is set
K6(NAT) is set
PFuncs (REAL,REAL) is set
K7(NAT,(PFuncs (REAL,REAL))) is set
K6(K7(NAT,(PFuncs (REAL,REAL)))) is set
0 is set
the empty V4() V5() V6() V8() V9() V10() V12() ext-real non positive non negative V21() V24() V48() V84() V85() V86() V87() V88() V89() V90() set is empty V4() V5() V6() V8() V9() V10() V12() ext-real non positive non negative V21() V24() V48() V84() V85() V86() V87() V88() V89() V90() set
1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
{0,1} is set
RAT is non empty V57() V84() V85() V86() V87() V90() set
INT is non empty V57() V84() V85() V86() V87() V88() V90() set
K7(K7(COMPLEX,COMPLEX),COMPLEX) is V74() set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(K7(REAL,REAL),REAL) is V74() V75() V76() set
K6(K7(K7(REAL,REAL),REAL)) is set
K7(RAT,RAT) is V20( RAT ) V74() V75() V76() set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is V20( RAT ) V74() V75() V76() set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is V20( RAT ) V20( INT ) V74() V75() V76() set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is V20( RAT ) V20( INT ) V74() V75() V76() set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is V20( RAT ) V20( INT ) V74() V75() V76() V77() set
K7(K7(NAT,NAT),NAT) is V20( RAT ) V20( INT ) V74() V75() V76() V77() set
K6(K7(K7(NAT,NAT),NAT)) is set
K376() is set
0 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
{0} is V84() V85() V86() V87() V88() V89() set
- 1 is V11() V12() ext-real V48() Element of REAL
0 ! is V11() V12() ext-real Element of REAL
1 ! is V11() V12() ext-real Element of REAL
2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
sin is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom sin is V84() V85() V86() Element of K6(REAL)
cos is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom cos is V84() V85() V86() Element of K6(REAL)
cos . 0 is V11() V12() ext-real Element of REAL
sin . 0 is V11() V12() ext-real Element of REAL
exp_R is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom exp_R is V84() V85() V86() Element of K6(REAL)
tan is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin / cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cot is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos / sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
PI is V11() V12() ext-real Element of REAL
2 * PI is V11() V12() ext-real Element of REAL
PI / 2 is V11() V12() ext-real Element of REAL
[#] REAL is V84() V85() V86() Element of K6(REAL)
rng exp_R is V84() V85() V86() Element of K6(REAL)
K138(0) is V84() V85() V86() Element of K6(REAL)
ln is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K401(REAL,REAL,exp_R) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ln is V84() V85() V86() Element of K6(REAL)
rng ln is V84() V85() V86() Element of K6(REAL)
- sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) is V11() V12() V48() set
K38(1) (#) sin is V16() V21() set
dom tan is V84() V85() V86() Element of K6(REAL)
dom cot is V84() V85() V86() Element of K6(REAL)
cos ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
f is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f | Z) is V84() V85() V86() Element of K6(REAL)
dom f is V84() V85() V86() Element of K6(REAL)
(dom f) /\ Z is V84() V85() V86() set
Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) Z is V16() V21() set
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) f is V16() V21() set
(- Z) (#) (- f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (- Z) is V84() V85() V86() Element of K6(REAL)
dom Z is V84() V85() V86() Element of K6(REAL)
dom (- f) is V84() V85() V86() Element of K6(REAL)
dom f is V84() V85() V86() Element of K6(REAL)
dom ((- Z) (#) (- f)) is V84() V85() V86() Element of K6(REAL)
(dom Z) /\ (dom f) is V84() V85() V86() set
dom (Z (#) f) is V84() V85() V86() Element of K6(REAL)
g1 is V11() V12() ext-real Element of REAL
((- Z) (#) (- f)) . g1 is V11() V12() ext-real Element of REAL
(Z (#) f) . g1 is V11() V12() ext-real Element of REAL
(dom f) /\ (dom Z) is V84() V85() V86() set
f (#) Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) Z) is V84() V85() V86() Element of K6(REAL)
(- 1) (#) f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((- 1) (#) f) is V84() V85() V86() Element of K6(REAL)
(- 1) (#) Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((- 1) (#) Z) is V84() V85() V86() Element of K6(REAL)
(- Z) . g1 is V11() V12() ext-real Element of REAL
(- f) . g1 is V11() V12() ext-real Element of REAL
((- Z) . g1) * ((- f) . g1) is V11() V12() ext-real Element of REAL
Z . g1 is V11() V12() ext-real Element of REAL
(- 1) * (Z . g1) is V11() V12() ext-real Element of REAL
((- 1) (#) f) . g1 is V11() V12() ext-real Element of REAL
((- 1) * (Z . g1)) * (((- 1) (#) f) . g1) is V11() V12() ext-real Element of REAL
f . g1 is V11() V12() ext-real Element of REAL
(- 1) * (f . g1) is V11() V12() ext-real Element of REAL
((- 1) * (Z . g1)) * ((- 1) * (f . g1)) is V11() V12() ext-real Element of REAL
(Z . g1) * (f . g1) is V11() V12() ext-real Element of REAL
REAL \ {0} is V84() V85() V86() set
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z Z) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((#Z Z) ^) is V84() V85() V86() Element of K6(REAL)
(#Z Z) " {0} is V84() V85() V86() Element of K6(REAL)
f is set
g1 is V11() V12() ext-real Element of REAL
(#Z Z) . g1 is V11() V12() ext-real Element of REAL
g1 #Z Z is V11() V12() ext-real Element of REAL
g1 |^ Z is V11() V12() ext-real Element of REAL
f is set
dom (#Z Z) is V84() V85() V86() Element of K6(REAL)
(#Z Z) . 0 is V11() V12() ext-real Element of REAL
0 #Z Z is V11() V12() ext-real Element of REAL
0 |^ Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
dom (#Z Z) is V84() V85() V86() Element of K6(REAL)
(dom (#Z Z)) \ {0} is V84() V85() V86() set
Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
Z * f is V11() V12() ext-real Element of REAL
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z g1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z g1) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z * f) (#) ((#Z g1) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((#Z g1) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) (f (#) ((#Z g1) ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((Z * f) (#) ((#Z g1) ^)) is V84() V85() V86() Element of K6(REAL)
dom ((#Z g1) ^) is V84() V85() V86() Element of K6(REAL)
dom (f (#) ((#Z g1) ^)) is V84() V85() V86() Element of K6(REAL)
dom (Z (#) (f (#) ((#Z g1) ^))) is V84() V85() V86() Element of K6(REAL)
g2 is set
((Z * f) (#) ((#Z g1) ^)) . g2 is V11() V12() ext-real Element of REAL
((#Z g1) ^) . g2 is V11() V12() ext-real Element of REAL
(Z * f) * (((#Z g1) ^) . g2) is V11() V12() ext-real Element of REAL
f * (((#Z g1) ^) . g2) is V11() V12() ext-real Element of REAL
Z * (f * (((#Z g1) ^) . g2)) is V11() V12() ext-real Element of REAL
(f (#) ((#Z g1) ^)) . g2 is V11() V12() ext-real Element of REAL
Z * ((f (#) ((#Z g1) ^)) . g2) is V11() V12() ext-real Element of REAL
(Z (#) (f (#) ((#Z g1) ^))) . g2 is V11() V12() ext-real Element of REAL
Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is V11() V12() ext-real Element of REAL
f (#) Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V11() V12() ext-real Element of REAL
g1 (#) Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) Z) + (g1 (#) Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f + g1 is V11() V12() ext-real Element of REAL
(f + g1) (#) Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((f (#) Z) + (g1 (#) Z)) is V84() V85() V86() Element of K6(REAL)
dom (f (#) Z) is V84() V85() V86() Element of K6(REAL)
dom (g1 (#) Z) is V84() V85() V86() Element of K6(REAL)
(dom (f (#) Z)) /\ (dom (g1 (#) Z)) is V84() V85() V86() set
dom Z is V84() V85() V86() Element of K6(REAL)
(dom Z) /\ (dom (g1 (#) Z)) is V84() V85() V86() set
(dom Z) /\ (dom Z) is V84() V85() V86() set
g2 is V11() V12() ext-real Element of REAL
((f (#) Z) + (g1 (#) Z)) . g2 is V11() V12() ext-real Element of REAL
((f + g1) (#) Z) . g2 is V11() V12() ext-real Element of REAL
dom ((f + g1) (#) Z) is V84() V85() V86() Element of K6(REAL)
Z . g2 is V11() V12() ext-real Element of REAL
(f + g1) * (Z . g2) is V11() V12() ext-real Element of REAL
f * (Z . g2) is V11() V12() ext-real Element of REAL
g1 * (Z . g2) is V11() V12() ext-real Element of REAL
(f * (Z . g2)) + (g1 * (Z . g2)) is V11() V12() ext-real Element of REAL
(f (#) Z) . g2 is V11() V12() ext-real Element of REAL
(g1 (#) Z) . g2 is V11() V12() ext-real Element of REAL
((f (#) Z) . g2) + ((g1 (#) Z) . g2) is V11() V12() ext-real Element of REAL
(f * (Z . g2)) + ((g1 (#) Z) . g2) is V11() V12() ext-real Element of REAL
dom ((f + g1) (#) Z) is V84() V85() V86() Element of K6(REAL)
Z is open V84() V85() V86() Element of K6(REAL)
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f | Z) is V84() V85() V86() Element of K6(REAL)
dom f is V84() V85() V86() Element of K6(REAL)
g1 is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is open V84() V85() V86() Element of K6(REAL)
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 - 1 is V11() V12() ext-real V48() Element of REAL
Z - 1 is V11() V12() ext-real V48() Element of REAL
diff (g1,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (#Z Z) is V84() V85() V86() Element of K6(REAL)
(#Z Z) | REAL is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
sin . Z is V11() V12() ext-real Element of REAL
- (sin . Z) is V11() V12() ext-real Element of REAL
f is open V84() V85() V86() Element of K6(REAL)
diff (sin,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,f)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,f)) . 2) . Z is V11() V12() ext-real Element of REAL
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,f)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,f)) . (2 * 1)) . Z is V11() V12() ext-real Element of REAL
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,f)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,f)) . (1 + 1)) . Z is V11() V12() ext-real Element of REAL
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,f)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,f)) . (1 + 0)) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,f)) . (1 + 0)) `| f) . Z is V11() V12() ext-real Element of REAL
(diff (sin,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,f)) . 0) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,f)) . 0) `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (sin,f)) . 0) `| f) `| f) . Z is V11() V12() ext-real Element of REAL
sin | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((sin | f) `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((sin | f) `| f) `| f) . Z is V11() V12() ext-real Element of REAL
sin `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((sin `| f) `| f) . Z is V11() V12() ext-real Element of REAL
cos | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos | f) `| f) . Z is V11() V12() ext-real Element of REAL
cos `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos `| f) . Z is V11() V12() ext-real Element of REAL
diff (cos,Z) is V11() V12() ext-real Element of REAL
3 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
- cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) cos is V16() V21() set
Z is V11() V12() ext-real Element of REAL
(- cos) . Z is V11() V12() ext-real Element of REAL
f is open V84() V85() V86() Element of K6(REAL)
diff (sin,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,f)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,f)) . 3) . Z is V11() V12() ext-real Element of REAL
cos | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (cos | f) is V84() V85() V86() Element of K6(REAL)
(- cos) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((- cos) | f) is V84() V85() V86() Element of K6(REAL)
dom (- cos) is V84() V85() V86() Element of K6(REAL)
(dom (- cos)) /\ f is V84() V85() V86() set
(dom cos) /\ f is V84() V85() V86() set
- (cos | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) (cos | f) is V16() V21() set
dom (- (cos | f)) is V84() V85() V86() Element of K6(REAL)
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,f)) . ((2 * 1) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,f)) . ((2 * 1) + 1)) . Z is V11() V12() ext-real Element of REAL
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (cos | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ 1) (#) (cos | f)) . Z is V11() V12() ext-real Element of REAL
(- 1) (#) (cos | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (cos | f)) . Z is V11() V12() ext-real Element of REAL
((- cos) | f) . Z is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f * PI is V11() V12() ext-real Element of REAL
(f * PI) / 2 is V11() V12() ext-real Element of REAL
Z + ((f * PI) / 2) is V11() V12() ext-real Element of REAL
sin . (Z + ((f * PI) / 2)) is V11() V12() ext-real Element of REAL
g1 is open V84() V85() V86() Element of K6(REAL)
diff (sin,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . f) . Z is V11() V12() ext-real Element of REAL
(- 1) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) cos) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((- 1) (#) cos) | g1) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) cos) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) cos)) /\ g1 is V84() V85() V86() set
(dom cos) /\ g1 is V84() V85() V86() set
(- 1) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) sin) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((- 1) (#) sin) | g1) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) sin) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) sin)) /\ g1 is V84() V85() V86() set
(dom sin) /\ g1 is V84() V85() V86() set
0 + f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f - 1 is V11() V12() ext-real V48() Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (sin,g1)) . (2 * x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . (2 * x)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,g1)) . (2 * x)) `| g1) . Z is V11() V12() ext-real Element of REAL
sin | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ x is V11() V12() ext-real Element of REAL
((- 1) |^ x) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ x) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ x) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 |^ (2 * x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * x)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 |^ (2 * x)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * x)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(sin | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((sin | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
sin `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| g1) . Z is V11() V12() ext-real Element of REAL
diff (sin,Z) is V11() V12() ext-real Element of REAL
cos . Z is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
Z + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
cos . (Z + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
g2 / 2 is V11() V12() ext-real Element of REAL
(g2 / 2) * PI is V11() V12() ext-real Element of REAL
Z + ((g2 / 2) * PI) is V11() V12() ext-real Element of REAL
(Z + ((g2 / 2) * PI)) + (PI / 2) is V11() V12() ext-real Element of REAL
sin . ((Z + ((g2 / 2) * PI)) + (PI / 2)) is V11() V12() ext-real Element of REAL
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * x) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (sin,g1)) . (2 * x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . (2 * x)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,g1)) . (2 * x)) `| g1) . Z is V11() V12() ext-real Element of REAL
sin | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ ((2 * x) + 1) is V11() V12() ext-real Element of REAL
((- 1) |^ ((2 * x) + 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ ((2 * x) + 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ ((2 * x) + 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- 1) |^ (2 * x) is V11() V12() ext-real Element of REAL
((- 1) |^ (2 * x)) * (- 1) is V11() V12() ext-real Element of REAL
(((- 1) |^ (2 * x)) * (- 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 |^ (2 * x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * x)) * (- 1) is V11() V12() ext-real V48() Element of REAL
((1 |^ (2 * x)) * (- 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((1 |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 * (- 1) is V11() V12() ext-real V48() Element of REAL
(1 * (- 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 * (- 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 * (- 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- sin) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- sin) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- sin) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
((- 1) (#) sin) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) sin) `| g1) . Z is V11() V12() ext-real Element of REAL
diff (sin,Z) is V11() V12() ext-real Element of REAL
(- 1) * (diff (sin,Z)) is V11() V12() ext-real Element of REAL
cos . Z is V11() V12() ext-real Element of REAL
(- 1) * (cos . Z) is V11() V12() ext-real Element of REAL
- (cos . Z) is V11() V12() ext-real Element of REAL
Z + PI is V11() V12() ext-real Element of REAL
cos . (Z + PI) is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
(Z + PI) + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
cos . ((Z + PI) + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
g2 / 2 is V11() V12() ext-real Element of REAL
(g2 / 2) * PI is V11() V12() ext-real Element of REAL
Z + ((g2 / 2) * PI) is V11() V12() ext-real Element of REAL
(Z + ((g2 / 2) * PI)) + (PI / 2) is V11() V12() ext-real Element of REAL
sin . ((Z + ((g2 / 2) * PI)) + (PI / 2)) is V11() V12() ext-real Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * x) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (sin,g1)) . ((2 * x) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . ((2 * x) + 1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,g1)) . ((2 * x) + 1)) `| g1) . Z is V11() V12() ext-real Element of REAL
cos | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ (2 * x) is V11() V12() ext-real Element of REAL
((- 1) |^ (2 * x)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ (2 * x)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ (2 * x)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 |^ (2 * x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * x)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 |^ (2 * x)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * x)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(cos | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
cos `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos `| g1) . Z is V11() V12() ext-real Element of REAL
diff (cos,Z) is V11() V12() ext-real Element of REAL
sin . Z is V11() V12() ext-real Element of REAL
- (sin . Z) is V11() V12() ext-real Element of REAL
Z + PI is V11() V12() ext-real Element of REAL
sin . (Z + PI) is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
(Z + PI) + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
sin . ((Z + PI) + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
g2 - 1 is V11() V12() ext-real V48() Element of REAL
(g2 - 1) / 2 is V11() V12() ext-real Element of REAL
((g2 - 1) / 2) * PI is V11() V12() ext-real Element of REAL
Z + (((g2 - 1) / 2) * PI) is V11() V12() ext-real Element of REAL
(Z + (((g2 - 1) / 2) * PI)) + PI is V11() V12() ext-real Element of REAL
sin . ((Z + (((g2 - 1) / 2) * PI)) + PI) is V11() V12() ext-real Element of REAL
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * x) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (sin,g1)) . ((2 * x) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g1)) . ((2 * x) + 1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,g1)) . ((2 * x) + 1)) `| g1) . Z is V11() V12() ext-real Element of REAL
cos | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ x is V11() V12() ext-real Element of REAL
((- 1) |^ x) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ x) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ x) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- 1) |^ (2 * x) is V11() V12() ext-real Element of REAL
((- 1) |^ (2 * x)) * (- 1) is V11() V12() ext-real Element of REAL
(((- 1) |^ (2 * x)) * (- 1)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 |^ (2 * x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * x)) * (- 1) is V11() V12() ext-real V48() Element of REAL
((1 |^ (2 * x)) * (- 1)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((1 |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 * (- 1) is V11() V12() ext-real V48() Element of REAL
(1 * (- 1)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 * (- 1)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 * (- 1)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- cos) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- cos) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- cos) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
((- 1) (#) cos) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) cos) `| g1) . Z is V11() V12() ext-real Element of REAL
diff (cos,Z) is V11() V12() ext-real Element of REAL
(- 1) * (diff (cos,Z)) is V11() V12() ext-real Element of REAL
sin . Z is V11() V12() ext-real Element of REAL
- (sin . Z) is V11() V12() ext-real Element of REAL
(- 1) * (- (sin . Z)) is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
Z + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
sin . (Z + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
g2 - 3 is V11() V12() ext-real V48() Element of REAL
(g2 - 3) / 2 is V11() V12() ext-real Element of REAL
((g2 - 3) / 2) * PI is V11() V12() ext-real Element of REAL
Z + (((g2 - 3) / 2) * PI) is V11() V12() ext-real Element of REAL
(Z + (((g2 - 3) / 2) * PI)) + (2 * PI) is V11() V12() ext-real Element of REAL
sin . ((Z + (((g2 - 3) / 2) * PI)) + (2 * PI)) is V11() V12() ext-real Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
sin | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin | g1) . Z is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
cos . Z is V11() V12() ext-real Element of REAL
- (cos . Z) is V11() V12() ext-real Element of REAL
f is open V84() V85() V86() Element of K6(REAL)
diff (cos,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,f)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,f)) . 2) . Z is V11() V12() ext-real Element of REAL
(- 1) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) sin) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((- 1) (#) sin) | f) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) sin) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) sin)) /\ f is V84() V85() V86() set
(dom sin) /\ f is V84() V85() V86() set
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,f)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,f)) . (1 + 1)) . Z is V11() V12() ext-real Element of REAL
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,f)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,f)) . (1 + 0)) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cos,f)) . (1 + 0)) `| f) . Z is V11() V12() ext-real Element of REAL
(diff (cos,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,f)) . 0) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cos,f)) . 0) `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (cos,f)) . 0) `| f) `| f) . Z is V11() V12() ext-real Element of REAL
cos | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos | f) `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((cos | f) `| f) `| f) . Z is V11() V12() ext-real Element of REAL
cos `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos `| f) `| f) . Z is V11() V12() ext-real Element of REAL
(- sin) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- sin) | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- sin) | f) `| f) . Z is V11() V12() ext-real Element of REAL
((- 1) (#) sin) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) sin) `| f) . Z is V11() V12() ext-real Element of REAL
diff (sin,Z) is V11() V12() ext-real Element of REAL
(- 1) * (diff (sin,Z)) is V11() V12() ext-real Element of REAL
(- 1) * (cos . Z) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
sin . Z is V11() V12() ext-real Element of REAL
f is open V84() V85() V86() Element of K6(REAL)
diff (cos,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,f)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,f)) . 3) . Z is V11() V12() ext-real Element of REAL
sin | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (sin | f) is V84() V85() V86() Element of K6(REAL)
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,f)) . ((2 * 1) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,f)) . ((2 * 1) + 1)) . Z is V11() V12() ext-real Element of REAL
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(- 1) |^ (1 + 1) is V11() V12() ext-real Element of REAL
((- 1) |^ (1 + 1)) (#) (sin | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ (1 + 1)) (#) (sin | f)) . Z is V11() V12() ext-real Element of REAL
1 |^ 2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ 2) (#) (sin | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 |^ 2) (#) (sin | f)) . Z is V11() V12() ext-real Element of REAL
1 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 * 1) (#) (sin | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 * 1) (#) (sin | f)) . Z is V11() V12() ext-real Element of REAL
(sin | f) . Z is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f * PI is V11() V12() ext-real Element of REAL
(f * PI) / 2 is V11() V12() ext-real Element of REAL
Z + ((f * PI) / 2) is V11() V12() ext-real Element of REAL
cos . (Z + ((f * PI) / 2)) is V11() V12() ext-real Element of REAL
g1 is open V84() V85() V86() Element of K6(REAL)
diff (cos,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . f) . Z is V11() V12() ext-real Element of REAL
(- 1) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) sin) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((- 1) (#) sin) | g1) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) sin) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) sin)) /\ g1 is V84() V85() V86() set
(dom sin) /\ g1 is V84() V85() V86() set
(- 1) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) cos) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((- 1) (#) cos) | g1) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) cos) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) cos)) /\ g1 is V84() V85() V86() set
(dom cos) /\ g1 is V84() V85() V86() set
0 + f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f - 1 is V11() V12() ext-real V48() Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (cos,g1)) . (2 * x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . (2 * x)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cos,g1)) . (2 * x)) `| g1) . Z is V11() V12() ext-real Element of REAL
cos | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ (2 * x) is V11() V12() ext-real Element of REAL
((- 1) |^ (2 * x)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ (2 * x)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ (2 * x)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 |^ (2 * x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * x)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 |^ (2 * x)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * x)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(cos | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
cos `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos `| g1) . Z is V11() V12() ext-real Element of REAL
diff (cos,Z) is V11() V12() ext-real Element of REAL
sin . Z is V11() V12() ext-real Element of REAL
- (sin . Z) is V11() V12() ext-real Element of REAL
Z + (PI / 2) is V11() V12() ext-real Element of REAL
cos . (Z + (PI / 2)) is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
(Z + (PI / 2)) + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
cos . ((Z + (PI / 2)) + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
g2 / 2 is V11() V12() ext-real Element of REAL
(g2 / 2) * PI is V11() V12() ext-real Element of REAL
(Z + (PI / 2)) + ((g2 / 2) * PI) is V11() V12() ext-real Element of REAL
cos . ((Z + (PI / 2)) + ((g2 / 2) * PI)) is V11() V12() ext-real Element of REAL
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * x) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (cos,g1)) . (2 * x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . (2 * x)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cos,g1)) . (2 * x)) `| g1) . Z is V11() V12() ext-real Element of REAL
cos | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ ((2 * x) + 1) is V11() V12() ext-real Element of REAL
((- 1) |^ ((2 * x) + 1)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ ((2 * x) + 1)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ ((2 * x) + 1)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- 1) |^ (2 * x) is V11() V12() ext-real Element of REAL
((- 1) |^ (2 * x)) * (- 1) is V11() V12() ext-real Element of REAL
(((- 1) |^ (2 * x)) * (- 1)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 |^ (2 * x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * x)) * (- 1) is V11() V12() ext-real V48() Element of REAL
((1 |^ (2 * x)) * (- 1)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((1 |^ (2 * x)) * (- 1)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 * (- 1) is V11() V12() ext-real V48() Element of REAL
(1 * (- 1)) (#) (cos | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 * (- 1)) (#) (cos | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 * (- 1)) (#) (cos | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- cos) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- cos) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- cos) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
((- 1) (#) cos) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) cos) `| g1) . Z is V11() V12() ext-real Element of REAL
diff (cos,Z) is V11() V12() ext-real Element of REAL
(- 1) * (diff (cos,Z)) is V11() V12() ext-real Element of REAL
sin . Z is V11() V12() ext-real Element of REAL
- (sin . Z) is V11() V12() ext-real Element of REAL
(- 1) * (- (sin . Z)) is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
Z + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
sin . (Z + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
g2 / 2 is V11() V12() ext-real Element of REAL
(g2 / 2) - 1 is V11() V12() ext-real Element of REAL
((g2 / 2) - 1) * PI is V11() V12() ext-real Element of REAL
Z + (((g2 / 2) - 1) * PI) is V11() V12() ext-real Element of REAL
(Z + (((g2 / 2) - 1) * PI)) + (2 * PI) is V11() V12() ext-real Element of REAL
sin . ((Z + (((g2 / 2) - 1) * PI)) + (2 * PI)) is V11() V12() ext-real Element of REAL
(g2 / 2) + 1 is V11() V12() ext-real Element of REAL
((g2 / 2) + 1) * PI is V11() V12() ext-real Element of REAL
Z + (((g2 / 2) + 1) * PI) is V11() V12() ext-real Element of REAL
(PI / 2) - (Z + (((g2 / 2) + 1) * PI)) is V11() V12() ext-real Element of REAL
cos . ((PI / 2) - (Z + (((g2 / 2) + 1) * PI))) is V11() V12() ext-real Element of REAL
- ((PI / 2) - (Z + (((g2 / 2) + 1) * PI))) is V11() V12() ext-real Element of REAL
cos . (- ((PI / 2) - (Z + (((g2 / 2) + 1) * PI)))) is V11() V12() ext-real Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * x) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (cos,g1)) . ((2 * x) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . ((2 * x) + 1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cos,g1)) . ((2 * x) + 1)) `| g1) . Z is V11() V12() ext-real Element of REAL
sin | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 * x) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(- 1) |^ ((2 * x) + 1) is V11() V12() ext-real Element of REAL
((- 1) |^ ((2 * x) + 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ ((2 * x) + 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ ((2 * x) + 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- 1) |^ (2 * x) is V11() V12() ext-real Element of REAL
((- 1) |^ (2 * x)) * (- 1) is V11() V12() ext-real Element of REAL
(((- 1) |^ (2 * x)) * (- 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 |^ (2 * x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * x)) * (- 1) is V11() V12() ext-real V48() Element of REAL
((1 |^ (2 * x)) * (- 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((1 |^ (2 * x)) * (- 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 * (- 1) is V11() V12() ext-real V48() Element of REAL
(1 * (- 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 * (- 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 * (- 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(- sin) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- sin) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- sin) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
((- 1) (#) sin) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) sin) `| g1) . Z is V11() V12() ext-real Element of REAL
diff (sin,Z) is V11() V12() ext-real Element of REAL
(- 1) * (diff (sin,Z)) is V11() V12() ext-real Element of REAL
cos . Z is V11() V12() ext-real Element of REAL
(- 1) * (cos . Z) is V11() V12() ext-real Element of REAL
- (cos . Z) is V11() V12() ext-real Element of REAL
Z + PI is V11() V12() ext-real Element of REAL
cos . (Z + PI) is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
(Z + PI) + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
cos . ((Z + PI) + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
(g2 + 1) * PI is V11() V12() ext-real Element of REAL
((g2 + 1) * PI) / 2 is V11() V12() ext-real Element of REAL
Z + (((g2 + 1) * PI) / 2) is V11() V12() ext-real Element of REAL
cos . (Z + (((g2 + 1) * PI) / 2)) is V11() V12() ext-real Element of REAL
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * x) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . (g2 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (cos,g1)) . ((2 * x) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g1)) . ((2 * x) + 1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cos,g1)) . ((2 * x) + 1)) `| g1) . Z is V11() V12() ext-real Element of REAL
sin | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(- 1) |^ (x + 1) is V11() V12() ext-real Element of REAL
((- 1) |^ (x + 1)) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ (x + 1)) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ (x + 1)) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
2 * (x + 1) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
1 |^ (2 * (x + 1)) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 |^ (2 * (x + 1))) (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 |^ (2 * (x + 1))) (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 |^ (2 * (x + 1))) (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
1 (#) (sin | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (sin | g1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (sin | g1)) `| g1) . Z is V11() V12() ext-real Element of REAL
(sin | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((sin | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
sin `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| g1) . Z is V11() V12() ext-real Element of REAL
diff (sin,Z) is V11() V12() ext-real Element of REAL
cos . Z is V11() V12() ext-real Element of REAL
(2 * PI) * x is V11() V12() ext-real Element of REAL
Z + ((2 * PI) * x) is V11() V12() ext-real Element of REAL
cos . (Z + ((2 * PI) * x)) is V11() V12() ext-real Element of REAL
g2 - 1 is V11() V12() ext-real V48() Element of REAL
(g2 - 1) / 2 is V11() V12() ext-real Element of REAL
((g2 - 1) / 2) - 1 is V11() V12() ext-real Element of REAL
(((g2 - 1) / 2) - 1) * PI is V11() V12() ext-real Element of REAL
Z + ((((g2 - 1) / 2) - 1) * PI) is V11() V12() ext-real Element of REAL
(Z + ((((g2 - 1) / 2) - 1) * PI)) + (2 * PI) is V11() V12() ext-real Element of REAL
cos . ((Z + ((((g2 - 1) / 2) - 1) * PI)) + (2 * PI)) is V11() V12() ext-real Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
cos | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | g1) . Z is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is open V84() V85() V86() Element of K6(REAL)
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 + g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((g1 + g2),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((g1 + g2),f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g2,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . Z) + ((diff (g2,f)) . Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((g1 + g2),f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . x) + ((diff (g2,f)) . x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((g1 + g2),f)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,f)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,f)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . (x + 1)) + ((diff (g2,f)) . (x + 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(x + 1) - 1 is V11() V12() ext-real V48() Element of REAL
(((diff (g1,f)) . x) + ((diff (g2,f)) . x)) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . x) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g2,f)) . x) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (g1,f)) . x) `| f) + (((diff (g2,f)) . x) `| f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . (x + 1)) + (((diff (g2,f)) . x) `| f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((g1 + g2),f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . 0) + ((diff (g2,f)) . 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 + g2) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 | f) + (g2 | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . 0) + (g2 | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is open V84() V85() V86() Element of K6(REAL)
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 - g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- g2 is V16() V21() V74() set
K38(1) (#) g2 is V16() V21() set
g1 + (- g2) is V16() V21() set
diff ((g1 - g2),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((g1 - g2),f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g2,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . Z) - ((diff (g2,f)) . Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((diff (g2,f)) . Z) is V16() V21() V74() set
K38(1) (#) ((diff (g2,f)) . Z) is V16() V21() set
((diff (g1,f)) . Z) + (- ((diff (g2,f)) . Z)) is V16() V21() set
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((g1 - g2),f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . x) - ((diff (g2,f)) . x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((diff (g2,f)) . x) is V16() V21() V74() set
K38(1) (#) ((diff (g2,f)) . x) is V16() V21() set
((diff (g1,f)) . x) + (- ((diff (g2,f)) . x)) is V16() V21() set
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((g1 - g2),f)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,f)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,f)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . (x + 1)) - ((diff (g2,f)) . (x + 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((diff (g2,f)) . (x + 1)) is V16() V21() V74() set
K38(1) (#) ((diff (g2,f)) . (x + 1)) is V16() V21() set
((diff (g1,f)) . (x + 1)) + (- ((diff (g2,f)) . (x + 1))) is V16() V21() set
(x + 1) - 1 is V11() V12() ext-real V48() Element of REAL
(((diff (g1,f)) . x) - ((diff (g2,f)) . x)) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . x) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g2,f)) . x) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (g1,f)) . x) `| f) - (((diff (g2,f)) . x) `| f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- (((diff (g2,f)) . x) `| f) is V16() V21() V74() set
K38(1) (#) (((diff (g2,f)) . x) `| f) is V16() V21() set
(((diff (g1,f)) . x) `| f) + (- (((diff (g2,f)) . x) `| f)) is V16() V21() set
((diff (g1,f)) . (x + 1)) - (((diff (g2,f)) . x) `| f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . (x + 1)) + (- (((diff (g2,f)) . x) `| f)) is V16() V21() set
(diff ((g1 - g2),f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . 0) - ((diff (g2,f)) . 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((diff (g2,f)) . 0) is V16() V21() V74() set
K38(1) (#) ((diff (g2,f)) . 0) is V16() V21() set
((diff (g1,f)) . 0) + (- ((diff (g2,f)) . 0)) is V16() V21() set
(g1 - g2) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 | f) - (g2 | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- (g2 | f) is V16() V21() V74() set
K38(1) (#) (g2 | f) is V16() V21() set
(g1 | f) + (- (g2 | f)) is V16() V21() set
((diff (g1,f)) . 0) - (g2 | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . 0) + (- (g2 | f)) is V16() V21() set
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 is open V84() V85() V86() Element of K6(REAL)
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g2,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 + x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((g2 + x),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((g2 + x),g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (x,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (x,g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g2,g1)) . f) + ((diff (x,g1)) . f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 is open V84() V85() V86() Element of K6(REAL)
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g2,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 - x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- x is V16() V21() V74() set
K38(1) (#) x is V16() V21() set
g2 + (- x) is V16() V21() set
diff ((g2 - x),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((g2 - x),g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (x,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (x,g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g2,g1)) . f) - ((diff (x,g1)) . f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((diff (x,g1)) . f) is V16() V21() V74() set
K38(1) (#) ((diff (x,g1)) . f) is V16() V21() set
((diff (g2,g1)) . f) + (- ((diff (x,g1)) . f)) is V16() V21() set
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is open V84() V85() V86() Element of K6(REAL)
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 + g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z - 1 is V11() V12() ext-real V48() Element of REAL
diff (g2,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (g2,f)) . x) is V84() V85() V86() Element of K6(REAL)
diff ((g1 + g2),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((g1 + g2),f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . x) + ((diff (g2,f)) . x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (g1,f)) . x) is V84() V85() V86() Element of K6(REAL)
(dom ((diff (g1,f)) . x)) /\ (dom ((diff (g2,f)) . x)) is V84() V85() V86() set
dom (((diff (g1,f)) . x) + ((diff (g2,f)) . x)) is V84() V85() V86() Element of K6(REAL)
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is open V84() V85() V86() Element of K6(REAL)
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 - g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- g2 is V16() V21() V74() set
K38(1) (#) g2 is V16() V21() set
g1 + (- g2) is V16() V21() set
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z - 1 is V11() V12() ext-real V48() Element of REAL
diff (g2,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (g2,f)) . x) is V84() V85() V86() Element of K6(REAL)
diff ((g1 - g2),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((g1 - g2),f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,f)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . x) - ((diff (g2,f)) . x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((diff (g2,f)) . x) is V16() V21() V74() set
K38(1) (#) ((diff (g2,f)) . x) is V16() V21() set
((diff (g1,f)) . x) + (- ((diff (g2,f)) . x)) is V16() V21() set
dom ((diff (g1,f)) . x) is V84() V85() V86() Element of K6(REAL)
(dom ((diff (g1,f)) . x)) /\ (dom ((diff (g2,f)) . x)) is V84() V85() V86() set
dom (((diff (g1,f)) . x) - ((diff (g2,f)) . x)) is V84() V85() V86() Element of K6(REAL)
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 is open V84() V85() V86() Element of K6(REAL)
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((Z (#) g2),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((Z (#) g2),g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g2,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) ((diff (g2,g1)) . f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((Z (#) g2),g1)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,g1)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) ((diff (g2,g1)) . x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((Z (#) g2),g1)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,g1)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) ((diff (g2,g1)) . (x + 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(x + 1) - 1 is V11() V12() ext-real V48() Element of REAL
(Z (#) ((diff (g2,g1)) . x)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g2,g1)) . x) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) (((diff (g2,g1)) . x) `| g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((Z (#) g2),g1)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g2,g1)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) ((diff (g2,g1)) . 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z (#) g2) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) (g2 | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 is open V84() V85() V86() Element of K6(REAL)
g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f - 1 is V11() V12() ext-real V48() Element of REAL
diff (g2,g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g2,g1)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) ((diff (g2,g1)) . x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((Z (#) g2),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((Z (#) g2),g1)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (f,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (f,Z)) . 1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f `| Z) is V84() V85() V86() Element of K6(REAL)
g1 is V11() V12() ext-real Element of REAL
((diff (f,Z)) . 1) . g1 is V11() V12() ext-real Element of REAL
(f `| Z) . g1 is V11() V12() ext-real Element of REAL
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . (1 + 0)) . g1 is V11() V12() ext-real Element of REAL
(diff (f,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 0) `| Z) . g1 is V11() V12() ext-real Element of REAL
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f | Z) `| Z) . g1 is V11() V12() ext-real Element of REAL
dom ((diff (f,Z)) . 1) is V84() V85() V86() Element of K6(REAL)
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (f,Z)) . (1 + 0)) is V84() V85() V86() Element of K6(REAL)
(diff (f,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff (f,Z)) . 0) `| Z) is V84() V85() V86() Element of K6(REAL)
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((f | Z) `| Z) is V84() V85() V86() Element of K6(REAL)
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is open V84() V85() V86() Element of K6(REAL)
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,f)) . 1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (g1,f)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,f)) . 0) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
f (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 * PI is V11() V12() ext-real Element of REAL
(g1 * PI) / 2 is V11() V12() ext-real Element of REAL
Z + ((g1 * PI) / 2) is V11() V12() ext-real Element of REAL
sin . (Z + ((g1 * PI) / 2)) is V11() V12() ext-real Element of REAL
f * (sin . (Z + ((g1 * PI) / 2))) is V11() V12() ext-real Element of REAL
g2 is open V84() V85() V86() Element of K6(REAL)
diff ((f (#) sin),g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f (#) sin),g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) sin),g2)) . g1) . Z is V11() V12() ext-real Element of REAL
0 + g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 - 1 is V11() V12() ext-real V48() Element of REAL
diff (sin,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,g2)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (sin,g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (sin,g2)) . g1) is V84() V85() V86() Element of K6(REAL)
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,g2)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (sin,g2)) . (x + 1)) is V84() V85() V86() Element of K6(REAL)
((diff (sin,g2)) . x) `| g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff (sin,g2)) . x) `| g2) is V84() V85() V86() Element of K6(REAL)
f (#) ((diff (sin,g2)) . g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) ((diff (sin,g2)) . g1)) is V84() V85() V86() Element of K6(REAL)
(f (#) ((diff (sin,g2)) . g1)) . Z is V11() V12() ext-real Element of REAL
((diff (sin,g2)) . g1) . Z is V11() V12() ext-real Element of REAL
f * (((diff (sin,g2)) . g1) . Z) is V11() V12() ext-real Element of REAL
sin | g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (sin | g2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) (sin | g2)) is V84() V85() V86() Element of K6(REAL)
dom (sin | g2) is V84() V85() V86() Element of K6(REAL)
diff (sin,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,g2)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (sin,g2)) . 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((diff (sin,g2)) . 0)) . Z is V11() V12() ext-real Element of REAL
(f (#) (sin | g2)) . Z is V11() V12() ext-real Element of REAL
(sin | g2) . Z is V11() V12() ext-real Element of REAL
f * ((sin | g2) . Z) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
f (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 * PI is V11() V12() ext-real Element of REAL
(g1 * PI) / 2 is V11() V12() ext-real Element of REAL
Z + ((g1 * PI) / 2) is V11() V12() ext-real Element of REAL
cos . (Z + ((g1 * PI) / 2)) is V11() V12() ext-real Element of REAL
f * (cos . (Z + ((g1 * PI) / 2))) is V11() V12() ext-real Element of REAL
g2 is open V84() V85() V86() Element of K6(REAL)
diff ((f (#) cos),g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f (#) cos),g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) cos),g2)) . g1) . Z is V11() V12() ext-real Element of REAL
0 + g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 - 1 is V11() V12() ext-real V48() Element of REAL
diff (cos,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,g2)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (cos,g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (cos,g2)) . g1) is V84() V85() V86() Element of K6(REAL)
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,g2)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (cos,g2)) . (x + 1)) is V84() V85() V86() Element of K6(REAL)
((diff (cos,g2)) . x) `| g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff (cos,g2)) . x) `| g2) is V84() V85() V86() Element of K6(REAL)
f (#) ((diff (cos,g2)) . g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) ((diff (cos,g2)) . g1)) is V84() V85() V86() Element of K6(REAL)
(f (#) ((diff (cos,g2)) . g1)) . Z is V11() V12() ext-real Element of REAL
((diff (cos,g2)) . g1) . Z is V11() V12() ext-real Element of REAL
f * (((diff (cos,g2)) . g1) . Z) is V11() V12() ext-real Element of REAL
cos | g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (cos | g2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) (cos | g2)) is V84() V85() V86() Element of K6(REAL)
dom (cos | g2) is V84() V85() V86() Element of K6(REAL)
diff (cos,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,g2)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (cos,g2)) . 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((diff (cos,g2)) . 0)) . Z is V11() V12() ext-real Element of REAL
(f (#) (cos | g2)) . Z is V11() V12() ext-real Element of REAL
(cos | g2) . Z is V11() V12() ext-real Element of REAL
f * ((cos | g2) . Z) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
exp_R . Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
f (#) exp_R is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f * (exp_R . Z) is V11() V12() ext-real Element of REAL
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 is open V84() V85() V86() Element of K6(REAL)
diff ((f (#) exp_R),g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f (#) exp_R),g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) exp_R),g2)) . g1) . Z is V11() V12() ext-real Element of REAL
0 + g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 - 1 is V11() V12() ext-real V48() Element of REAL
diff (exp_R,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (exp_R,g2)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (exp_R,g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (exp_R,g2)) . g1) is V84() V85() V86() Element of K6(REAL)
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (exp_R,g2)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (exp_R,g2)) . (x + 1)) is V84() V85() V86() Element of K6(REAL)
((diff (exp_R,g2)) . x) `| g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff (exp_R,g2)) . x) `| g2) is V84() V85() V86() Element of K6(REAL)
f (#) ((diff (exp_R,g2)) . g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) ((diff (exp_R,g2)) . g1)) is V84() V85() V86() Element of K6(REAL)
(f (#) ((diff (exp_R,g2)) . g1)) . Z is V11() V12() ext-real Element of REAL
((diff (exp_R,g2)) . g1) . Z is V11() V12() ext-real Element of REAL
f * (((diff (exp_R,g2)) . g1) . Z) is V11() V12() ext-real Element of REAL
exp_R | g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (exp_R | g2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) (exp_R | g2)) is V84() V85() V86() Element of K6(REAL)
dom (exp_R | g2) is V84() V85() V86() Element of K6(REAL)
diff (exp_R,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (exp_R,g2)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (exp_R,g2)) . 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((diff (exp_R,g2)) . 0)) . Z is V11() V12() ext-real Element of REAL
(f (#) (exp_R | g2)) . Z is V11() V12() ext-real Element of REAL
(exp_R | g2) . Z is V11() V12() ext-real Element of REAL
f * ((exp_R | g2) . Z) is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - 1 is V11() V12() ext-real V48() Element of REAL
#Z (Z - 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) (#Z (Z - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is open V84() V85() V86() Element of K6(REAL)
(#Z Z) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z (#) (#Z (Z - 1))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (Z (#) (#Z (Z - 1))) is V84() V85() V86() Element of K6(REAL)
dom (#Z (Z - 1)) is V84() V85() V86() Element of K6(REAL)
dom ((Z (#) (#Z (Z - 1))) | f) is V84() V85() V86() Element of K6(REAL)
g1 is V11() V12() ext-real Element of REAL
((#Z Z) `| f) . g1 is V11() V12() ext-real Element of REAL
((Z (#) (#Z (Z - 1))) | f) . g1 is V11() V12() ext-real Element of REAL
diff ((#Z Z),g1) is V11() V12() ext-real Element of REAL
g1 #Z (Z - 1) is V11() V12() ext-real Element of REAL
Z * (g1 #Z (Z - 1)) is V11() V12() ext-real Element of REAL
(#Z (Z - 1)) . g1 is V11() V12() ext-real Element of REAL
Z * ((#Z (Z - 1)) . g1) is V11() V12() ext-real Element of REAL
(Z (#) (#Z (Z - 1))) . g1 is V11() V12() ext-real Element of REAL
dom ((#Z Z) `| f) is V84() V85() V86() Element of K6(REAL)
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z f is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z f) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (((#Z f) ^),Z) is V11() V12() ext-real Element of REAL
f - 1 is V11() V12() ext-real V48() Element of REAL
Z #Z (f - 1) is V11() V12() ext-real Element of REAL
f * (Z #Z (f - 1)) is V11() V12() ext-real Element of REAL
Z #Z f is V11() V12() ext-real Element of REAL
(Z #Z f) ^2 is V11() V12() ext-real Element of REAL
K37((Z #Z f),(Z #Z f)) is set
(f * (Z #Z (f - 1))) / ((Z #Z f) ^2) is V11() V12() ext-real Element of REAL
- ((f * (Z #Z (f - 1))) / ((Z #Z f) ^2)) is V11() V12() ext-real Element of REAL
(#Z f) . Z is V11() V12() ext-real Element of REAL
Z |^ f is V11() V12() ext-real Element of REAL
diff ((#Z f),Z) is V11() V12() ext-real Element of REAL
((#Z f) . Z) ^2 is V11() V12() ext-real Element of REAL
K37(((#Z f) . Z),((#Z f) . Z)) is set
(diff ((#Z f),Z)) / (((#Z f) . Z) ^2) is V11() V12() ext-real Element of REAL
- ((diff ((#Z f),Z)) / (((#Z f) . Z) ^2)) is V11() V12() ext-real Element of REAL
(f * (Z #Z (f - 1))) / (((#Z f) . Z) ^2) is V11() V12() ext-real Element of REAL
- ((f * (Z #Z (f - 1))) / (((#Z f) . Z) ^2)) is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - 2 is V11() V12() ext-real V48() Element of REAL
#Z (Z - 2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - 1 is V11() V12() ext-real V48() Element of REAL
Z * (Z - 1) is V11() V12() ext-real V48() Element of REAL
(Z * (Z - 1)) (#) (#Z (Z - 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is open V84() V85() V86() Element of K6(REAL)
diff ((#Z Z),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z Z),f)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z * (Z - 1)) (#) (#Z (Z - 2))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z g1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(g1 + 1) (#) (#Z g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((#Z Z),f)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((#Z Z),f)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z Z),f)) . (1 + 0)) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((#Z Z),f)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z Z),f)) . 0) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff ((#Z Z),f)) . 0) `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z Z) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((#Z Z) | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((#Z Z) | f) `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z Z) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((#Z Z) `| f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 + 1) - 1 is V11() V12() ext-real V48() Element of REAL
#Z ((g1 + 1) - 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 + 1) (#) (#Z ((g1 + 1) - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g1 + 1) (#) (#Z ((g1 + 1) - 1))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((g1 + 1) (#) (#Z ((g1 + 1) - 1))) | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g1 + 1) (#) (#Z g1)) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z g1) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 + 1) (#) ((#Z g1) `| f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 - 1 is V11() V12() ext-real V48() Element of REAL
#Z (g1 - 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 (#) (#Z (g1 - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 (#) (#Z (g1 - 1))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 + 1) (#) ((g1 (#) (#Z (g1 - 1))) | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 + 1) (#) (g1 (#) (#Z (g1 - 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g1 + 1) (#) (g1 (#) (#Z (g1 - 1)))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - 3 is V11() V12() ext-real V48() Element of REAL
#Z (Z - 3) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - 1 is V11() V12() ext-real V48() Element of REAL
Z * (Z - 1) is V11() V12() ext-real V48() Element of REAL
Z - 2 is V11() V12() ext-real V48() Element of REAL
(Z * (Z - 1)) * (Z - 2) is V11() V12() ext-real V48() Element of REAL
((Z * (Z - 1)) * (Z - 2)) (#) (#Z (Z - 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is open V84() V85() V86() Element of K6(REAL)
diff ((#Z Z),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z Z),f)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z * (Z - 1)) * (Z - 2)) (#) (#Z (Z - 3))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 + (- 1) is V11() V12() ext-real V48() Element of REAL
Z + 0 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z g1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(g1 + 2) * (g1 + 1) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
((g1 + 2) * (g1 + 1)) (#) (#Z g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((#Z Z),f)) . (2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((#Z Z),f)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z Z),f)) . 2) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
#Z (Z - 2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z * (Z - 1)) (#) (#Z (Z - 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z * (Z - 1)) (#) (#Z (Z - 2))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z * (Z - 1)) (#) (#Z (Z - 2))) | f) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((g1 + 2) * (g1 + 1)) (#) (#Z g1)) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z g1) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g1 + 2) * (g1 + 1)) (#) ((#Z g1) `| f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 - 1 is V11() V12() ext-real V48() Element of REAL
#Z (g1 - 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 (#) (#Z (g1 - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 (#) (#Z (g1 - 1))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g1 + 2) * (g1 + 1)) (#) ((g1 (#) (#Z (g1 - 1))) | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z - 2) (#) (#Z (Z - 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z * (Z - 1)) (#) ((Z - 2) (#) (#Z (Z - 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z * (Z - 1)) (#) ((Z - 2) (#) (#Z (Z - 3)))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z ! is V11() V12() ext-real Element of REAL
Z -' 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(Z -' 1) ! is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f ! is V11() V12() ext-real Element of REAL
(f !) / (Z !) is V11() V12() ext-real Element of REAL
((f !) / (Z !)) * Z is V11() V12() ext-real Element of REAL
(f !) / ((Z -' 1) !) is V11() V12() ext-real Element of REAL
Z - 1 is V11() V12() ext-real V48() Element of REAL
(Z -' 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
((Z -' 1) !) * Z is V11() V12() ext-real Element of REAL
(f !) / (((Z -' 1) !) * Z) is V11() V12() ext-real Element of REAL
((f !) / (((Z -' 1) !) * Z)) * Z is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z - f is V11() V12() ext-real V48() Element of REAL
#Z (Z - f) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z choose f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f ! is V11() V12() ext-real Element of REAL
(Z choose f) * (f !) is V11() V12() ext-real Element of REAL
((Z choose f) * (f !)) (#) (#Z (Z - f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is open V84() V85() V86() Element of K6(REAL)
diff ((#Z Z),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z Z),g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z choose f) * (f !)) (#) (#Z (Z - f))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 is V4() V5() V6() V10() V12() ext-real non negative V48() set
(diff ((#Z Z),g1)) . g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - g2 is V11() V12() ext-real V48() Element of REAL
#Z (Z - g2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z choose g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 ! is V11() V12() ext-real Element of REAL
(Z choose g2) * (g2 !) is V11() V12() ext-real Element of REAL
((Z choose g2) * (g2 !)) (#) (#Z (Z - g2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z choose g2) * (g2 !)) (#) (#Z (Z - g2))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((#Z Z),g1)) . (g2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - (g2 + 1) is V11() V12() ext-real V48() Element of REAL
#Z (Z - (g2 + 1)) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z choose (g2 + 1) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(g2 + 1) ! is V11() V12() ext-real Element of REAL
(Z choose (g2 + 1)) * ((g2 + 1) !) is V11() V12() ext-real Element of REAL
((Z choose (g2 + 1)) * ((g2 + 1) !)) (#) (#Z (Z - (g2 + 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z choose (g2 + 1)) * ((g2 + 1) !)) (#) (#Z (Z - (g2 + 1)))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g2 + 1) - g2 is V11() V12() ext-real V48() Element of REAL
(g2 + 1) + (- 1) is V11() V12() ext-real V48() Element of REAL
Z + 0 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x -' 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(Z - g2) - 1 is V11() V12() ext-real V48() Element of REAL
#Z x is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z choose g2) * (g2 !)) (#) (#Z x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + g2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
0 + g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(((Z choose g2) * (g2 !)) (#) (#Z x)) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((Z choose g2) * (g2 !)) (#) (#Z x)) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z choose g2) * (g2 !)) (#) (#Z x)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z x) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z choose g2) * (g2 !)) (#) ((#Z x) `| g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x - 1 is V11() V12() ext-real V48() Element of REAL
#Z (x - 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
x (#) (#Z (x - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(x (#) (#Z (x - 1))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z choose g2) * (g2 !)) (#) ((x (#) (#Z (x - 1))) | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z choose g2) * (g2 !)) (#) (x (#) (#Z (x - 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z choose g2) * (g2 !)) (#) (x (#) (#Z (x - 1)))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z choose g2) * (g2 !)) * x is V11() V12() ext-real Element of REAL
(((Z choose g2) * (g2 !)) * x) (#) (#Z (x - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((Z choose g2) * (g2 !)) * x) (#) (#Z (x - 1))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z ! is V11() V12() ext-real Element of REAL
x ! is V11() V12() ext-real Element of REAL
(g2 !) * (x !) is V11() V12() ext-real Element of REAL
(Z !) / ((g2 !) * (x !)) is V11() V12() ext-real Element of REAL
((Z !) / ((g2 !) * (x !))) * (g2 !) is V11() V12() ext-real Element of REAL
(((Z !) / ((g2 !) * (x !))) * (g2 !)) * (Z - g2) is V11() V12() ext-real Element of REAL
((((Z !) / ((g2 !) * (x !))) * (g2 !)) * (Z - g2)) (#) (#Z (x - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((Z !) / ((g2 !) * (x !))) * (g2 !)) * (Z - g2)) (#) (#Z (x - 1))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z !) / (x !) is V11() V12() ext-real Element of REAL
((Z !) / (x !)) * x is V11() V12() ext-real Element of REAL
(((Z !) / (x !)) * x) (#) (#Z (x - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((Z !) / (x !)) * x) (#) (#Z (x - 1))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(x -' 1) ! is V11() V12() ext-real Element of REAL
(Z !) / ((x -' 1) !) is V11() V12() ext-real Element of REAL
((Z !) / ((x -' 1) !)) (#) (#Z (x - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z !) / ((x -' 1) !)) (#) (#Z (x - 1))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
#Z ((Z - g2) - 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
x ! is V11() V12() ext-real Element of REAL
(x !) * ((g2 + 1) !) is V11() V12() ext-real Element of REAL
(Z !) / ((x !) * ((g2 + 1) !)) is V11() V12() ext-real Element of REAL
((Z !) / ((x !) * ((g2 + 1) !))) * ((g2 + 1) !) is V11() V12() ext-real Element of REAL
(((Z !) / ((x !) * ((g2 + 1) !))) * ((g2 + 1) !)) (#) (#Z ((Z - g2) - 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((Z !) / ((x !) * ((g2 + 1) !))) * ((g2 + 1) !)) (#) (#Z ((Z - g2) - 1))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((#Z Z),g1)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - 0 is V11() V12() ext-real V48() Element of REAL
#Z (Z - 0) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
Z choose 0 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(Z choose 0) * (0 !) is V11() V12() ext-real Element of REAL
((Z choose 0) * (0 !)) (#) (#Z (Z - 0)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z choose 0) * (0 !)) (#) (#Z (Z - 0))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z Z) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 * 1) (#) (#Z Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 * 1) (#) (#Z Z)) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is open V84() V85() V86() Element of K6(REAL)
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) g1 is V16() V21() set
diff ((- g1),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((- g1),f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,f)) . Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((diff (g1,f)) . Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) ((diff (g1,f)) . Z) is V16() V21() set
(- 1) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((diff (g1,f)) . Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
f - Z is V11() V12() ext-real Element of REAL
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 * PI is V11() V12() ext-real Element of REAL
(g1 * PI) / 2 is V11() V12() ext-real Element of REAL
Z + ((g1 * PI) / 2) is V11() V12() ext-real Element of REAL
sin . (Z + ((g1 * PI) / 2)) is V11() V12() ext-real Element of REAL
(f - Z) |^ g1 is V11() V12() ext-real Element of REAL
(sin . (Z + ((g1 * PI) / 2))) * ((f - Z) |^ g1) is V11() V12() ext-real Element of REAL
g1 ! is V11() V12() ext-real Element of REAL
((sin . (Z + ((g1 * PI) / 2))) * ((f - Z) |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
cos . (Z + ((g1 * PI) / 2)) is V11() V12() ext-real Element of REAL
(cos . (Z + ((g1 * PI) / 2))) * ((f - Z) |^ g1) is V11() V12() ext-real Element of REAL
((cos . (Z + ((g1 * PI) / 2))) * ((f - Z) |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
g2 is open V84() V85() V86() Element of K6(REAL)
Taylor (sin,g2,Z,f) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
(Taylor (sin,g2,Z,f)) . g1 is V11() V12() ext-real Element of REAL
Taylor (cos,g2,Z,f) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
(Taylor (cos,g2,Z,f)) . g1 is V11() V12() ext-real Element of REAL
diff (cos,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,g2)) . g1) . Z is V11() V12() ext-real Element of REAL
(((diff (cos,g2)) . g1) . Z) * ((f - Z) |^ g1) is V11() V12() ext-real Element of REAL
((((diff (cos,g2)) . g1) . Z) * ((f - Z) |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
diff (sin,g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,g2)) . g1) . Z is V11() V12() ext-real Element of REAL
(((diff (sin,g2)) . g1) . Z) * ((f - Z) |^ g1) is V11() V12() ext-real Element of REAL
((((diff (sin,g2)) . g1) . Z) * ((f - Z) |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
- Z is V11() V12() ext-real Element of REAL
].(- Z),Z.[ is open V84() V85() V86() Element of K6(REAL)
f is V11() V12() ext-real Element of REAL
Maclaurin (sin,].(- Z),Z.[,f) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
Maclaurin (cos,].(- Z),Z.[,f) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(Maclaurin (sin,].(- Z),Z.[,f)) . g1 is V11() V12() ext-real Element of REAL
g1 * PI is V11() V12() ext-real Element of REAL
(g1 * PI) / 2 is V11() V12() ext-real Element of REAL
sin . ((g1 * PI) / 2) is V11() V12() ext-real Element of REAL
f |^ g1 is V11() V12() ext-real Element of REAL
(sin . ((g1 * PI) / 2)) * (f |^ g1) is V11() V12() ext-real Element of REAL
g1 ! is V11() V12() ext-real Element of REAL
((sin . ((g1 * PI) / 2)) * (f |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
(Maclaurin (cos,].(- Z),Z.[,f)) . g1 is V11() V12() ext-real Element of REAL
cos . ((g1 * PI) / 2) is V11() V12() ext-real Element of REAL
(cos . ((g1 * PI) / 2)) * (f |^ g1) is V11() V12() ext-real Element of REAL
((cos . ((g1 * PI) / 2)) * (f |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
0 - 0 is V11() V12() ext-real V48() Element of REAL
abs (0 - 0) is V11() V12() ext-real Element of REAL
0 - Z is V11() V12() ext-real Element of REAL
0 + Z is V11() V12() ext-real Element of REAL
].(0 - Z),(0 + Z).[ is open V84() V85() V86() Element of K6(REAL)
Taylor (cos,].(- Z),Z.[,0,f) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
(Taylor (cos,].(- Z),Z.[,0,f)) . g1 is V11() V12() ext-real Element of REAL
diff (cos,].(- Z),Z.[) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,].(- Z),Z.[)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,].(- Z),Z.[)) . g1) . 0 is V11() V12() ext-real Element of REAL
f - 0 is V11() V12() ext-real Element of REAL
(f - 0) |^ g1 is V11() V12() ext-real Element of REAL
(((diff (cos,].(- Z),Z.[)) . g1) . 0) * ((f - 0) |^ g1) is V11() V12() ext-real Element of REAL
((((diff (cos,].(- Z),Z.[)) . g1) . 0) * ((f - 0) |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
0 + ((g1 * PI) / 2) is V11() V12() ext-real Element of REAL
cos . (0 + ((g1 * PI) / 2)) is V11() V12() ext-real Element of REAL
(cos . (0 + ((g1 * PI) / 2))) * (f |^ g1) is V11() V12() ext-real Element of REAL
((cos . (0 + ((g1 * PI) / 2))) * (f |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
Taylor (sin,].(- Z),Z.[,0,f) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
(Taylor (sin,].(- Z),Z.[,0,f)) . g1 is V11() V12() ext-real Element of REAL
diff (sin,].(- Z),Z.[) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,].(- Z),Z.[)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,].(- Z),Z.[)) . g1) . 0 is V11() V12() ext-real Element of REAL
(((diff (sin,].(- Z),Z.[)) . g1) . 0) * ((f - 0) |^ g1) is V11() V12() ext-real Element of REAL
((((diff (sin,].(- Z),Z.[)) . g1) . 0) * ((f - 0) |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
sin . (0 + ((g1 * PI) / 2)) is V11() V12() ext-real Element of REAL
(sin . (0 + ((g1 * PI) / 2))) * (f |^ g1) is V11() V12() ext-real Element of REAL
((sin . (0 + ((g1 * PI) / 2))) * (f |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z f is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f choose g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 ! is V11() V12() ext-real Element of REAL
(f choose g1) * (g1 !) is V11() V12() ext-real Element of REAL
f - g1 is V11() V12() ext-real V48() Element of REAL
Z #Z (f - g1) is V11() V12() ext-real Element of REAL
((f choose g1) * (g1 !)) * (Z #Z (f - g1)) is V11() V12() ext-real Element of REAL
g2 is open V84() V85() V86() Element of K6(REAL)
diff ((#Z f),g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z f),g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z f),g2)) . g1) . Z is V11() V12() ext-real Element of REAL
#Z (f - g1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (#Z (f - g1)) is V84() V85() V86() Element of K6(REAL)
((f choose g1) * (g1 !)) (#) (#Z (f - g1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((f choose g1) * (g1 !)) (#) (#Z (f - g1))) is V84() V85() V86() Element of K6(REAL)
(((f choose g1) * (g1 !)) (#) (#Z (f - g1))) | g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((f choose g1) * (g1 !)) (#) (#Z (f - g1))) | g2) is V84() V85() V86() Element of K6(REAL)
REAL /\ g2 is V84() V85() V86() set
((((f choose g1) * (g1 !)) (#) (#Z (f - g1))) | g2) . Z is V11() V12() ext-real Element of REAL
(((f choose g1) * (g1 !)) (#) (#Z (f - g1))) . Z is V11() V12() ext-real Element of REAL
(#Z (f - g1)) . Z is V11() V12() ext-real Element of REAL
((f choose g1) * (g1 !)) * ((#Z (f - g1)) . Z) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z f is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
f ! is V11() V12() ext-real Element of REAL
g1 is open V84() V85() V86() Element of K6(REAL)
diff ((#Z f),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z f),g1)) . f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z f),g1)) . f) . Z is V11() V12() ext-real Element of REAL
0 + f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f - 1 is V11() V12() ext-real V48() Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
0 + g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 ! is V11() V12() ext-real Element of REAL
#Z 1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(g2 + 1) ! is V11() V12() ext-real Element of REAL
((g2 + 1) !) (#) (#Z 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (#Z 1) is V84() V85() V86() Element of K6(REAL)
dom (((g2 + 1) !) (#) (#Z 1)) is V84() V85() V86() Element of K6(REAL)
#Z (g2 + 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((#Z (g2 + 1)),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z (g2 + 1)),g1)) . g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z (g2 + 1)),g1)) . g2) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff ((#Z (g2 + 1)),g1)) . g2) `| g1) . Z is V11() V12() ext-real Element of REAL
(g2 + 1) - g2 is V11() V12() ext-real V48() Element of REAL
#Z ((g2 + 1) - g2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(g2 + 1) choose g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
((g2 + 1) choose g2) * (g2 !) is V11() V12() ext-real Element of REAL
(((g2 + 1) choose g2) * (g2 !)) (#) (#Z ((g2 + 1) - g2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((g2 + 1) choose g2) * (g2 !)) (#) (#Z ((g2 + 1) - g2))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((g2 + 1) choose g2) * (g2 !)) (#) (#Z ((g2 + 1) - g2))) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((((g2 + 1) choose g2) * (g2 !)) (#) (#Z ((g2 + 1) - g2))) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
(g2 !) * 1 is V11() V12() ext-real Element of REAL
((g2 + 1) !) / ((g2 !) * 1) is V11() V12() ext-real Element of REAL
(((g2 + 1) !) / ((g2 !) * 1)) * (g2 !) is V11() V12() ext-real Element of REAL
((((g2 + 1) !) / ((g2 !) * 1)) * (g2 !)) (#) (#Z ((g2 + 1) - g2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((g2 + 1) !) / ((g2 !) * 1)) * (g2 !)) (#) (#Z ((g2 + 1) - g2))) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((((g2 + 1) !) / ((g2 !) * 1)) * (g2 !)) (#) (#Z ((g2 + 1) - g2))) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((((g2 + 1) !) / ((g2 !) * 1)) * (g2 !)) (#) (#Z ((g2 + 1) - g2))) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
((g2 + 1) !) / 1 is V11() V12() ext-real Element of REAL
(((g2 + 1) !) / 1) (#) (#Z 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((g2 + 1) !) / 1) (#) (#Z 1)) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((g2 + 1) !) / 1) (#) (#Z 1)) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((((g2 + 1) !) / 1) (#) (#Z 1)) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
(((g2 + 1) !) (#) (#Z 1)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((g2 + 1) !) (#) (#Z 1)) `| g1) . Z is V11() V12() ext-real Element of REAL
diff ((#Z 1),Z) is V11() V12() ext-real Element of REAL
((g2 + 1) !) * (diff ((#Z 1),Z)) is V11() V12() ext-real Element of REAL
1 - 1 is V11() V12() ext-real V48() Element of REAL
Z #Z (1 - 1) is V11() V12() ext-real Element of REAL
1 * (Z #Z (1 - 1)) is V11() V12() ext-real Element of REAL
((g2 + 1) !) * (1 * (Z #Z (1 - 1))) is V11() V12() ext-real Element of REAL
((g2 + 1) !) * 1 is V11() V12() ext-real Element of REAL
#Z 0 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z 0) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((#Z 0) | g1) . Z is V11() V12() ext-real Element of REAL
(#Z 0) . Z is V11() V12() ext-real Element of REAL
Z #Z 0 is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
f is open V84() V85() V86() Element of K6(REAL)
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z - 1 is V11() V12() ext-real V48() Element of REAL
diff ((#Z Z),f) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z Z),f)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - 1 is V11() V12() ext-real V48() Element of REAL
0 + Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(- 1) + Z is V11() V12() ext-real V48() Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((#Z Z),f)) . g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z Z),f)) . g2) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 + 0 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(Z - 1) + 1 is V11() V12() ext-real V48() Element of REAL
Z - g2 is V11() V12() ext-real V48() Element of REAL
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z x is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
x is V11() V12() ext-real Element of REAL
(#Z x) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z choose g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 ! is V11() V12() ext-real Element of REAL
(Z choose g2) * (g2 !) is V11() V12() ext-real Element of REAL
((Z choose g2) * (g2 !)) (#) (#Z x) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((Z choose g2) * (g2 !)) (#) (#Z x)) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((Z choose g2) * (g2 !)) (#) (#Z x)) | f) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((Z choose g2) * (g2 !)) (#) ((#Z x) | f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z - g2 is V11() V12() ext-real V48() Element of REAL
#Z (Z - g2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (#Z (Z - g2)) is V84() V85() V86() Element of K6(REAL)
Z choose g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 ! is V11() V12() ext-real Element of REAL
(Z choose g2) * (g2 !) is V11() V12() ext-real Element of REAL
((Z choose g2) * (g2 !)) (#) (#Z (Z - g2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((Z choose g2) * (g2 !)) (#) (#Z (Z - g2))) is V84() V85() V86() Element of K6(REAL)
dom ((diff ((#Z Z),f)) . g2) is V84() V85() V86() Element of K6(REAL)
(((Z choose g2) * (g2 !)) (#) (#Z (Z - g2))) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((Z choose g2) * (g2 !)) (#) (#Z (Z - g2))) | f) is V84() V85() V86() Element of K6(REAL)
REAL /\ f is V84() V85() V86() set
Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z g1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (#Z g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 choose g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f * (g1 choose g2) is V11() V12() ext-real Element of REAL
g2 ! is V11() V12() ext-real Element of REAL
(f * (g1 choose g2)) * (g2 !) is V11() V12() ext-real Element of REAL
g1 - g2 is V11() V12() ext-real V48() Element of REAL
Z #Z (g1 - g2) is V11() V12() ext-real Element of REAL
((f * (g1 choose g2)) * (g2 !)) * (Z #Z (g1 - g2)) is V11() V12() ext-real Element of REAL
x is open V84() V85() V86() Element of K6(REAL)
diff ((f (#) (#Z g1)),x) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f (#) (#Z g1)),x)) . g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) (#Z g1)),x)) . g2) . Z is V11() V12() ext-real Element of REAL
#Z (g1 - g2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (#Z (g1 - g2)) is V84() V85() V86() Element of K6(REAL)
(g1 choose g2) * (g2 !) is V11() V12() ext-real Element of REAL
((g1 choose g2) * (g2 !)) (#) (#Z (g1 - g2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((g1 choose g2) * (g2 !)) (#) (#Z (g1 - g2))) is V84() V85() V86() Element of K6(REAL)
diff ((#Z g1),x) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z g1),x)) . g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff ((#Z g1),x)) . g2) is V84() V85() V86() Element of K6(REAL)
(((g1 choose g2) * (g2 !)) (#) (#Z (g1 - g2))) | x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((g1 choose g2) * (g2 !)) (#) (#Z (g1 - g2))) | x) is V84() V85() V86() Element of K6(REAL)
REAL /\ x is V84() V85() V86() set
f (#) ((diff ((#Z g1),x)) . g2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) ((diff ((#Z g1),x)) . g2)) is V84() V85() V86() Element of K6(REAL)
(f (#) ((diff ((#Z g1),x)) . g2)) . Z is V11() V12() ext-real Element of REAL
((diff ((#Z g1),x)) . g2) . Z is V11() V12() ext-real Element of REAL
f * (((diff ((#Z g1),x)) . g2) . Z) is V11() V12() ext-real Element of REAL
((g1 choose g2) * (g2 !)) * (Z #Z (g1 - g2)) is V11() V12() ext-real Element of REAL
f * (((g1 choose g2) * (g2 !)) * (Z #Z (g1 - g2))) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z g1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (#Z g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 ! is V11() V12() ext-real Element of REAL
f * (g1 !) is V11() V12() ext-real Element of REAL
g2 is open V84() V85() V86() Element of K6(REAL)
diff ((f (#) (#Z g1)),g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f (#) (#Z g1)),g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) (#Z g1)),g2)) . g1) . Z is V11() V12() ext-real Element of REAL
0 + g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 - 1 is V11() V12() ext-real V48() Element of REAL
diff ((#Z g1),g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z g1),g2)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff ((#Z g1),g2)) . g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) ((diff ((#Z g1),g2)) . g1)) is V84() V85() V86() Element of K6(REAL)
dom ((diff ((#Z g1),g2)) . g1) is V84() V85() V86() Element of K6(REAL)
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((#Z g1),g2)) . x is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
x + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((#Z g1),g2)) . (x + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff ((#Z g1),g2)) . (x + 1)) is V84() V85() V86() Element of K6(REAL)
((diff ((#Z g1),g2)) . x) `| g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff ((#Z g1),g2)) . x) `| g2) is V84() V85() V86() Element of K6(REAL)
(f (#) ((diff ((#Z g1),g2)) . g1)) . Z is V11() V12() ext-real Element of REAL
((diff ((#Z g1),g2)) . g1) . Z is V11() V12() ext-real Element of REAL
f * (((diff ((#Z g1),g2)) . g1) . Z) is V11() V12() ext-real Element of REAL
#Z 0 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (#Z 0) is V84() V85() V86() Element of K6(REAL)
f (#) (#Z 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (f (#) (#Z 0)) is V84() V85() V86() Element of K6(REAL)
diff ((#Z 0),g2) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z 0),g2)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff ((#Z 0),g2)) . 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((diff ((#Z 0),g2)) . 0)) . Z is V11() V12() ext-real Element of REAL
(#Z 0) | g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((#Z 0) | g2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((#Z 0) | g2)) . Z is V11() V12() ext-real Element of REAL
(f (#) (#Z 0)) | g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f (#) (#Z 0)) | g2) . Z is V11() V12() ext-real Element of REAL
(f (#) (#Z 0)) . Z is V11() V12() ext-real Element of REAL
(#Z 0) . Z is V11() V12() ext-real Element of REAL
f * ((#Z 0) . Z) is V11() V12() ext-real Element of REAL
Z #Z 0 is V11() V12() ext-real Element of REAL
f * (Z #Z 0) is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V11() V12() ext-real Element of REAL
f - Z is V11() V12() ext-real Element of REAL
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z g1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(f - Z) |^ g1 is V11() V12() ext-real Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 choose g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 - g2 is V11() V12() ext-real V48() Element of REAL
Z #Z (g1 - g2) is V11() V12() ext-real Element of REAL
(g1 choose g2) * (Z #Z (g1 - g2)) is V11() V12() ext-real Element of REAL
(f - Z) |^ g2 is V11() V12() ext-real Element of REAL
((g1 choose g2) * (Z #Z (g1 - g2))) * ((f - Z) |^ g2) is V11() V12() ext-real Element of REAL
x is open V84() V85() V86() Element of K6(REAL)
Taylor ((#Z g1),x,Z,f) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
(Taylor ((#Z g1),x,Z,f)) . g2 is V11() V12() ext-real Element of REAL
(Taylor ((#Z g1),x,Z,f)) . g1 is V11() V12() ext-real Element of REAL
g1 ! is V11() V12() ext-real Element of REAL
diff ((#Z g1),x) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((#Z g1),x)) . g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z g1),x)) . g1) . Z is V11() V12() ext-real Element of REAL
(((diff ((#Z g1),x)) . g1) . Z) * ((f - Z) |^ g1) is V11() V12() ext-real Element of REAL
((((diff ((#Z g1),x)) . g1) . Z) * ((f - Z) |^ g1)) / (g1 !) is V11() V12() ext-real Element of REAL
((f - Z) |^ g1) * (g1 !) is V11() V12() ext-real Element of REAL
(((f - Z) |^ g1) * (g1 !)) / (g1 !) is V11() V12() ext-real Element of REAL
g2 ! is V11() V12() ext-real Element of REAL
(diff ((#Z g1),x)) . g2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((#Z g1),x)) . g2) . Z is V11() V12() ext-real Element of REAL
(((diff ((#Z g1),x)) . g2) . Z) * ((f - Z) |^ g2) is V11() V12() ext-real Element of REAL
((((diff ((#Z g1),x)) . g2) . Z) * ((f - Z) |^ g2)) / (g2 !) is V11() V12() ext-real Element of REAL
(g1 choose g2) * (g2 !) is V11() V12() ext-real Element of REAL
((g1 choose g2) * (g2 !)) * (Z #Z (g1 - g2)) is V11() V12() ext-real Element of REAL
(((g1 choose g2) * (g2 !)) * (Z #Z (g1 - g2))) * ((f - Z) |^ g2) is V11() V12() ext-real Element of REAL
((((g1 choose g2) * (g2 !)) * (Z #Z (g1 - g2))) * ((f - Z) |^ g2)) / (g2 !) is V11() V12() ext-real Element of REAL
(Z #Z (g1 - g2)) * ((f - Z) |^ g2) is V11() V12() ext-real Element of REAL
(g1 choose g2) * ((Z #Z (g1 - g2)) * ((f - Z) |^ g2)) is V11() V12() ext-real Element of REAL
((g1 choose g2) * ((Z #Z (g1 - g2)) * ((f - Z) |^ g2))) * (g2 !) is V11() V12() ext-real Element of REAL
(((g1 choose g2) * ((Z #Z (g1 - g2)) * ((f - Z) |^ g2))) * (g2 !)) / (g2 !) is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V11() V12() ext-real Element of REAL
- g1 is V11() V12() ext-real Element of REAL
].(- g1),g1.[ is open V84() V85() V86() Element of K6(REAL)
g2 is V11() V12() ext-real Element of REAL
Maclaurin ((#Z Z),].(- g1),g1.[,g2) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
(Maclaurin ((#Z Z),].(- g1),g1.[,g2)) . f is V11() V12() ext-real Element of REAL
(Maclaurin ((#Z Z),].(- g1),g1.[,g2)) . Z is V11() V12() ext-real Element of REAL
g2 |^ Z is V11() V12() ext-real Element of REAL
0 - 0 is V11() V12() ext-real V48() Element of REAL
abs (0 - 0) is V11() V12() ext-real Element of REAL
0 - g1 is V11() V12() ext-real Element of REAL
0 + g1 is V11() V12() ext-real Element of REAL
].(0 - g1),(0 + g1).[ is open V84() V85() V86() Element of K6(REAL)
Z - f is V11() V12() ext-real V48() Element of REAL
f - f is V11() V12() ext-real V48() Element of REAL
Taylor ((#Z Z),].(- g1),g1.[,0,g2) is non empty V16() V19( NAT ) V20( REAL ) V21() total V30( NAT , REAL ) V74() V75() V76() Element of K6(K7(NAT,REAL))
(Taylor ((#Z Z),].(- g1),g1.[,0,g2)) . Z is V11() V12() ext-real Element of REAL
g2 - 0 is V11() V12() ext-real Element of REAL
(g2 - 0) |^ Z is V11() V12() ext-real Element of REAL
(Taylor ((#Z Z),].(- g1),g1.[,0,g2)) . f is V11() V12() ext-real Element of REAL
Z choose f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
0 #Z (Z - f) is V11() V12() ext-real Element of REAL
(Z choose f) * (0 #Z (Z - f)) is V11() V12() ext-real Element of REAL
(g2 - 0) |^ f is V11() V12() ext-real Element of REAL
((Z choose f) * (0 #Z (Z - f))) * ((g2 - 0) |^ f) is V11() V12() ext-real Element of REAL
x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
0 |^ x is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(Z choose f) * (0 |^ x) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 |^ f is V11() V12() ext-real Element of REAL
((Z choose f) * (0 |^ x)) * (g2 |^ f) is V11() V12() ext-real Element of REAL
(Z choose f) * 0 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
((Z choose f) * 0) * (g2 |^ f) is V11() V12() ext-real Element of REAL
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z Z) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is open V84() V85() V86() Element of K6(REAL)
g1 is V11() V12() ext-real Element of REAL
(#Z Z) . g1 is V11() V12() ext-real Element of REAL
g1 #Z Z is V11() V12() ext-real Element of REAL
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z f is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z f) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z (f + 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z (f + 1)) . Z is V11() V12() ext-real Element of REAL
f / ((#Z (f + 1)) . Z) is V11() V12() ext-real Element of REAL
- (f / ((#Z (f + 1)) . Z)) is V11() V12() ext-real Element of REAL
g1 is open V84() V85() V86() Element of K6(REAL)
((#Z f) ^) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((#Z f) ^) `| g1) . Z is V11() V12() ext-real Element of REAL
0 + f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f - 1 is V11() V12() ext-real V48() Element of REAL
g2 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z #Z g2 is V11() V12() ext-real Element of REAL
Z |^ g2 is V11() V12() ext-real Element of REAL
diff (((#Z f) ^),Z) is V11() V12() ext-real Element of REAL
f * (Z #Z g2) is V11() V12() ext-real Element of REAL
Z #Z f is V11() V12() ext-real Element of REAL
(Z #Z f) ^2 is V11() V12() ext-real Element of REAL
K37((Z #Z f),(Z #Z f)) is set
(f * (Z #Z g2)) / ((Z #Z f) ^2) is V11() V12() ext-real Element of REAL
- ((f * (Z #Z g2)) / ((Z #Z f) ^2)) is V11() V12() ext-real Element of REAL
Z |^ f is V11() V12() ext-real Element of REAL
(Z |^ f) ^2 is V11() V12() ext-real Element of REAL
K37((Z |^ f),(Z |^ f)) is set
(f * (Z #Z g2)) / ((Z |^ f) ^2) is V11() V12() ext-real Element of REAL
- ((f * (Z #Z g2)) / ((Z |^ f) ^2)) is V11() V12() ext-real Element of REAL
f * (Z |^ g2) is V11() V12() ext-real Element of REAL
(f * (Z |^ g2)) / ((Z |^ f) ^2) is V11() V12() ext-real Element of REAL
- ((f * (Z |^ g2)) / ((Z |^ f) ^2)) is V11() V12() ext-real Element of REAL
g2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z |^ (g2 + 1) is V11() V12() ext-real Element of REAL
Z |^ 1 is V11() V12() ext-real Element of REAL
(Z |^ 1) * (Z |^ g2) is V11() V12() ext-real Element of REAL
(Z |^ (g2 + 1)) * ((Z |^ 1) * (Z |^ g2)) is V11() V12() ext-real Element of REAL
(f * (Z |^ g2)) / ((Z |^ (g2 + 1)) * ((Z |^ 1) * (Z |^ g2))) is V11() V12() ext-real Element of REAL
- ((f * (Z |^ g2)) / ((Z |^ (g2 + 1)) * ((Z |^ 1) * (Z |^ g2)))) is V11() V12() ext-real Element of REAL
(Z |^ (g2 + 1)) * (Z |^ 1) is V11() V12() ext-real Element of REAL
((Z |^ (g2 + 1)) * (Z |^ 1)) * (Z |^ g2) is V11() V12() ext-real Element of REAL
(f * (Z |^ g2)) / (((Z |^ (g2 + 1)) * (Z |^ 1)) * (Z |^ g2)) is V11() V12() ext-real Element of REAL
- ((f * (Z |^ g2)) / (((Z |^ (g2 + 1)) * (Z |^ 1)) * (Z |^ g2))) is V11() V12() ext-real Element of REAL
(g2 + 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z |^ ((g2 + 1) + 1) is V11() V12() ext-real Element of REAL
(Z |^ ((g2 + 1) + 1)) * (Z |^ g2) is V11() V12() ext-real Element of REAL
(f * (Z |^ g2)) / ((Z |^ ((g2 + 1) + 1)) * (Z |^ g2)) is V11() V12() ext-real Element of REAL
- ((f * (Z |^ g2)) / ((Z |^ ((g2 + 1) + 1)) * (Z |^ g2))) is V11() V12() ext-real Element of REAL
g2 + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z |^ (g2 + 2) is V11() V12() ext-real Element of REAL
f / (Z |^ (g2 + 2)) is V11() V12() ext-real Element of REAL
- (f / (Z |^ (g2 + 2))) is V11() V12() ext-real Element of REAL
Z #Z (g2 + 2) is V11() V12() ext-real Element of REAL
f / (Z #Z (g2 + 2)) is V11() V12() ext-real Element of REAL
- (f / (Z #Z (g2 + 2))) is V11() V12() ext-real Element of REAL
diff (((#Z f) ^),Z) is V11() V12() ext-real Element of REAL
f - 1 is V11() V12() ext-real V48() Element of REAL
Z #Z (f - 1) is V11() V12() ext-real Element of REAL
0 * (Z #Z (f - 1)) is V11() V12() ext-real Element of REAL
Z #Z f is V11() V12() ext-real Element of REAL
(Z #Z f) ^2 is V11() V12() ext-real Element of REAL
K37((Z #Z f),(Z #Z f)) is set
(0 * (Z #Z (f - 1))) / ((Z #Z f) ^2) is V11() V12() ext-real Element of REAL
- ((0 * (Z #Z (f - 1))) / ((Z #Z f) ^2)) is V11() V12() ext-real Element of REAL
#Z 1 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
id REAL is non empty V16() V19( REAL ) V20( REAL ) V21() V22() total V30( REAL , REAL ) V74() V75() V76() V78() V80() Element of K6(K7(REAL,REAL))
Z is V11() V12() ext-real Element of REAL
(#Z 1) . Z is V11() V12() ext-real Element of REAL
(id REAL) . Z is V11() V12() ext-real Element of REAL
Z #Z 1 is V11() V12() ext-real Element of REAL
(id REAL) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V11() V12() ext-real Element of REAL
diff (((id REAL) ^),Z) is V11() V12() ext-real Element of REAL
Z ^2 is V11() V12() ext-real Element of REAL
K37(Z,Z) is set
1 / (Z ^2) is V11() V12() ext-real Element of REAL
- (1 / (Z ^2)) is V11() V12() ext-real Element of REAL
(id REAL) . Z is V11() V12() ext-real Element of REAL
Z #Z 1 is V11() V12() ext-real Element of REAL
Z |^ 1 is V11() V12() ext-real Element of REAL
diff ((id REAL),Z) is V11() V12() ext-real Element of REAL
((id REAL) . Z) ^2 is V11() V12() ext-real Element of REAL
K37(((id REAL) . Z),((id REAL) . Z)) is set
(diff ((id REAL),Z)) / (((id REAL) . Z) ^2) is V11() V12() ext-real Element of REAL
- ((diff ((id REAL),Z)) / (((id REAL) . Z) ^2)) is V11() V12() ext-real Element of REAL
1 - 1 is V11() V12() ext-real V48() Element of REAL
Z #Z (1 - 1) is V11() V12() ext-real Element of REAL
1 * (Z #Z (1 - 1)) is V11() V12() ext-real Element of REAL
(1 * (Z #Z (1 - 1))) / (((id REAL) . Z) ^2) is V11() V12() ext-real Element of REAL
- ((1 * (Z #Z (1 - 1))) / (((id REAL) . Z) ^2)) is V11() V12() ext-real Element of REAL
Z #Z 0 is V11() V12() ext-real Element of REAL
1 * (Z #Z 0) is V11() V12() ext-real Element of REAL
(1 * (Z #Z 0)) / (Z ^2) is V11() V12() ext-real Element of REAL
- ((1 * (Z #Z 0)) / (Z ^2)) is V11() V12() ext-real Element of REAL
#Z 2 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z 2) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((#Z 2) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
((id REAL) ^) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) ((#Z 2) ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((id REAL) ^) `| Z) is V84() V85() V86() Element of K6(REAL)
dom ((#Z 2) ^) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) ((#Z 2) ^)) is V84() V85() V86() Element of K6(REAL)
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z (1 + 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z (1 + 1)) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((#Z (1 + 1)) ^) is V84() V85() V86() Element of K6(REAL)
f is V11() V12() ext-real Element of REAL
(((id REAL) ^) `| Z) . f is V11() V12() ext-real Element of REAL
(((- 1) (#) ((#Z 2) ^)) | Z) . f is V11() V12() ext-real Element of REAL
diff (((id REAL) ^),f) is V11() V12() ext-real Element of REAL
f ^2 is V11() V12() ext-real Element of REAL
K37(f,f) is set
1 / (f ^2) is V11() V12() ext-real Element of REAL
- (1 / (f ^2)) is V11() V12() ext-real Element of REAL
f |^ (1 + 1) is V11() V12() ext-real Element of REAL
1 / (f |^ (1 + 1)) is V11() V12() ext-real Element of REAL
- (1 / (f |^ (1 + 1))) is V11() V12() ext-real Element of REAL
f #Z 2 is V11() V12() ext-real Element of REAL
1 / (f #Z 2) is V11() V12() ext-real Element of REAL
- (1 / (f #Z 2)) is V11() V12() ext-real Element of REAL
(#Z 2) . f is V11() V12() ext-real Element of REAL
1 / ((#Z 2) . f) is V11() V12() ext-real Element of REAL
- (1 / ((#Z 2) . f)) is V11() V12() ext-real Element of REAL
((#Z 2) . f) " is V11() V12() ext-real Element of REAL
1 * (((#Z 2) . f) ") is V11() V12() ext-real Element of REAL
- (1 * (((#Z 2) . f) ")) is V11() V12() ext-real Element of REAL
((#Z 2) ^) . f is V11() V12() ext-real Element of REAL
1 * (((#Z 2) ^) . f) is V11() V12() ext-real Element of REAL
- (1 * (((#Z 2) ^) . f)) is V11() V12() ext-real Element of REAL
(- 1) * (((#Z 2) ^) . f) is V11() V12() ext-real Element of REAL
((- 1) (#) ((#Z 2) ^)) . f is V11() V12() ext-real Element of REAL
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z (1 + 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z (1 + 1)) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((#Z (1 + 1)) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) ((#Z (1 + 1)) ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((- 1) (#) ((#Z (1 + 1)) ^)) | Z) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) ((#Z 2) ^)) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) ((#Z 2) ^))) /\ Z is V84() V85() V86() set
(dom ((#Z 2) ^)) /\ Z is V84() V85() V86() set
Z is V11() V12() ext-real Element of REAL
diff (((#Z 2) ^),Z) is V11() V12() ext-real Element of REAL
2 * Z is V11() V12() ext-real Element of REAL
Z #Z 2 is V11() V12() ext-real Element of REAL
(Z #Z 2) ^2 is V11() V12() ext-real Element of REAL
K37((Z #Z 2),(Z #Z 2)) is set
(2 * Z) / ((Z #Z 2) ^2) is V11() V12() ext-real Element of REAL
- ((2 * Z) / ((Z #Z 2) ^2)) is V11() V12() ext-real Element of REAL
(#Z 2) . Z is V11() V12() ext-real Element of REAL
Z |^ 2 is V11() V12() ext-real Element of REAL
diff ((#Z 2),Z) is V11() V12() ext-real Element of REAL
((#Z 2) . Z) ^2 is V11() V12() ext-real Element of REAL
K37(((#Z 2) . Z),((#Z 2) . Z)) is set
(diff ((#Z 2),Z)) / (((#Z 2) . Z) ^2) is V11() V12() ext-real Element of REAL
- ((diff ((#Z 2),Z)) / (((#Z 2) . Z) ^2)) is V11() V12() ext-real Element of REAL
2 - 1 is V11() V12() ext-real V48() Element of REAL
Z #Z (2 - 1) is V11() V12() ext-real Element of REAL
2 * (Z #Z (2 - 1)) is V11() V12() ext-real Element of REAL
(2 * (Z #Z (2 - 1))) / (((#Z 2) . Z) ^2) is V11() V12() ext-real Element of REAL
- ((2 * (Z #Z (2 - 1))) / (((#Z 2) . Z) ^2)) is V11() V12() ext-real Element of REAL
Z #Z 1 is V11() V12() ext-real Element of REAL
2 * (Z #Z 1) is V11() V12() ext-real Element of REAL
(2 * (Z #Z 1)) / ((Z #Z 2) ^2) is V11() V12() ext-real Element of REAL
- ((2 * (Z #Z 1)) / ((Z #Z 2) ^2)) is V11() V12() ext-real Element of REAL
#Z 3 is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z 3) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- 2 is V11() V12() ext-real V48() Element of REAL
(- 2) (#) ((#Z 3) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
((#Z 2) ^) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 2) (#) ((#Z 3) ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((#Z 2) ^) `| Z) is V84() V85() V86() Element of K6(REAL)
dom ((#Z 3) ^) is V84() V85() V86() Element of K6(REAL)
2 - 1 is V11() V12() ext-real V48() Element of REAL
g1 is V11() V12() ext-real Element of REAL
(((#Z 2) ^) `| Z) . g1 is V11() V12() ext-real Element of REAL
(((- 2) (#) ((#Z 3) ^)) | Z) . g1 is V11() V12() ext-real Element of REAL
dom ((- 2) (#) ((#Z 3) ^)) is V84() V85() V86() Element of K6(REAL)
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 #Z f is V11() V12() ext-real Element of REAL
g1 |^ f is V11() V12() ext-real Element of REAL
diff (((#Z 2) ^),g1) is V11() V12() ext-real Element of REAL
2 * g1 is V11() V12() ext-real Element of REAL
g1 #Z 2 is V11() V12() ext-real Element of REAL
(g1 #Z 2) ^2 is V11() V12() ext-real Element of REAL
K37((g1 #Z 2),(g1 #Z 2)) is set
(2 * g1) / ((g1 #Z 2) ^2) is V11() V12() ext-real Element of REAL
- ((2 * g1) / ((g1 #Z 2) ^2)) is V11() V12() ext-real Element of REAL
g1 #Z 1 is V11() V12() ext-real Element of REAL
2 * (g1 #Z 1) is V11() V12() ext-real Element of REAL
(2 * (g1 #Z 1)) / ((g1 #Z 2) ^2) is V11() V12() ext-real Element of REAL
- ((2 * (g1 #Z 1)) / ((g1 #Z 2) ^2)) is V11() V12() ext-real Element of REAL
g1 |^ 2 is V11() V12() ext-real Element of REAL
(g1 |^ 2) ^2 is V11() V12() ext-real Element of REAL
K37((g1 |^ 2),(g1 |^ 2)) is set
(2 * (g1 #Z 1)) / ((g1 |^ 2) ^2) is V11() V12() ext-real Element of REAL
- ((2 * (g1 #Z 1)) / ((g1 |^ 2) ^2)) is V11() V12() ext-real Element of REAL
g1 |^ 1 is V11() V12() ext-real Element of REAL
2 * (g1 |^ 1) is V11() V12() ext-real Element of REAL
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 |^ (1 + 1) is V11() V12() ext-real Element of REAL
(g1 |^ 2) * (g1 |^ (1 + 1)) is V11() V12() ext-real Element of REAL
(2 * (g1 |^ 1)) / ((g1 |^ 2) * (g1 |^ (1 + 1))) is V11() V12() ext-real Element of REAL
- ((2 * (g1 |^ 1)) / ((g1 |^ 2) * (g1 |^ (1 + 1)))) is V11() V12() ext-real Element of REAL
(g1 |^ 1) * (g1 |^ 1) is V11() V12() ext-real Element of REAL
(g1 |^ 2) * ((g1 |^ 1) * (g1 |^ 1)) is V11() V12() ext-real Element of REAL
(2 * (g1 |^ 1)) / ((g1 |^ 2) * ((g1 |^ 1) * (g1 |^ 1))) is V11() V12() ext-real Element of REAL
- ((2 * (g1 |^ 1)) / ((g1 |^ 2) * ((g1 |^ 1) * (g1 |^ 1)))) is V11() V12() ext-real Element of REAL
(g1 |^ 2) * (g1 |^ 1) is V11() V12() ext-real Element of REAL
((g1 |^ 2) * (g1 |^ 1)) * (g1 |^ 1) is V11() V12() ext-real Element of REAL
(2 * (g1 |^ 1)) / (((g1 |^ 2) * (g1 |^ 1)) * (g1 |^ 1)) is V11() V12() ext-real Element of REAL
- ((2 * (g1 |^ 1)) / (((g1 |^ 2) * (g1 |^ 1)) * (g1 |^ 1))) is V11() V12() ext-real Element of REAL
2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 |^ (2 + 1) is V11() V12() ext-real Element of REAL
(g1 |^ (2 + 1)) * (g1 |^ 1) is V11() V12() ext-real Element of REAL
(2 * (g1 |^ 1)) / ((g1 |^ (2 + 1)) * (g1 |^ 1)) is V11() V12() ext-real Element of REAL
- ((2 * (g1 |^ 1)) / ((g1 |^ (2 + 1)) * (g1 |^ 1))) is V11() V12() ext-real Element of REAL
1 + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g1 |^ (1 + 2) is V11() V12() ext-real Element of REAL
2 / (g1 |^ (1 + 2)) is V11() V12() ext-real Element of REAL
- (2 / (g1 |^ (1 + 2))) is V11() V12() ext-real Element of REAL
g1 #Z 3 is V11() V12() ext-real Element of REAL
2 / (g1 #Z 3) is V11() V12() ext-real Element of REAL
- (2 / (g1 #Z 3)) is V11() V12() ext-real Element of REAL
(#Z 3) . g1 is V11() V12() ext-real Element of REAL
2 / ((#Z 3) . g1) is V11() V12() ext-real Element of REAL
- (2 / ((#Z 3) . g1)) is V11() V12() ext-real Element of REAL
((#Z 3) . g1) " is V11() V12() ext-real Element of REAL
2 * (((#Z 3) . g1) ") is V11() V12() ext-real Element of REAL
- (2 * (((#Z 3) . g1) ")) is V11() V12() ext-real Element of REAL
((#Z 3) ^) . g1 is V11() V12() ext-real Element of REAL
2 * (((#Z 3) ^) . g1) is V11() V12() ext-real Element of REAL
- (2 * (((#Z 3) ^) . g1)) is V11() V12() ext-real Element of REAL
(- 2) * (((#Z 3) ^) . g1) is V11() V12() ext-real Element of REAL
((- 2) (#) ((#Z 3) ^)) . g1 is V11() V12() ext-real Element of REAL
dom (((- 2) (#) ((#Z 3) ^)) | Z) is V84() V85() V86() Element of K6(REAL)
dom ((- 2) (#) ((#Z 3) ^)) is V84() V85() V86() Element of K6(REAL)
(dom ((- 2) (#) ((#Z 3) ^))) /\ Z is V84() V85() V86() set
(dom ((#Z 3) ^)) /\ Z is V84() V85() V86() set
Z is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z Z is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z Z) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z (Z + 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z (Z + 1)) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- Z is V11() V12() ext-real V48() Element of REAL
(- Z) (#) ((#Z (Z + 1)) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is open V84() V85() V86() Element of K6(REAL)
((#Z Z) ^) `| f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- Z) (#) ((#Z (Z + 1)) ^)) | f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
dom ((#Z (Z + 1)) ^) is V84() V85() V86() Element of K6(REAL)
Z - 1 is V11() V12() ext-real V48() Element of REAL
g2 is V11() V12() ext-real Element of REAL
(((#Z Z) ^) `| f) . g2 is V11() V12() ext-real Element of REAL
(((- Z) (#) ((#Z (Z + 1)) ^)) | f) . g2 is V11() V12() ext-real Element of REAL
dom ((- Z) (#) ((#Z (Z + 1)) ^)) is V84() V85() V86() Element of K6(REAL)
g1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 #Z g1 is V11() V12() ext-real Element of REAL
g2 |^ g1 is V11() V12() ext-real Element of REAL
diff (((#Z Z) ^),g2) is V11() V12() ext-real Element of REAL
g2 #Z (Z - 1) is V11() V12() ext-real Element of REAL
Z * (g2 #Z (Z - 1)) is V11() V12() ext-real Element of REAL
g2 #Z Z is V11() V12() ext-real Element of REAL
(g2 #Z Z) ^2 is V11() V12() ext-real Element of REAL
K37((g2 #Z Z),(g2 #Z Z)) is set
(Z * (g2 #Z (Z - 1))) / ((g2 #Z Z) ^2) is V11() V12() ext-real Element of REAL
- ((Z * (g2 #Z (Z - 1))) / ((g2 #Z Z) ^2)) is V11() V12() ext-real Element of REAL
Z * (g2 #Z g1) is V11() V12() ext-real Element of REAL
g2 |^ Z is V11() V12() ext-real Element of REAL
(g2 |^ Z) ^2 is V11() V12() ext-real Element of REAL
K37((g2 |^ Z),(g2 |^ Z)) is set
(Z * (g2 #Z g1)) / ((g2 |^ Z) ^2) is V11() V12() ext-real Element of REAL
- ((Z * (g2 #Z g1)) / ((g2 |^ Z) ^2)) is V11() V12() ext-real Element of REAL
Z * (g2 |^ g1) is V11() V12() ext-real Element of REAL
(Z * (g2 |^ g1)) / ((g2 |^ Z) ^2) is V11() V12() ext-real Element of REAL
- ((Z * (g2 |^ g1)) / ((g2 |^ Z) ^2)) is V11() V12() ext-real Element of REAL
g1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 |^ (g1 + 1) is V11() V12() ext-real Element of REAL
g2 |^ 1 is V11() V12() ext-real Element of REAL
(g2 |^ 1) * (g2 |^ g1) is V11() V12() ext-real Element of REAL
(g2 |^ (g1 + 1)) * ((g2 |^ 1) * (g2 |^ g1)) is V11() V12() ext-real Element of REAL
(Z * (g2 |^ g1)) / ((g2 |^ (g1 + 1)) * ((g2 |^ 1) * (g2 |^ g1))) is V11() V12() ext-real Element of REAL
- ((Z * (g2 |^ g1)) / ((g2 |^ (g1 + 1)) * ((g2 |^ 1) * (g2 |^ g1)))) is V11() V12() ext-real Element of REAL
(g2 |^ (g1 + 1)) * (g2 |^ 1) is V11() V12() ext-real Element of REAL
((g2 |^ (g1 + 1)) * (g2 |^ 1)) * (g2 |^ g1) is V11() V12() ext-real Element of REAL
(Z * (g2 |^ g1)) / (((g2 |^ (g1 + 1)) * (g2 |^ 1)) * (g2 |^ g1)) is V11() V12() ext-real Element of REAL
- ((Z * (g2 |^ g1)) / (((g2 |^ (g1 + 1)) * (g2 |^ 1)) * (g2 |^ g1))) is V11() V12() ext-real Element of REAL
(g1 + 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 |^ ((g1 + 1) + 1) is V11() V12() ext-real Element of REAL
(g2 |^ ((g1 + 1) + 1)) * (g2 |^ g1) is V11() V12() ext-real Element of REAL
(Z * (g2 |^ g1)) / ((g2 |^ ((g1 + 1) + 1)) * (g2 |^ g1)) is V11() V12() ext-real Element of REAL
- ((Z * (g2 |^ g1)) / ((g2 |^ ((g1 + 1) + 1)) * (g2 |^ g1))) is V11() V12() ext-real Element of REAL
g1 + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
g2 |^ (g1 + 2) is V11() V12() ext-real Element of REAL
Z / (g2 |^ (g1 + 2)) is V11() V12() ext-real Element of REAL
- (Z / (g2 |^ (g1 + 2))) is V11() V12() ext-real Element of REAL
g2 #Z (g1 + 2) is V11() V12() ext-real Element of REAL
Z / (g2 #Z (g1 + 2)) is V11() V12() ext-real Element of REAL
- (Z / (g2 #Z (g1 + 2))) is V11() V12() ext-real Element of REAL
#Z (g1 + 2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z (g1 + 2)) . g2 is V11() V12() ext-real Element of REAL
Z / ((#Z (g1 + 2)) . g2) is V11() V12() ext-real Element of REAL
- (Z / ((#Z (g1 + 2)) . g2)) is V11() V12() ext-real Element of REAL
(#Z (Z + 1)) . g2 is V11() V12() ext-real Element of REAL
((#Z (Z + 1)) . g2) " is V11() V12() ext-real Element of REAL
Z * (((#Z (Z + 1)) . g2) ") is V11() V12() ext-real Element of REAL
- (Z * (((#Z (Z + 1)) . g2) ")) is V11() V12() ext-real Element of REAL
((#Z (Z + 1)) ^) . g2 is V11() V12() ext-real Element of REAL
Z * (((#Z (Z + 1)) ^) . g2) is V11() V12() ext-real Element of REAL
- (Z * (((#Z (Z + 1)) ^) . g2)) is V11() V12() ext-real Element of REAL
(- Z) * (((#Z (Z + 1)) ^) . g2) is V11() V12() ext-real Element of REAL
((- Z) (#) ((#Z (Z + 1)) ^)) . g2 is V11() V12() ext-real Element of REAL
dom (((#Z Z) ^) `| f) is V84() V85() V86() Element of K6(REAL)
dom (((- Z) (#) ((#Z (Z + 1)) ^)) | f) is V84() V85() V86() Element of K6(REAL)
dom ((- Z) (#) ((#Z (Z + 1)) ^)) is V84() V85() V86() Element of K6(REAL)
(dom ((- Z) (#) ((#Z (Z + 1)) ^))) /\ f is V84() V85() V86() set
(dom ((#Z (Z + 1)) ^)) /\ f is V84() V85() V86() set
Z is open V84() V85() V86() Element of K6(REAL)
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (f,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (f,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((f (#) g1),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f (#) g1),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 2) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) (g1 `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) + (2 (#) ((f `| Z) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (g1,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + (2 (#) ((f `| Z) (#) (g1 `| Z)))) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 - 1 is V11() V12() ext-real V48() Element of REAL
(diff (f,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,Z)) . 1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (g1 `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . 1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (g1,Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g1 | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((f (#) g1),Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((f (#) g1),Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) g1),Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((f (#) g1),Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) g1),Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff ((f (#) g1),Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) g1) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f (#) g1) | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f (#) g1) | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) g1) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f (#) g1) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) g1) + (f (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f `| Z) (#) g1) + (f (#) (g1 `| Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) g1) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) (g1 `| Z)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f `| Z) (#) g1) `| Z) + ((f (#) (g1 `| Z)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) `| Z) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f `| Z) `| Z) (#) g1) + ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((f `| Z) `| Z) (#) g1) + ((f `| Z) (#) (g1 `| Z))) + ((f (#) (g1 `| Z)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) + ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) (g1 `| Z)) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + ((f `| Z) (#) (g1 `| Z))) + (((f `| Z) (#) (g1 `| Z)) + (f (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + ((f `| Z) (#) (g1 `| Z))) + ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 2) (#) g1) + ((f `| Z) (#) (g1 `| Z))) + ((f `| Z) (#) (g1 `| Z))) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) (g1 `| Z)) + ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) + (((f `| Z) (#) (g1 `| Z)) + ((f `| Z) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + (((f `| Z) (#) (g1 `| Z)) + ((f `| Z) (#) (g1 `| Z)))) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) ((f `| Z) (#) (g1 `| Z))) + ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) + ((1 (#) ((f `| Z) (#) (g1 `| Z))) + ((f `| Z) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + ((1 (#) ((f `| Z) (#) (g1 `| Z))) + ((f `| Z) (#) (g1 `| Z)))) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) ((f `| Z) (#) (g1 `| Z))) + (1 (#) ((f `| Z) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) + ((1 (#) ((f `| Z) (#) (g1 `| Z))) + (1 (#) ((f `| Z) (#) (g1 `| Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + ((1 (#) ((f `| Z) (#) (g1 `| Z))) + (1 (#) ((f `| Z) (#) (g1 `| Z))))) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 + 1) (#) ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) + ((1 + 1) (#) ((f `| Z) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + ((1 + 1) (#) ((f `| Z) (#) (g1 `| Z)))) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((id REAL) ^) is V84() V85() V86() Element of K6(REAL)
Z is open V84() V85() V86() Element of K6(REAL)
ln `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((id REAL) ^) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((id REAL) ^) | Z) is V84() V85() V86() Element of K6(REAL)
(dom ((id REAL) ^)) /\ Z is V84() V85() V86() set
f is V11() V12() ext-real Element of REAL
(ln `| Z) . f is V11() V12() ext-real Element of REAL
(((id REAL) ^) | Z) . f is V11() V12() ext-real Element of REAL
diff (ln,f) is V11() V12() ext-real Element of REAL
1 / f is V11() V12() ext-real Element of REAL
(id REAL) . f is V11() V12() ext-real Element of REAL
1 / ((id REAL) . f) is V11() V12() ext-real Element of REAL
((id REAL) . f) " is V11() V12() ext-real Element of REAL
1 * (((id REAL) . f) ") is V11() V12() ext-real Element of REAL
((id REAL) ^) . f is V11() V12() ext-real Element of REAL
1 * (((id REAL) ^) . f) is V11() V12() ext-real Element of REAL
dom (ln `| Z) is V84() V85() V86() Element of K6(REAL)
Z is V11() V12() ext-real Element of REAL
f is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z f is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z f) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f * (f + 1) is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
f + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
#Z (f + 2) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z (f + 2)) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((#Z (f + 2)) ^) . Z is V11() V12() ext-real Element of REAL
(f * (f + 1)) * (((#Z (f + 2)) ^) . Z) is V11() V12() ext-real Element of REAL
g1 is open V84() V85() V86() Element of K6(REAL)
diff (((#Z f) ^),g1) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (((#Z f) ^),g1)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (((#Z f) ^),g1)) . 2) . Z is V11() V12() ext-real Element of REAL
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(f + 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
dom ((#Z (f + 2)) ^) is V84() V85() V86() Element of K6(REAL)
((#Z (f + 2)) ^) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- (f + 1) is V11() V12() ext-real V48() Element of REAL
(- (f + 1)) (#) (((#Z (f + 2)) ^) | g1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((- (f + 1)) (#) (((#Z (f + 2)) ^) | g1)) is V84() V85() V86() Element of K6(REAL)
dom (((#Z (f + 2)) ^) | g1) is V84() V85() V86() Element of K6(REAL)
(dom ((#Z (f + 2)) ^)) /\ g1 is V84() V85() V86() set
- f is V11() V12() ext-real V48() Element of REAL
#Z (f + 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z (f + 1)) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g2 is V11() V12() ext-real Element of REAL
g2 (#) ((#Z (f + 1)) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (g2 (#) ((#Z (f + 1)) ^)) is V84() V85() V86() Element of K6(REAL)
dom ((#Z (f + 1)) ^) is V84() V85() V86() Element of K6(REAL)
(- f) (#) ((#Z (f + 1)) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((- f) (#) ((#Z (f + 1)) ^)) is V84() V85() V86() Element of K6(REAL)
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (((#Z f) ^),g1)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (((#Z f) ^),g1)) . (1 + 1)) . Z is V11() V12() ext-real Element of REAL
(diff (((#Z f) ^),g1)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (((#Z f) ^),g1)) . (1 + 0)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (((#Z f) ^),g1)) . (1 + 0)) `| g1) . Z is V11() V12() ext-real Element of REAL
(diff (((#Z f) ^),g1)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (((#Z f) ^),g1)) . 0) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (((#Z f) ^),g1)) . 0) `| g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (((#Z f) ^),g1)) . 0) `| g1) `| g1) . Z is V11() V12() ext-real Element of REAL
((#Z f) ^) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((#Z f) ^) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((#Z f) ^) | g1) `| g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((#Z f) ^) | g1) `| g1) `| g1) . Z is V11() V12() ext-real Element of REAL
((#Z f) ^) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((#Z f) ^) `| g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((#Z f) ^) `| g1) `| g1) . Z is V11() V12() ext-real Element of REAL
(g2 (#) ((#Z (f + 1)) ^)) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g2 (#) ((#Z (f + 1)) ^)) | g1) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((g2 (#) ((#Z (f + 1)) ^)) | g1) `| g1) . Z is V11() V12() ext-real Element of REAL
(g2 (#) ((#Z (f + 1)) ^)) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((g2 (#) ((#Z (f + 1)) ^)) `| g1) . Z is V11() V12() ext-real Element of REAL
diff (((#Z (f + 1)) ^),Z) is V11() V12() ext-real Element of REAL
g2 * (diff (((#Z (f + 1)) ^),Z)) is V11() V12() ext-real Element of REAL
((#Z (f + 1)) ^) `| g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((#Z (f + 1)) ^) `| g1) . Z is V11() V12() ext-real Element of REAL
g2 * ((((#Z (f + 1)) ^) `| g1) . Z) is V11() V12() ext-real Element of REAL
#Z ((f + 1) + 1) is non empty V16() V19( REAL ) V20( REAL ) V21() total V30( REAL , REAL ) V74() V75() V76() Element of K6(K7(REAL,REAL))
(#Z ((f + 1) + 1)) ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- (f + 1)) (#) ((#Z ((f + 1) + 1)) ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- (f + 1)) (#) ((#Z ((f + 1) + 1)) ^)) | g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- (f + 1)) (#) ((#Z ((f + 1) + 1)) ^)) | g1) . Z is V11() V12() ext-real Element of REAL
g2 * ((((- (f + 1)) (#) ((#Z ((f + 1) + 1)) ^)) | g1) . Z) is V11() V12() ext-real Element of REAL
((- (f + 1)) (#) (((#Z (f + 2)) ^) | g1)) . Z is V11() V12() ext-real Element of REAL
g2 * (((- (f + 1)) (#) (((#Z (f + 2)) ^) | g1)) . Z) is V11() V12() ext-real Element of REAL
(((#Z (f + 2)) ^) | g1) . Z is V11() V12() ext-real Element of REAL
(- (f + 1)) * ((((#Z (f + 2)) ^) | g1) . Z) is V11() V12() ext-real Element of REAL
g2 * ((- (f + 1)) * ((((#Z (f + 2)) ^) | g1) . Z)) is V11() V12() ext-real Element of REAL
(f * (f + 1)) * ((((#Z (f + 2)) ^) | g1) . Z) is V11() V12() ext-real Element of REAL
sin ^2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) sin is V16() V21() set
cos ^2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) cos is V16() V21() set
Z is open V84() V85() V86() Element of K6(REAL)
diff ((sin ^2),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((sin ^2),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos ^2) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((cos ^2) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin ^2) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) (#) ((sin ^2) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos ^2) | Z)) + ((- 2) (#) ((sin ^2) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (sin,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,Z)) . (2 * 1)) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| Z) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((sin `| Z) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,Z)) . (2 * 1)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) ((diff (sin,Z)) . (2 * 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (sin,Z)) . (2 * 1)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z)))) + (sin (#) ((diff (sin,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ 1) (#) (sin | Z)) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ 1) (#) (sin | Z)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (sin | Z)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z)))) + (sin (#) ((diff (sin,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) (((- 1) |^ 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (sin | Z)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z)))) + (sin (#) (((- 1) |^ 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) ((- 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (sin | Z)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z)))) + (sin (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (sin | Z)) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (sin | Z)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (sin | Z)) (#) sin) + (2 (#) ((sin `| Z) (#) (sin `| Z)))) + (sin (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin (#) ((- 1) (#) (sin | Z))) + (sin (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((sin `| Z) (#) (sin `| Z))) + ((sin (#) ((- 1) (#) (sin | Z))) + (sin (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (sin (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (sin (#) ((- 1) (#) (sin | Z)))) + (sin (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((sin `| Z) (#) (sin `| Z))) + ((1 (#) (sin (#) ((- 1) (#) (sin | Z)))) + (sin (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (sin (#) ((- 1) (#) (sin | Z)))) + (1 (#) (sin (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((sin `| Z) (#) (sin `| Z))) + ((1 (#) (sin (#) ((- 1) (#) (sin | Z)))) + (1 (#) (sin (#) ((- 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 + 1) (#) (sin (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((sin `| Z) (#) (sin `| Z))) + ((1 + 1) (#) (sin (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((cos | Z) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (sin (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos | Z) (#) (sin `| Z))) + (2 (#) (sin (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((cos | Z) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos | Z) (#) (cos | Z))) + (2 (#) (sin (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((cos (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- 1) (#) (sin | Z)) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos (#) cos) | Z)) + (2 (#) (((- 1) (#) (sin | Z)) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin | Z) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((sin | Z) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((- 1) (#) ((sin | Z) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos (#) cos) | Z)) + (2 (#) ((- 1) (#) ((sin | Z) (#) sin))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin (#) sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((sin (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((- 1) (#) ((sin (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos (#) cos) | Z)) + (2 (#) ((- 1) (#) ((sin (#) sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 * (- 1) is V11() V12() ext-real V48() Element of REAL
(2 * (- 1)) (#) ((sin (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos (#) cos) | Z)) + ((2 * (- 1)) (#) ((sin (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) (#) ((sin (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos (#) cos) | Z)) + ((- 2) (#) ((sin (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
diff ((cos ^2),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((cos ^2),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin ^2) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((sin ^2) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos ^2) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) (#) ((cos ^2) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((sin ^2) | Z)) + ((- 2) (#) ((cos ^2) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (cos,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cos,Z)) . (2 * 1)) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos `| Z) (#) (cos `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((cos `| Z) (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cos,Z)) . (2 * 1)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) ((diff (cos,Z)) . (2 * 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (cos,Z)) . (2 * 1)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z)))) + (cos (#) ((diff (cos,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ 1) (#) (cos | Z)) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ 1) (#) (cos | Z)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (cos | Z)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z)))) + (cos (#) ((diff (cos,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) (((- 1) |^ 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (cos | Z)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z)))) + (cos (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) ((- 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (cos | Z)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z)))) + (cos (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (cos | Z)) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) cos) + (2 (#) ((cos `| Z) (#) (cos `| Z)))) + (cos (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos (#) ((- 1) (#) (cos | Z))) + (cos (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos `| Z) (#) (cos `| Z))) + ((cos (#) ((- 1) (#) (cos | Z))) + (cos (#) ((- 1) (#) (cos | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (cos (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (cos (#) ((- 1) (#) (cos | Z)))) + (cos (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos `| Z) (#) (cos `| Z))) + ((1 (#) (cos (#) ((- 1) (#) (cos | Z)))) + (cos (#) ((- 1) (#) (cos | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (cos (#) ((- 1) (#) (cos | Z)))) + (1 (#) (cos (#) ((- 1) (#) (cos | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos `| Z) (#) (cos `| Z))) + ((1 (#) (cos (#) ((- 1) (#) (cos | Z)))) + (1 (#) (cos (#) ((- 1) (#) (cos | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 + 1) (#) (cos (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((cos `| Z) (#) (cos `| Z))) + ((1 + 1) (#) (cos (#) ((- 1) (#) (cos | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- sin) | Z) (#) (cos `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- sin) | Z) (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (cos (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((- sin) | Z) (#) (cos `| Z))) + (2 (#) (cos (#) ((- 1) (#) (cos | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- sin) | Z) (#) ((- sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- sin) | Z) (#) ((- sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((- sin) | Z) (#) ((- sin) | Z))) + (2 (#) (cos (#) ((- 1) (#) (cos | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- sin) (#) (- sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- sin) (#) (- sin)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- sin) (#) (- sin)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- 1) (#) (cos | Z)) (#) cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((- sin) (#) (- sin)) | Z)) + (2 (#) (((- 1) (#) (cos | Z)) (#) cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((cos | Z) (#) cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((- 1) (#) ((cos | Z) (#) cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((- sin) (#) (- sin)) | Z)) + (2 (#) ((- 1) (#) ((cos | Z) (#) cos))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 * (- 1) is V11() V12() ext-real V48() Element of REAL
(2 * (- 1)) (#) ((cos | Z) (#) cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((- sin) (#) (- sin)) | Z)) + ((2 * (- 1)) (#) ((cos | Z) (#) cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) (#) ((cos (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((- sin) (#) (- sin)) | Z)) + ((- 2) (#) ((cos (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin (#) sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((sin (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((sin (#) sin) | Z)) + ((- 2) (#) ((cos (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- sin) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
4 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
Z is open V84() V85() V86() Element of K6(REAL)
diff ((sin (#) cos),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((sin (#) cos),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- sin) (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
4 (#) (((- sin) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (sin,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,Z)) . (2 * 1)) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| Z) (#) (cos `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((sin `| Z) (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,Z)) . (2 * 1)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (cos,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) ((diff (cos,Z)) . (2 * 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (sin,Z)) . (2 * 1)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z)))) + (sin (#) ((diff (cos,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ 1) (#) (sin | Z)) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ 1) (#) (sin | Z)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (sin | Z)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z)))) + (sin (#) ((diff (cos,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) |^ 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) (((- 1) |^ 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (sin | Z)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z)))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (sin | Z)) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (sin | Z)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (sin | Z)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z)))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) ((- 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (sin | Z)) (#) cos) + (2 (#) ((sin `| Z) (#) (cos `| Z)))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) (cos `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((cos | Z) (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (sin | Z)) (#) cos) + (2 (#) ((cos | Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (sin | Z)) (#) cos) + (2 (#) ((cos | Z) (#) (cos `| Z)))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) ((- sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((cos | Z) (#) ((- sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (sin | Z)) (#) cos) + (2 (#) ((cos | Z) (#) ((- sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (sin | Z)) (#) cos) + (2 (#) ((cos | Z) (#) ((- sin) | Z)))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) sin) | Z) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) sin) | Z) (#) cos) + (2 (#) ((cos | Z) (#) ((- sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) (#) sin) | Z) (#) cos) + (2 (#) ((cos | Z) (#) ((- sin) | Z)))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) (((- 1) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) (#) sin) | Z) (#) cos) + (2 (#) ((cos | Z) (#) ((- sin) | Z)))) + (sin (#) (((- 1) (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- sin) (#) cos) | Z) + (2 (#) ((cos | Z) (#) ((- sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) ((- cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- sin) (#) cos) | Z) + (2 (#) ((cos | Z) (#) ((- sin) | Z)))) + (sin (#) ((- cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) (- cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin (#) (- cos)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- sin) (#) cos) | Z) + (2 (#) ((cos | Z) (#) ((- sin) | Z)))) + ((sin (#) (- cos)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- sin) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- sin) (#) cos) | Z) + (2 (#) (((- sin) (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- sin) (#) cos) | Z) + (2 (#) (((- sin) (#) cos) | Z))) + ((sin (#) (- cos)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (sin (#) cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (sin (#) cos)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- sin) (#) cos) | Z) + (2 (#) (((- sin) (#) cos) | Z))) + (((- 1) (#) (sin (#) cos)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) sin) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) sin) (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- sin) (#) cos) | Z) + (2 (#) (((- sin) (#) cos) | Z))) + ((((- 1) (#) sin) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (((- sin) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((- sin) (#) cos) | Z)) + (2 (#) (((- sin) (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (((- sin) (#) cos) | Z)) + (2 (#) (((- sin) (#) cos) | Z))) + (((- sin) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (((- sin) (#) cos) | Z)) + (2 (#) (((- sin) (#) cos) | Z))) + (1 (#) (((- sin) (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 + 2) (#) (((- sin) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 + 2) (#) (((- sin) (#) cos) | Z)) + (1 (#) (((- sin) (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(3 + 1) (#) (((- sin) (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos ^) ^2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos ^) (#) (cos ^) is V16() V21() set
Z is open V84() V85() V86() Element of K6(REAL)
tan `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos ^) ^2) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (cos ^) is V84() V85() V86() Element of K6(REAL)
(dom sin) /\ (dom (cos ^)) is V84() V85() V86() set
sin (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (sin (#) (cos ^)) is V84() V85() V86() Element of K6(REAL)
(cos ^) (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((cos ^) (#) (cos ^)) is V84() V85() V86() Element of K6(REAL)
(dom (cos ^)) /\ (dom (cos ^)) is V84() V85() V86() set
((cos ^) (#) (cos ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((cos ^) (#) (cos ^)) | Z) is V84() V85() V86() Element of K6(REAL)
(dom (cos ^)) /\ Z is V84() V85() V86() set
g1 is V11() V12() ext-real Element of REAL
cos . g1 is V11() V12() ext-real Element of REAL
dom (tan `| Z) is V84() V85() V86() Element of K6(REAL)
g1 is V11() V12() ext-real Element of REAL
(tan `| Z) . g1 is V11() V12() ext-real Element of REAL
(((cos ^) (#) (cos ^)) | Z) . g1 is V11() V12() ext-real Element of REAL
cos . g1 is V11() V12() ext-real Element of REAL
diff ((sin / cos),g1) is V11() V12() ext-real Element of REAL
(cos . g1) ^2 is V11() V12() ext-real Element of REAL
K37((cos . g1),(cos . g1)) is set
1 / ((cos . g1) ^2) is V11() V12() ext-real Element of REAL
1 / (cos . g1) is V11() V12() ext-real Element of REAL
(1 / (cos . g1)) * (1 / (cos . g1)) is V11() V12() ext-real Element of REAL
(cos . g1) " is V11() V12() ext-real Element of REAL
1 * ((cos . g1) ") is V11() V12() ext-real Element of REAL
(1 * ((cos . g1) ")) * (1 / (cos . g1)) is V11() V12() ext-real Element of REAL
(cos ^) . g1 is V11() V12() ext-real Element of REAL
((cos ^) . g1) * (1 / (cos . g1)) is V11() V12() ext-real Element of REAL
((cos ^) . g1) * (1 * ((cos . g1) ")) is V11() V12() ext-real Element of REAL
((cos ^) . g1) * ((cos ^) . g1) is V11() V12() ext-real Element of REAL
((cos ^) (#) (cos ^)) . g1 is V11() V12() ext-real Element of REAL
(cos ^) (#) tan is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
(cos ^) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos ^) (#) tan) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (cos ^) is V84() V85() V86() Element of K6(REAL)
(dom sin) /\ (dom (cos ^)) is V84() V85() V86() set
f is V11() V12() ext-real Element of REAL
cos . f is V11() V12() ext-real Element of REAL
dom ((cos ^) `| Z) is V84() V85() V86() Element of K6(REAL)
sin (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (sin (#) (cos ^)) is V84() V85() V86() Element of K6(REAL)
f is V11() V12() ext-real Element of REAL
((cos ^) `| Z) . f is V11() V12() ext-real Element of REAL
(((cos ^) (#) tan) | Z) . f is V11() V12() ext-real Element of REAL
(cos ^) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((cos ^) (#) sin) is V84() V85() V86() Element of K6(REAL)
((cos ^) (#) sin) (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((cos ^) (#) sin) (#) (cos ^)) is V84() V85() V86() Element of K6(REAL)
(dom tan) /\ (dom (cos ^)) is V84() V85() V86() set
sin . f is V11() V12() ext-real Element of REAL
cos . f is V11() V12() ext-real Element of REAL
(cos . f) ^2 is V11() V12() ext-real Element of REAL
K37((cos . f),(cos . f)) is set
(sin . f) / ((cos . f) ^2) is V11() V12() ext-real Element of REAL
1 / (cos . f) is V11() V12() ext-real Element of REAL
(sin . f) / (cos . f) is V11() V12() ext-real Element of REAL
(1 / (cos . f)) * ((sin . f) / (cos . f)) is V11() V12() ext-real Element of REAL
(1 / (cos . f)) * (sin . f) is V11() V12() ext-real Element of REAL
((1 / (cos . f)) * (sin . f)) * (1 / (cos . f)) is V11() V12() ext-real Element of REAL
(cos . f) " is V11() V12() ext-real Element of REAL
1 * ((cos . f) ") is V11() V12() ext-real Element of REAL
((1 / (cos . f)) * (sin . f)) * (1 * ((cos . f) ")) is V11() V12() ext-real Element of REAL
(1 * ((cos . f) ")) * (sin . f) is V11() V12() ext-real Element of REAL
((1 * ((cos . f) ")) * (sin . f)) * (1 * ((cos . f) ")) is V11() V12() ext-real Element of REAL
(cos ^) . f is V11() V12() ext-real Element of REAL
((cos ^) . f) * (sin . f) is V11() V12() ext-real Element of REAL
(((cos ^) . f) * (sin . f)) * (1 * ((cos . f) ")) is V11() V12() ext-real Element of REAL
(((cos ^) . f) * (sin . f)) * ((cos ^) . f) is V11() V12() ext-real Element of REAL
((cos ^) (#) sin) . f is V11() V12() ext-real Element of REAL
(((cos ^) (#) sin) . f) * ((cos ^) . f) is V11() V12() ext-real Element of REAL
(((cos ^) (#) sin) (#) (cos ^)) . f is V11() V12() ext-real Element of REAL
(((cos ^) (#) sin) (#) (cos ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((cos ^) (#) sin) (#) (cos ^)) | Z) . f is V11() V12() ext-real Element of REAL
dom (((cos ^) (#) tan) | Z) is V84() V85() V86() Element of K6(REAL)
dom ((cos ^) (#) tan) is V84() V85() V86() Element of K6(REAL)
(dom ((cos ^) (#) tan)) /\ Z is V84() V85() V86() set
(dom (cos ^)) /\ (dom tan) is V84() V85() V86() set
((dom (cos ^)) /\ (dom tan)) /\ Z is V84() V85() V86() set
tan (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(tan (#) (cos ^)) (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
diff (tan,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (tan,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((tan (#) (cos ^)) (#) (cos ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((tan (#) (cos ^)) (#) (cos ^)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos ^) (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (tan,Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (tan,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (tan,Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (tan,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (tan,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (tan,Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
tan | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(tan | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((tan | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
tan `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(tan `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos ^) ^2) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((cos ^) ^2) | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos ^) (#) (cos ^)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos ^) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos ^) `| Z) (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((cos ^) `| Z) (#) (cos ^)) + (((cos ^) `| Z) (#) (cos ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (((cos ^) `| Z) (#) (cos ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((cos ^) `| Z) (#) (cos ^))) + (((cos ^) `| Z) (#) (cos ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((cos ^) `| Z) (#) (cos ^))) + (1 (#) (((cos ^) `| Z) (#) (cos ^))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 + 1) (#) (((cos ^) `| Z) (#) (cos ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cos ^) (#) tan) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((cos ^) (#) tan) | Z) (#) (cos ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((((cos ^) (#) tan) | Z) (#) (cos ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin ^) ^2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin ^) (#) (sin ^) is V16() V21() set
(- 1) (#) ((sin ^) ^2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
cot `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) ((sin ^) ^2)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (sin ^) is V84() V85() V86() Element of K6(REAL)
(dom cos) /\ (dom (sin ^)) is V84() V85() V86() set
f is V11() V12() ext-real Element of REAL
sin . f is V11() V12() ext-real Element of REAL
cos (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (cos (#) (sin ^)) is V84() V85() V86() Element of K6(REAL)
dom (cot `| Z) is V84() V85() V86() Element of K6(REAL)
(sin ^) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((sin ^) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) ((sin ^) (#) (sin ^))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f is V11() V12() ext-real Element of REAL
(cot `| Z) . f is V11() V12() ext-real Element of REAL
(((- 1) (#) ((sin ^) (#) (sin ^))) | Z) . f is V11() V12() ext-real Element of REAL
sin . f is V11() V12() ext-real Element of REAL
dom ((sin ^) (#) (sin ^)) is V84() V85() V86() Element of K6(REAL)
(dom (sin ^)) /\ (dom (sin ^)) is V84() V85() V86() set
dom ((- 1) (#) ((sin ^) (#) (sin ^))) is V84() V85() V86() Element of K6(REAL)
diff ((cos / sin),f) is V11() V12() ext-real Element of REAL
(sin . f) ^2 is V11() V12() ext-real Element of REAL
K37((sin . f),(sin . f)) is set
1 / ((sin . f) ^2) is V11() V12() ext-real Element of REAL
- (1 / ((sin . f) ^2)) is V11() V12() ext-real Element of REAL
(sin . f) * (sin . f) is V11() V12() ext-real Element of REAL
1 / ((sin . f) * (sin . f)) is V11() V12() ext-real Element of REAL
(- 1) * (1 / ((sin . f) * (sin . f))) is V11() V12() ext-real Element of REAL
1 / (sin . f) is V11() V12() ext-real Element of REAL
(1 / (sin . f)) * (1 / (sin . f)) is V11() V12() ext-real Element of REAL
(- 1) * ((1 / (sin . f)) * (1 / (sin . f))) is V11() V12() ext-real Element of REAL
(sin . f) " is V11() V12() ext-real Element of REAL
1 * ((sin . f) ") is V11() V12() ext-real Element of REAL
(1 * ((sin . f) ")) * (1 / (sin . f)) is V11() V12() ext-real Element of REAL
(- 1) * ((1 * ((sin . f) ")) * (1 / (sin . f))) is V11() V12() ext-real Element of REAL
(sin ^) . f is V11() V12() ext-real Element of REAL
((sin ^) . f) * (1 / (sin . f)) is V11() V12() ext-real Element of REAL
(- 1) * (((sin ^) . f) * (1 / (sin . f))) is V11() V12() ext-real Element of REAL
((sin ^) . f) * (1 * ((sin . f) ")) is V11() V12() ext-real Element of REAL
(- 1) * (((sin ^) . f) * (1 * ((sin . f) "))) is V11() V12() ext-real Element of REAL
((sin ^) . f) * ((sin ^) . f) is V11() V12() ext-real Element of REAL
(- 1) * (((sin ^) . f) * ((sin ^) . f)) is V11() V12() ext-real Element of REAL
((sin ^) (#) (sin ^)) . f is V11() V12() ext-real Element of REAL
(- 1) * (((sin ^) (#) (sin ^)) . f) is V11() V12() ext-real Element of REAL
((- 1) (#) ((sin ^) (#) (sin ^))) . f is V11() V12() ext-real Element of REAL
dom (((- 1) (#) ((sin ^) (#) (sin ^))) | Z) is V84() V85() V86() Element of K6(REAL)
dom ((- 1) (#) ((sin ^) ^2)) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) ((sin ^) ^2))) /\ Z is V84() V85() V86() set
dom ((sin ^) ^2) is V84() V85() V86() Element of K6(REAL)
(dom ((sin ^) ^2)) /\ Z is V84() V85() V86() set
(dom (sin ^)) /\ (dom (sin ^)) is V84() V85() V86() set
((dom (sin ^)) /\ (dom (sin ^))) /\ Z is V84() V85() V86() set
(sin ^) (#) cot is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((sin ^) (#) cot) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) ((sin ^) (#) cot) is V16() V21() set
Z is open V84() V85() V86() Element of K6(REAL)
(sin ^) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- ((sin ^) (#) cot)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (cos (#) (sin ^)) is V84() V85() V86() Element of K6(REAL)
dom (sin ^) is V84() V85() V86() Element of K6(REAL)
(dom cos) /\ (dom (sin ^)) is V84() V85() V86() set
f is V11() V12() ext-real Element of REAL
sin . f is V11() V12() ext-real Element of REAL
dom ((sin ^) `| Z) is V84() V85() V86() Element of K6(REAL)
f is V11() V12() ext-real Element of REAL
((sin ^) `| Z) . f is V11() V12() ext-real Element of REAL
((- ((sin ^) (#) cot)) | Z) . f is V11() V12() ext-real Element of REAL
(- 1) (#) ((sin ^) (#) cot) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((- 1) (#) ((sin ^) (#) cot)) is V84() V85() V86() Element of K6(REAL)
(sin ^) (#) (cos / sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((sin ^) (#) (cos / sin)) is V84() V85() V86() Element of K6(REAL)
(sin ^) (#) (cos (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((sin ^) (#) (cos (#) (sin ^))) is V84() V85() V86() Element of K6(REAL)
(dom (sin ^)) /\ (dom (cos (#) (sin ^))) is V84() V85() V86() set
cos . f is V11() V12() ext-real Element of REAL
sin . f is V11() V12() ext-real Element of REAL
(sin . f) ^2 is V11() V12() ext-real Element of REAL
K37((sin . f),(sin . f)) is set
(cos . f) / ((sin . f) ^2) is V11() V12() ext-real Element of REAL
- ((cos . f) / ((sin . f) ^2)) is V11() V12() ext-real Element of REAL
1 * (cos . f) is V11() V12() ext-real Element of REAL
(sin . f) * (sin . f) is V11() V12() ext-real Element of REAL
(1 * (cos . f)) / ((sin . f) * (sin . f)) is V11() V12() ext-real Element of REAL
- ((1 * (cos . f)) / ((sin . f) * (sin . f))) is V11() V12() ext-real Element of REAL
1 / (sin . f) is V11() V12() ext-real Element of REAL
(cos . f) / (sin . f) is V11() V12() ext-real Element of REAL
(1 / (sin . f)) * ((cos . f) / (sin . f)) is V11() V12() ext-real Element of REAL
- ((1 / (sin . f)) * ((cos . f) / (sin . f))) is V11() V12() ext-real Element of REAL
(cos . f) * (1 / (sin . f)) is V11() V12() ext-real Element of REAL
(1 / (sin . f)) * ((cos . f) * (1 / (sin . f))) is V11() V12() ext-real Element of REAL
- ((1 / (sin . f)) * ((cos . f) * (1 / (sin . f)))) is V11() V12() ext-real Element of REAL
(sin . f) " is V11() V12() ext-real Element of REAL
1 * ((sin . f) ") is V11() V12() ext-real Element of REAL
(1 * ((sin . f) ")) * ((cos . f) * (1 / (sin . f))) is V11() V12() ext-real Element of REAL
- ((1 * ((sin . f) ")) * ((cos . f) * (1 / (sin . f)))) is V11() V12() ext-real Element of REAL
(cos . f) * (1 * ((sin . f) ")) is V11() V12() ext-real Element of REAL
((sin . f) ") * ((cos . f) * (1 * ((sin . f) "))) is V11() V12() ext-real Element of REAL
- (((sin . f) ") * ((cos . f) * (1 * ((sin . f) ")))) is V11() V12() ext-real Element of REAL
(sin ^) . f is V11() V12() ext-real Element of REAL
(cos . f) * ((sin . f) ") is V11() V12() ext-real Element of REAL
((sin ^) . f) * ((cos . f) * ((sin . f) ")) is V11() V12() ext-real Element of REAL
- (((sin ^) . f) * ((cos . f) * ((sin . f) "))) is V11() V12() ext-real Element of REAL
(cos . f) * ((sin ^) . f) is V11() V12() ext-real Element of REAL
((sin ^) . f) * ((cos . f) * ((sin ^) . f)) is V11() V12() ext-real Element of REAL
- (((sin ^) . f) * ((cos . f) * ((sin ^) . f))) is V11() V12() ext-real Element of REAL
(cos (#) (sin ^)) . f is V11() V12() ext-real Element of REAL
((sin ^) . f) * ((cos (#) (sin ^)) . f) is V11() V12() ext-real Element of REAL
- (((sin ^) . f) * ((cos (#) (sin ^)) . f)) is V11() V12() ext-real Element of REAL
((sin ^) (#) (cos (#) (sin ^))) . f is V11() V12() ext-real Element of REAL
- (((sin ^) (#) (cos (#) (sin ^))) . f) is V11() V12() ext-real Element of REAL
((sin ^) (#) cot) . f is V11() V12() ext-real Element of REAL
- (((sin ^) (#) cot) . f) is V11() V12() ext-real Element of REAL
(- 1) * (((sin ^) (#) cot) . f) is V11() V12() ext-real Element of REAL
((- 1) (#) ((sin ^) (#) cot)) . f is V11() V12() ext-real Element of REAL
dom ((- ((sin ^) (#) cot)) | Z) is V84() V85() V86() Element of K6(REAL)
(- 1) (#) ((sin ^) (#) cot) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((- 1) (#) ((sin ^) (#) cot)) is V84() V85() V86() Element of K6(REAL)
(dom ((- 1) (#) ((sin ^) (#) cot))) /\ Z is V84() V85() V86() set
dom ((sin ^) (#) cot) is V84() V85() V86() Element of K6(REAL)
(dom ((sin ^) (#) cot)) /\ Z is V84() V85() V86() set
(dom (sin ^)) /\ (dom cot) is V84() V85() V86() set
((dom (sin ^)) /\ (dom cot)) /\ Z is V84() V85() V86() set
cot (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cot (#) (sin ^)) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
diff (cot,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cot,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cot (#) (sin ^)) (#) (sin ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((cot (#) (sin ^)) (#) (sin ^)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin ^) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((sin ^) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cot,Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cot,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cot,Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (cot,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (cot,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (cot,Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cot | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cot | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((cot | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cot `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cot `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) ((sin ^) (#) (sin ^))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) ((sin ^) (#) (sin ^))) | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) ((sin ^) (#) (sin ^))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((sin ^) (#) (sin ^)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((sin ^) (#) (sin ^)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin ^) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((sin ^) `| Z) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((sin ^) `| Z) (#) (sin ^)) + (((sin ^) `| Z) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((((sin ^) `| Z) (#) (sin ^)) + (((sin ^) `| Z) (#) (sin ^))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (((sin ^) `| Z) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((sin ^) `| Z) (#) (sin ^))) + (((sin ^) `| Z) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((1 (#) (((sin ^) `| Z) (#) (sin ^))) + (((sin ^) `| Z) (#) (sin ^))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((sin ^) `| Z) (#) (sin ^))) + (1 (#) (((sin ^) `| Z) (#) (sin ^))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((1 (#) (((sin ^) `| Z) (#) (sin ^))) + (1 (#) (((sin ^) `| Z) (#) (sin ^)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 + 1) (#) (((sin ^) `| Z) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((1 + 1) (#) (((sin ^) `| Z) (#) (sin ^))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- ((sin ^) (#) cot)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- ((sin ^) (#) cot)) | Z) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- ((sin ^) (#) cot)) | Z) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (2 (#) (((- ((sin ^) (#) cot)) | Z) (#) (sin ^))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) * 2 is V11() V12() ext-real V48() Element of REAL
((- 1) * 2) (#) (((- ((sin ^) (#) cot)) | Z) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- ((sin ^) (#) cot)) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- ((sin ^) (#) cot)) (#) (sin ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) * 2) (#) (((- ((sin ^) (#) cot)) (#) (sin ^)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) * 2) (#) ((- ((sin ^) (#) cot)) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) * 2) (#) ((- ((sin ^) (#) cot)) (#) (sin ^))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) (#) (- ((sin ^) (#) cot)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 2) (#) (- ((sin ^) (#) cot))) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 2) (#) (- ((sin ^) (#) cot))) (#) (sin ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) * (- 1) is V11() V12() ext-real V48() Element of REAL
((- 2) * (- 1)) (#) ((sin ^) (#) cot) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 2) * (- 1)) (#) ((sin ^) (#) cot)) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 2) * (- 1)) (#) ((sin ^) (#) cot)) (#) (sin ^)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((sin ^) (#) cot) (#) (sin ^) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((sin ^) (#) cot) (#) (sin ^)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((sin ^) (#) cot) (#) (sin ^))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
diff ((exp_R (#) sin),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((exp_R (#) sin),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (2 (#) ((exp_R (#) cos) | Z)) is V84() V85() V86() Element of K6(REAL)
dom ((exp_R (#) cos) | Z) is V84() V85() V86() Element of K6(REAL)
dom (exp_R (#) cos) is V84() V85() V86() Element of K6(REAL)
(dom (exp_R (#) cos)) /\ Z is V84() V85() V86() set
REAL /\ REAL is V84() V85() V86() set
(REAL /\ REAL) /\ Z is V84() V85() V86() set
cos | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + (exp_R (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff ((exp_R (#) sin),Z)) . 2) is V84() V85() V86() Element of K6(REAL)
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((exp_R (#) sin),Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff ((exp_R (#) sin),Z)) . (1 + 1)) is V84() V85() V86() Element of K6(REAL)
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((exp_R (#) sin),Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((exp_R (#) sin),Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff ((exp_R (#) sin),Z)) . (1 + 0)) `| Z) is V84() V85() V86() Element of K6(REAL)
(diff ((exp_R (#) sin),Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((exp_R (#) sin),Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff ((exp_R (#) sin),Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((diff ((exp_R (#) sin),Z)) . 0) `| Z) `| Z) is V84() V85() V86() Element of K6(REAL)
(exp_R (#) sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R (#) sin) | Z) `| Z) `| Z) is V84() V85() V86() Element of K6(REAL)
(exp_R (#) sin) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((exp_R (#) sin) `| Z) `| Z) is V84() V85() V86() Element of K6(REAL)
exp_R `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R `| Z) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R `| Z) (#) sin) + (exp_R (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R `| Z) (#) sin) + (exp_R (#) (sin `| Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R `| Z) (#) sin) + (exp_R (#) (sin `| Z))) `| Z) is V84() V85() V86() Element of K6(REAL)
((exp_R | Z) (#) sin) + (exp_R (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + (exp_R (#) (sin `| Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R | Z) (#) sin) + (exp_R (#) (sin `| Z))) `| Z) is V84() V85() V86() Element of K6(REAL)
(((exp_R | Z) (#) sin) + (exp_R (#) (cos | Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R | Z) (#) sin) + (exp_R (#) (cos | Z))) `| Z) is V84() V85() V86() Element of K6(REAL)
0 (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (0 (#) ((exp_R (#) sin) | Z)) is V84() V85() V86() Element of K6(REAL)
dom ((exp_R (#) sin) | Z) is V84() V85() V86() Element of K6(REAL)
dom (exp_R (#) sin) is V84() V85() V86() Element of K6(REAL)
(dom (exp_R (#) sin)) /\ Z is V84() V85() V86() set
(0 (#) ((exp_R (#) sin) | Z)) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((0 (#) ((exp_R (#) sin) | Z)) + (2 (#) ((exp_R (#) cos) | Z))) is V84() V85() V86() Element of K6(REAL)
Z /\ Z is V84() V85() V86() set
f is V11() V12() ext-real Element of REAL
((diff ((exp_R (#) sin),Z)) . 2) . f is V11() V12() ext-real Element of REAL
(2 (#) ((exp_R (#) cos) | Z)) . f is V11() V12() ext-real Element of REAL
diff (exp_R,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (exp_R,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (exp_R,Z)) . 2) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R `| Z) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R `| Z) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (exp_R,Z)) . 2) (#) sin) + (2 (#) ((exp_R `| Z) (#) (sin `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (sin,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((diff (sin,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (exp_R,Z)) . 2) (#) sin) + (2 (#) ((exp_R `| Z) (#) (sin `| Z)))) + (exp_R (#) ((diff (sin,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (exp_R,Z)) . 2) (#) sin) + (2 (#) ((exp_R `| Z) (#) (sin `| Z)))) + (exp_R (#) ((diff (sin,Z)) . 2))) . f is V11() V12() ext-real Element of REAL
((exp_R | Z) (#) sin) + (2 (#) ((exp_R `| Z) (#) (sin `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + (2 (#) ((exp_R `| Z) (#) (sin `| Z)))) + (exp_R (#) ((diff (sin,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) sin) + (2 (#) ((exp_R `| Z) (#) (sin `| Z)))) + (exp_R (#) ((diff (sin,Z)) . 2))) . f is V11() V12() ext-real Element of REAL
(exp_R | Z) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R | Z) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (sin `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (sin `| Z)))) + (exp_R (#) ((diff (sin,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (sin `| Z)))) + (exp_R (#) ((diff (sin,Z)) . 2))) . f is V11() V12() ext-real Element of REAL
(exp_R | Z) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R | Z) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((diff (sin,Z)) . (2 * 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) ((diff (sin,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) ((diff (sin,Z)) . (2 * 1)))) . f is V11() V12() ext-real Element of REAL
sin | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) (((- 1) |^ 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) (((- 1) |^ 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) (((- 1) |^ 1) (#) (sin | Z)))) . f is V11() V12() ext-real Element of REAL
(- 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((- 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) sin) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) ((- 1) (#) (sin | Z)))) . f is V11() V12() ext-real Element of REAL
((exp_R (#) sin) | Z) + (2 (#) ((exp_R | Z) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) sin) | Z) + (2 (#) ((exp_R | Z) (#) (cos | Z)))) + (exp_R (#) ((- 1) (#) (sin | Z)))) . f is V11() V12() ext-real Element of REAL
((exp_R (#) sin) | Z) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + (2 (#) ((exp_R (#) cos) | Z))) + (exp_R (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) sin) | Z) + (2 (#) ((exp_R (#) cos) | Z))) + (exp_R (#) ((- 1) (#) (sin | Z)))) . f is V11() V12() ext-real Element of REAL
((exp_R (#) sin) | Z) + (exp_R (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + (exp_R (#) ((- 1) (#) (sin | Z)))) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) sin) | Z) + (exp_R (#) ((- 1) (#) (sin | Z)))) + (2 (#) ((exp_R (#) cos) | Z))) . f is V11() V12() ext-real Element of REAL
exp_R (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (exp_R (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + ((- 1) (#) (exp_R (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((- 1) (#) (exp_R (#) (sin | Z)))) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) sin) | Z) + ((- 1) (#) (exp_R (#) (sin | Z)))) + (2 (#) ((exp_R (#) cos) | Z))) . f is V11() V12() ext-real Element of REAL
(- 1) (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + ((- 1) (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((- 1) (#) ((exp_R (#) sin) | Z))) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) sin) | Z) + ((- 1) (#) ((exp_R (#) sin) | Z))) + (2 (#) ((exp_R (#) cos) | Z))) . f is V11() V12() ext-real Element of REAL
1 (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) ((exp_R (#) sin) | Z)) + ((- 1) (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) ((exp_R (#) sin) | Z)) + ((- 1) (#) ((exp_R (#) sin) | Z))) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 (#) ((exp_R (#) sin) | Z)) + ((- 1) (#) ((exp_R (#) sin) | Z))) + (2 (#) ((exp_R (#) cos) | Z))) . f is V11() V12() ext-real Element of REAL
1 + (- 1) is V11() V12() ext-real V48() Element of REAL
(1 + (- 1)) (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 + (- 1)) (#) ((exp_R (#) sin) | Z)) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 + (- 1)) (#) ((exp_R (#) sin) | Z)) + (2 (#) ((exp_R (#) cos) | Z))) . f is V11() V12() ext-real Element of REAL
(0 (#) ((exp_R (#) sin) | Z)) . f is V11() V12() ext-real Element of REAL
((0 (#) ((exp_R (#) sin) | Z)) . f) + ((2 (#) ((exp_R (#) cos) | Z)) . f) is V11() V12() ext-real Element of REAL
((exp_R (#) sin) | Z) . f is V11() V12() ext-real Element of REAL
0 * (((exp_R (#) sin) | Z) . f) is V11() V12() ext-real Element of REAL
(0 * (((exp_R (#) sin) | Z) . f)) + ((2 (#) ((exp_R (#) cos) | Z)) . f) is V11() V12() ext-real Element of REAL
exp_R (#) (- sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
diff ((exp_R (#) cos),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((exp_R (#) cos),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R (#) (- sin)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R (#) (- sin)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (2 (#) ((exp_R (#) (- sin)) | Z)) is V84() V85() V86() Element of K6(REAL)
dom ((exp_R (#) (- sin)) | Z) is V84() V85() V86() Element of K6(REAL)
dom (exp_R (#) (- sin)) is V84() V85() V86() Element of K6(REAL)
(dom (exp_R (#) (- sin))) /\ Z is V84() V85() V86() set
dom (- sin) is V84() V85() V86() Element of K6(REAL)
(dom exp_R) /\ (dom (- sin)) is V84() V85() V86() set
((dom exp_R) /\ (dom (- sin))) /\ Z is V84() V85() V86() set
REAL /\ REAL is V84() V85() V86() set
(REAL /\ REAL) /\ Z is V84() V85() V86() set
sin | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((- 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) cos) + (exp_R (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff ((exp_R (#) cos),Z)) . 2) is V84() V85() V86() Element of K6(REAL)
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((exp_R (#) cos),Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff ((exp_R (#) cos),Z)) . (1 + 1)) is V84() V85() V86() Element of K6(REAL)
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((exp_R (#) cos),Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((exp_R (#) cos),Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff ((exp_R (#) cos),Z)) . (1 + 0)) `| Z) is V84() V85() V86() Element of K6(REAL)
(diff ((exp_R (#) cos),Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((exp_R (#) cos),Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff ((exp_R (#) cos),Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((diff ((exp_R (#) cos),Z)) . 0) `| Z) `| Z) is V84() V85() V86() Element of K6(REAL)
(exp_R (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) cos) | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) cos) | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R (#) cos) | Z) `| Z) `| Z) is V84() V85() V86() Element of K6(REAL)
(exp_R (#) cos) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) cos) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((exp_R (#) cos) `| Z) `| Z) is V84() V85() V86() Element of K6(REAL)
exp_R `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R `| Z) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) (cos `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R `| Z) (#) cos) + (exp_R (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R `| Z) (#) cos) + (exp_R (#) (cos `| Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R `| Z) (#) cos) + (exp_R (#) (cos `| Z))) `| Z) is V84() V85() V86() Element of K6(REAL)
((exp_R | Z) (#) cos) + (exp_R (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (exp_R (#) (cos `| Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R | Z) (#) cos) + (exp_R (#) (cos `| Z))) `| Z) is V84() V85() V86() Element of K6(REAL)
(- sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((- sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) cos) + (exp_R (#) ((- sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (exp_R (#) ((- sin) | Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R | Z) (#) cos) + (exp_R (#) ((- sin) | Z))) `| Z) is V84() V85() V86() Element of K6(REAL)
(((exp_R | Z) (#) cos) + (exp_R (#) ((- 1) (#) (sin | Z)))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((exp_R | Z) (#) cos) + (exp_R (#) ((- 1) (#) (sin | Z)))) `| Z) is V84() V85() V86() Element of K6(REAL)
0 (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (0 (#) ((exp_R (#) cos) | Z)) is V84() V85() V86() Element of K6(REAL)
dom ((exp_R (#) cos) | Z) is V84() V85() V86() Element of K6(REAL)
dom (exp_R (#) cos) is V84() V85() V86() Element of K6(REAL)
(dom (exp_R (#) cos)) /\ Z is V84() V85() V86() set
(0 (#) ((exp_R (#) cos) | Z)) + (2 (#) ((exp_R (#) (- sin)) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((0 (#) ((exp_R (#) cos) | Z)) + (2 (#) ((exp_R (#) (- sin)) | Z))) is V84() V85() V86() Element of K6(REAL)
Z /\ Z is V84() V85() V86() set
f is V11() V12() ext-real Element of REAL
((diff ((exp_R (#) cos),Z)) . 2) . f is V11() V12() ext-real Element of REAL
(2 (#) ((exp_R (#) (- sin)) | Z)) . f is V11() V12() ext-real Element of REAL
diff (exp_R,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (exp_R,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (exp_R,Z)) . 2) (#) cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R `| Z) (#) (cos `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R `| Z) (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (exp_R,Z)) . 2) (#) cos) + (2 (#) ((exp_R `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (cos,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (cos,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((diff (cos,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (exp_R,Z)) . 2) (#) cos) + (2 (#) ((exp_R `| Z) (#) (cos `| Z)))) + (exp_R (#) ((diff (cos,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (exp_R,Z)) . 2) (#) cos) + (2 (#) ((exp_R `| Z) (#) (cos `| Z)))) + (exp_R (#) ((diff (cos,Z)) . 2))) . f is V11() V12() ext-real Element of REAL
((exp_R | Z) (#) cos) + (2 (#) ((exp_R `| Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (2 (#) ((exp_R `| Z) (#) (cos `| Z)))) + (exp_R (#) ((diff (cos,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) cos) + (2 (#) ((exp_R `| Z) (#) (cos `| Z)))) + (exp_R (#) ((diff (cos,Z)) . 2))) . f is V11() V12() ext-real Element of REAL
(exp_R | Z) (#) (cos `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R | Z) (#) (cos `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (cos `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (cos `| Z)))) + (exp_R (#) ((diff (cos,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (cos `| Z)))) + (exp_R (#) ((diff (cos,Z)) . 2))) . f is V11() V12() ext-real Element of REAL
(exp_R | Z) (#) ((- sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R | Z) (#) ((- sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) ((- sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (cos,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((diff (cos,Z)) . (2 * 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) ((- sin) | Z)))) + (exp_R (#) ((diff (cos,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) ((- sin) | Z)))) + (exp_R (#) ((diff (cos,Z)) . (2 * 1)))) . f is V11() V12() ext-real Element of REAL
- (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) (sin | Z) is V16() V21() set
(exp_R | Z) (#) (- (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R | Z) (#) (- (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (- (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) ((diff (cos,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) ((diff (cos,Z)) . (2 * 1)))) . f is V11() V12() ext-real Element of REAL
cos | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) (((- 1) |^ 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) (((- 1) |^ 1) (#) (cos | Z)))) . f is V11() V12() ext-real Element of REAL
(- 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((- 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R | Z) (#) cos) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) ((- 1) (#) (cos | Z)))) . f is V11() V12() ext-real Element of REAL
((exp_R (#) cos) | Z) + (2 (#) ((exp_R | Z) (#) (- (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) cos) | Z) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) cos) | Z) + (2 (#) ((exp_R | Z) (#) (- (sin | Z))))) + (exp_R (#) ((- 1) (#) (cos | Z)))) . f is V11() V12() ext-real Element of REAL
((exp_R (#) cos) | Z) + (2 (#) ((exp_R | Z) (#) ((- sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) cos) | Z) + (2 (#) ((exp_R | Z) (#) ((- sin) | Z)))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) cos) | Z) + (2 (#) ((exp_R | Z) (#) ((- sin) | Z)))) + (exp_R (#) ((- 1) (#) (cos | Z)))) . f is V11() V12() ext-real Element of REAL
((exp_R (#) cos) | Z) + (2 (#) ((exp_R (#) (- sin)) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) cos) | Z) + (2 (#) ((exp_R (#) (- sin)) | Z))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) cos) | Z) + (2 (#) ((exp_R (#) (- sin)) | Z))) + (exp_R (#) ((- 1) (#) (cos | Z)))) . f is V11() V12() ext-real Element of REAL
((exp_R (#) cos) | Z) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) cos) | Z) + (exp_R (#) ((- 1) (#) (cos | Z)))) + (2 (#) ((exp_R (#) (- sin)) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) cos) | Z) + (exp_R (#) ((- 1) (#) (cos | Z)))) + (2 (#) ((exp_R (#) (- sin)) | Z))) . f is V11() V12() ext-real Element of REAL
exp_R (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (exp_R (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) cos) | Z) + ((- 1) (#) (exp_R (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) cos) | Z) + ((- 1) (#) (exp_R (#) (cos | Z)))) + (2 (#) ((exp_R (#) (- sin)) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) cos) | Z) + ((- 1) (#) (exp_R (#) (cos | Z)))) + (2 (#) ((exp_R (#) (- sin)) | Z))) . f is V11() V12() ext-real Element of REAL
(- 1) (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) cos) | Z) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) cos) | Z) + ((- 1) (#) ((exp_R (#) cos) | Z))) + (2 (#) ((exp_R (#) (- sin)) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) cos) | Z) + ((- 1) (#) ((exp_R (#) cos) | Z))) + (2 (#) ((exp_R (#) (- sin)) | Z))) . f is V11() V12() ext-real Element of REAL
1 (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) ((exp_R (#) cos) | Z)) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) ((exp_R (#) cos) | Z)) + ((- 1) (#) ((exp_R (#) cos) | Z))) + (2 (#) ((exp_R (#) (- sin)) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 (#) ((exp_R (#) cos) | Z)) + ((- 1) (#) ((exp_R (#) cos) | Z))) + (2 (#) ((exp_R (#) (- sin)) | Z))) . f is V11() V12() ext-real Element of REAL
1 + (- 1) is V11() V12() ext-real V48() Element of REAL
(1 + (- 1)) (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 + (- 1)) (#) ((exp_R (#) cos) | Z)) + (2 (#) ((exp_R (#) (- sin)) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 + (- 1)) (#) ((exp_R (#) cos) | Z)) + (2 (#) ((exp_R (#) (- sin)) | Z))) . f is V11() V12() ext-real Element of REAL
(0 (#) ((exp_R (#) cos) | Z)) . f is V11() V12() ext-real Element of REAL
((0 (#) ((exp_R (#) cos) | Z)) . f) + ((2 (#) ((exp_R (#) (- sin)) | Z)) . f) is V11() V12() ext-real Element of REAL
((exp_R (#) cos) | Z) . f is V11() V12() ext-real Element of REAL
0 * (((exp_R (#) cos) | Z) . f) is V11() V12() ext-real Element of REAL
(0 * (((exp_R (#) cos) | Z) . f)) + ((2 (#) ((exp_R (#) (- sin)) | Z)) . f) is V11() V12() ext-real Element of REAL
Z is open V84() V85() V86() Element of K6(REAL)
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (f,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (f,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
0 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (0 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . (0 + 1)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (f,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (f,Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((f (#) g1),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f (#) g1),Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 3) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 2) (#) (g1 `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (g1,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (g1,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) ((diff (g1,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (3 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + ((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (3 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (g1,Z)) . 3) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + ((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (3 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))))) + (f (#) ((diff (g1,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 - 1 is V11() V12() ext-real V48() Element of REAL
(diff (g1,Z)) . 1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (g1,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
g1 | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 2) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . 1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) (g1 `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((f `| Z) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) + (2 (#) ((f `| Z) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (g1,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((f (#) g1),Z)) . (2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((f (#) g1),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f (#) g1),Z)) . 2) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + (2 (#) ((f `| Z) (#) (g1 `| Z)))) + (f (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 2) (#) g1) + (2 (#) ((f `| Z) (#) (g1 `| Z)))) + (f (#) ((diff (g1,Z)) . 2))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) + (2 (#) ((f `| Z) (#) (g1 `| Z)))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((diff (g1,Z)) . 2)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 2) (#) g1) + (2 (#) ((f `| Z) (#) (g1 `| Z)))) `| Z) + ((f (#) ((diff (g1,Z)) . 2)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) g1) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((f `| Z) (#) (g1 `| Z))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) `| Z) + ((2 (#) ((f `| Z) (#) (g1 `| Z))) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 2) (#) g1) `| Z) + ((2 (#) ((f `| Z) (#) (g1 `| Z))) `| Z)) + ((f (#) ((diff (g1,Z)) . 2)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) (g1 `| Z)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) g1) `| Z) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 2) (#) g1) `| Z) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z))) + ((f (#) ((diff (g1,Z)) . 2)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 2) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) `| Z) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) `| Z) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 2) `| Z) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((((diff (f,Z)) . 2) `| Z) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z))) + ((f (#) ((diff (g1,Z)) . 2)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (g1,Z)) . 2) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (((diff (g1,Z)) . 2) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) (((diff (g1,Z)) . 2) `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((((diff (f,Z)) . 2) `| Z) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) (((diff (g1,Z)) . 2) `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . (2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . (2 + 1)) (#) g1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . (2 + 1)) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . (2 + 1)) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . (2 + 1)) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) (((diff (g1,Z)) . 2) `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (g1,Z)) . (2 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (g1,Z)) . (2 + 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . (2 + 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((f `| Z) (#) (g1 `| Z)) `| Z))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . (2 + 1)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) `| Z) (#) (g1 `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(g1 `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) ((g1 `| Z) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f `| Z) `| Z) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((((f `| Z) `| Z) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((((f `| Z) `| Z) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((((f `| Z) `| Z) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((g1 `| Z) `| Z))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 3) (#) g1) + (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((diff (g1,Z)) . 2))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) ((diff (f,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + ((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + ((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z))) + (2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 3) (#) g1) + ((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z))) + (2 (#) ((((diff (f,Z)) . 2) (#) (g1 `| Z)) + ((f `| Z) (#) ((diff (g1,Z)) . 2))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + ((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z))) + ((2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((diff (f,Z)) . 3) (#) g1) + ((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z))) + ((2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) + ((2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + (((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) + ((2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + (((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) + ((2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + ((((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + ((((1 (#) ((diff (f,Z)) . 2)) (#) (g1 `| Z)) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + (((1 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + (((1 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 + 2) (#) (((diff (f,Z)) . 2) (#) (g1 `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 + 2) (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + (((1 + 2) (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 3) (#) g1) + (((1 + 2) (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + (((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + ((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + ((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + ((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (((f `| Z) (#) ((diff (g1,Z)) . 2)) + (f (#) ((diff (g1,Z)) . 3))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + ((f `| Z) (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (f (#) ((diff (g1,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + ((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (f (#) ((diff (g1,Z)) . 3)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (1 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (1 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) + (f (#) ((diff (g1,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (1 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + ((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (((2 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (1 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) + (f (#) ((diff (g1,Z)) . 3)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 + 1) (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((2 + 1) (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (f (#) ((diff (g1,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (((2 + 1) (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + ((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (((2 + 1) (#) ((f `| Z) (#) ((diff (g1,Z)) . 2))) + (f (#) ((diff (g1,Z)) . 3)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (3 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) + (f (#) ((diff (g1,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 3) (#) g1) + (((3 (#) (((diff (f,Z)) . 2) (#) (g1 `| Z))) + (3 (#) ((f `| Z) (#) ((diff (g1,Z)) . 2)))) + (f (#) ((diff (g1,Z)) . 3))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
8 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
- 8 is V11() V12() ext-real V48() Element of REAL
Z is open V84() V85() V86() Element of K6(REAL)
diff ((sin ^2),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((sin ^2),Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos (#) sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 8) (#) ((cos (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((sin (#) sin),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((sin (#) sin),Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (sin,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(2 * 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,Z)) . ((2 * 1) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,Z)) . ((2 * 1) + 1)) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (sin,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) (((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| Z) (#) ((diff (sin,Z)) . (2 * 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (sin,Z)) . ((2 * 1) + 1)) (#) sin) + ((3 (#) (((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) ((diff (sin,Z)) . ((2 * 1) + 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (sin,Z)) . ((2 * 1) + 1)) (#) sin) + ((3 (#) (((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1)))))) + (sin (#) ((diff (sin,Z)) . ((2 * 1) + 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ 1) (#) (cos | Z)) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1)))))) + (sin (#) ((diff (sin,Z)) . ((2 * 1) + 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) (((- 1) |^ 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((diff (sin,Z)) . (2 * 1)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1)))))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) |^ 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ 1) (#) (cos | Z)) (#) sin) + ((3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (cos | Z)) (#) sin) + ((3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((diff (sin,Z)) . (2 * 1)))))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) |^ 1) (#) (cos | Z)) (#) sin) + ((3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((((- 1) |^ 1) (#) (cos | Z)) (#) sin) + ((3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z)))))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (cos | Z)) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) ((((- 1) |^ 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z)))))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (sin | Z)) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) (((- 1) |^ 1) (#) (sin | Z)))))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(sin `| Z) (#) ((- 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z)))))) + (sin (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin (#) ((- 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (sin `| Z))) + (3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z)))))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (sin | Z)) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) (((- 1) (#) (sin | Z)) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((- 1) (#) (sin | Z)) (#) (cos | Z))) + (3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (cos | Z))) + (3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (cos | Z))) + (3 (#) ((sin `| Z) (#) ((- 1) (#) (sin | Z)))))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) ((- 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((- 1) (#) (sin | Z)) (#) (cos | Z))) + (3 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (cos | Z))) + (3 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) sin) + ((3 (#) (((- 1) (#) (sin | Z)) (#) (cos | Z))) + (3 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z)))))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 + 3 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(3 + 3) (#) ((cos | Z) (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) sin) + ((3 + 3) (#) ((cos | Z) (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((- 1) (#) (cos | Z)) (#) sin) + ((3 + 3) (#) ((cos | Z) (#) ((- 1) (#) (sin | Z))))) + (sin (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
6 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
6 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 1) (#) (cos | Z)) (#) sin) + (((- 1) (#) (cos | Z)) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z)))) + ((((- 1) (#) (cos | Z)) (#) sin) + (((- 1) (#) (cos | Z)) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (((- 1) (#) (cos | Z)) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((- 1) (#) (cos | Z)) (#) sin)) + (((- 1) (#) (cos | Z)) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z)))) + ((1 (#) (((- 1) (#) (cos | Z)) (#) sin)) + (((- 1) (#) (cos | Z)) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (((- 1) (#) (cos | Z)) (#) sin)) + (1 (#) (((- 1) (#) (cos | Z)) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z)))) + ((1 (#) (((- 1) (#) (cos | Z)) (#) sin)) + (1 (#) (((- 1) (#) (cos | Z)) (#) sin))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 + 1) (#) (((- 1) (#) (cos | Z)) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((cos | Z) (#) ((- 1) (#) (sin | Z)))) + ((1 + 1) (#) (((- 1) (#) (cos | Z)) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((cos | Z) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
6 (#) ((- 1) (#) ((cos | Z) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- 1) (#) (cos | Z)) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((- 1) (#) ((cos | Z) (#) (sin | Z)))) + (2 (#) (((- 1) (#) (cos | Z)) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((cos (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
6 (#) ((- 1) (#) ((cos (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((- 1) (#) ((cos (#) sin) | Z))) + (2 (#) (((- 1) (#) (cos | Z)) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(cos | Z) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((cos | Z) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((- 1) (#) ((cos | Z) (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((- 1) (#) ((cos (#) sin) | Z))) + (2 (#) ((- 1) (#) ((cos | Z) (#) sin))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((- 1) (#) ((cos (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(6 (#) ((- 1) (#) ((cos (#) sin) | Z))) + (2 (#) ((- 1) (#) ((cos (#) sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
6 + 2 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(6 + 2) (#) ((- 1) (#) ((cos (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
8 * (- 1) is V11() V12() ext-real V48() Element of REAL
(8 * (- 1)) (#) ((cos (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f ^2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) f is V16() V21() set
diff ((f ^2),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f ^2),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (f,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (f,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((diff (f,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (f (#) ((diff (f,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) ^2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) (f `| Z) is V16() V21() set
2 (#) ((f `| Z) ^2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (f (#) ((diff (f,Z)) . 2))) + (2 (#) ((f `| Z) ^2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 2) (#) f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((f `| Z) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((f `| Z) (#) (f `| Z))) + (f (#) ((diff (f,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) f) + ((2 (#) ((f `| Z) (#) (f `| Z))) + (f (#) ((diff (f,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) f) + (f (#) ((diff (f,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (f,Z)) . 2) (#) f) + (f (#) ((diff (f,Z)) . 2))) + (2 (#) ((f `| Z) (#) (f `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (f (#) ((diff (f,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (f (#) ((diff (f,Z)) . 2))) + (f (#) ((diff (f,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (f (#) ((diff (f,Z)) . 2))) + (f (#) ((diff (f,Z)) . 2))) + (2 (#) ((f `| Z) (#) (f `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (f (#) ((diff (f,Z)) . 2))) + (1 (#) (f (#) ((diff (f,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 (#) (f (#) ((diff (f,Z)) . 2))) + (1 (#) (f (#) ((diff (f,Z)) . 2)))) + (2 (#) ((f `| Z) (#) (f `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(1 + 1) (#) (f (#) ((diff (f,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((1 + 1) (#) (f (#) ((diff (f,Z)) . 2))) + (2 (#) ((f `| Z) (#) (f `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (f (#) ((diff (f,Z)) . 2))) + (2 (#) ((f `| Z) (#) (f `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z / Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom Z is V84() V85() V86() Element of K6(REAL)
Z " {0} is V84() V85() V86() Element of K6(REAL)
(dom Z) \ (Z " {0}) is V84() V85() V86() set
((dom Z) \ (Z " {0})) --> 1 is V16() V19((dom Z) \ (Z " {0})) V20( NAT ) V20( RAT ) V20( INT ) V21() total V30((dom Z) \ (Z " {0}), NAT ) V74() V75() V76() V77() Element of K6(K7(((dom Z) \ (Z " {0})),NAT))
K7(((dom Z) \ (Z " {0})),NAT) is V20( RAT ) V20( INT ) V74() V75() V76() V77() set
K6(K7(((dom Z) \ (Z " {0})),NAT)) is set
dom (Z / Z) is V84() V85() V86() Element of K6(REAL)
(dom Z) /\ ((dom Z) \ (Z " {0})) is V84() V85() V86() set
f is set
(Z / Z) . f is V11() V12() ext-real Element of REAL
Z . f is V11() V12() ext-real Element of REAL
(Z . f) " is V11() V12() ext-real Element of REAL
(Z . f) * ((Z . f) ") is V11() V12() ext-real Element of REAL
Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z (#) (Z (#) Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(Z (#) (Z (#) Z)) " {0} is V84() V85() V86() Element of K6(REAL)
Z " {0} is V84() V85() V86() Element of K6(REAL)
f is set
(Z (#) (Z (#) Z)) . f is V11() V12() ext-real Element of REAL
Z . f is V11() V12() ext-real Element of REAL
(Z (#) Z) . f is V11() V12() ext-real Element of REAL
(Z . f) * ((Z (#) Z) . f) is V11() V12() ext-real Element of REAL
(Z . f) * (Z . f) is V11() V12() ext-real Element of REAL
((Z . f) * (Z . f)) * (Z . f) is V11() V12() ext-real Element of REAL
dom (Z (#) (Z (#) Z)) is V84() V85() V86() Element of K6(REAL)
dom Z is V84() V85() V86() Element of K6(REAL)
dom (Z (#) Z) is V84() V85() V86() Element of K6(REAL)
(dom Z) /\ (dom (Z (#) Z)) is V84() V85() V86() set
f is set
Z . f is V11() V12() ext-real Element of REAL
dom Z is V84() V85() V86() Element of K6(REAL)
(dom Z) /\ (dom Z) is V84() V85() V86() set
dom (Z (#) Z) is V84() V85() V86() Element of K6(REAL)
(dom (Z (#) Z)) /\ (dom Z) is V84() V85() V86() set
dom (Z (#) (Z (#) Z)) is V84() V85() V86() Element of K6(REAL)
(Z (#) (Z (#) Z)) . f is V11() V12() ext-real Element of REAL
(Z (#) Z) . f is V11() V12() ext-real Element of REAL
(Z . f) * ((Z (#) Z) . f) is V11() V12() ext-real Element of REAL
(Z . f) * (Z . f) is V11() V12() ext-real Element of REAL
Z is open V84() V85() V86() Element of K6(REAL)
f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f ^ is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff ((f ^),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((f ^),Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (f `| Z)) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (f,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (f,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 2) (#) f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- (((diff (f,Z)) . 2) (#) f) is V16() V21() V74() set
K38(1) (#) (((diff (f,Z)) . 2) (#) f) is V16() V21() set
((2 (#) (f `| Z)) (#) (f `| Z)) + (- (((diff (f,Z)) . 2) (#) f)) is V16() V21() set
f (#) f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (f (#) f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom f is V84() V85() V86() Element of K6(REAL)
g1 is V11() V12() ext-real Element of REAL
(f (#) f) . g1 is V11() V12() ext-real Element of REAL
f . g1 is V11() V12() ext-real Element of REAL
dom (f (#) f) is V84() V85() V86() Element of K6(REAL)
(dom f) /\ (dom f) is V84() V85() V86() set
(f . g1) * (f . g1) is V11() V12() ext-real Element of REAL
2 - 1 is V11() V12() ext-real V48() Element of REAL
(diff (f,Z)) . 1 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 0 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (f,Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) / (f (#) f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff ((f ^),Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((f ^),Z)) . (1 + 0) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f ^),Z)) . (1 + 0)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff ((f ^),Z)) . 0 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff ((f ^),Z)) . 0) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff ((f ^),Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f ^) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f ^) | Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f ^) | Z) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f ^) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f ^) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((f `| Z) / (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
K38(1) (#) ((f `| Z) / (f (#) f)) is V16() V21() set
(- ((f `| Z) / (f (#) f))) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) / (f (#) f)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((f `| Z) / (f (#) f)) `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) `| Z) (#) (f (#) f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) f) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f (#) f) `| Z) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f `| Z) `| Z) (#) (f (#) f)) - (((f (#) f) `| Z) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- (((f (#) f) `| Z) (#) (f `| Z)) is V16() V21() V74() set
K38(1) (#) (((f (#) f) `| Z) (#) (f `| Z)) is V16() V21() set
(((f `| Z) `| Z) (#) (f (#) f)) + (- (((f (#) f) `| Z) (#) (f `| Z))) is V16() V21() set
(f (#) f) (#) (f (#) f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((f `| Z) `| Z) (#) (f (#) f)) - (((f (#) f) `| Z) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((((f `| Z) `| Z) (#) (f (#) f)) - (((f (#) f) `| Z) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . 2) (#) (f (#) f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (f (#) f)) - (((f (#) f) `| Z) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (f (#) f)) + (- (((f (#) f) `| Z) (#) (f `| Z))) is V16() V21() set
((((diff (f,Z)) . 2) (#) (f (#) f)) - (((f (#) f) `| Z) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((((diff (f,Z)) . 2) (#) (f (#) f)) - (((f (#) f) `| Z) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) (#) f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f `| Z) (#) f) + (f (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((f `| Z) (#) f) + (f (#) (f `| Z))) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (f (#) f)) - ((((f `| Z) (#) f) + (f (#) (f `| Z))) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((((f `| Z) (#) f) + (f (#) (f `| Z))) (#) (f `| Z)) is V16() V21() V74() set
K38(1) (#) ((((f `| Z) (#) f) + (f (#) (f `| Z))) (#) (f `| Z)) is V16() V21() set
(((diff (f,Z)) . 2) (#) (f (#) f)) + (- ((((f `| Z) (#) f) + (f (#) (f `| Z))) (#) (f `| Z))) is V16() V21() set
((((diff (f,Z)) . 2) (#) (f (#) f)) - ((((f `| Z) (#) f) + (f (#) (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((((diff (f,Z)) . 2) (#) (f (#) f)) - ((((f `| Z) (#) f) + (f (#) (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f ^2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) f is V16() V21() set
((diff (f,Z)) . 2) (#) (f ^2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f `| Z) + (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((f `| Z) + (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((f `| Z) + (f `| Z))) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((f `| Z) + (f `| Z))) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((f (#) ((f `| Z) + (f `| Z))) (#) (f `| Z)) is V16() V21() V74() set
K38(1) (#) ((f (#) ((f `| Z) + (f `| Z))) (#) (f `| Z)) is V16() V21() set
(((diff (f,Z)) . 2) (#) (f ^2)) + (- ((f (#) ((f `| Z) + (f `| Z))) (#) (f `| Z))) is V16() V21() set
((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((f `| Z) + (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((f `| Z) + (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (f `| Z)) + (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((1 (#) (f `| Z)) + (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((1 (#) (f `| Z)) + (f `| Z))) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 (#) (f `| Z)) + (f `| Z))) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((f (#) ((1 (#) (f `| Z)) + (f `| Z))) (#) (f `| Z)) is V16() V21() V74() set
K38(1) (#) ((f (#) ((1 (#) (f `| Z)) + (f `| Z))) (#) (f `| Z)) is V16() V21() set
(((diff (f,Z)) . 2) (#) (f ^2)) + (- ((f (#) ((1 (#) (f `| Z)) + (f `| Z))) (#) (f `| Z))) is V16() V21() set
((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 (#) (f `| Z)) + (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 (#) (f `| Z)) + (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) (f `| Z)) + (1 (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z)))) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z)))) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z)))) (#) (f `| Z)) is V16() V21() V74() set
K38(1) (#) ((f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z)))) (#) (f `| Z)) is V16() V21() set
(((diff (f,Z)) . 2) (#) (f ^2)) + (- ((f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z)))) (#) (f `| Z))) is V16() V21() set
((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z)))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 (#) (f `| Z)) + (1 (#) (f `| Z)))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 + 1) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((1 + 1) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((1 + 1) (#) (f `| Z))) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 + 1) (#) (f `| Z))) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((f (#) ((1 + 1) (#) (f `| Z))) (#) (f `| Z)) is V16() V21() V74() set
K38(1) (#) ((f (#) ((1 + 1) (#) (f `| Z))) (#) (f `| Z)) is V16() V21() set
(((diff (f,Z)) . 2) (#) (f ^2)) + (- ((f (#) ((1 + 1) (#) (f `| Z))) (#) (f `| Z))) is V16() V21() set
((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 + 1) (#) (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((((diff (f,Z)) . 2) (#) (f ^2)) - ((f (#) ((1 + 1) (#) (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (((diff (f,Z)) . 2) (#) f) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (2 (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) (2 (#) (f `| Z))) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) (((diff (f,Z)) . 2) (#) f)) - ((f (#) (2 (#) (f `| Z))) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- ((f (#) (2 (#) (f `| Z))) (#) (f `| Z)) is V16() V21() V74() set
K38(1) (#) ((f (#) (2 (#) (f `| Z))) (#) (f `| Z)) is V16() V21() set
(f (#) (((diff (f,Z)) . 2) (#) f)) + (- ((f (#) (2 (#) (f `| Z))) (#) (f `| Z))) is V16() V21() set
((f (#) (((diff (f,Z)) . 2) (#) f)) - ((f (#) (2 (#) (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (((f (#) (((diff (f,Z)) . 2) (#) f)) - ((f (#) (2 (#) (f `| Z))) (#) (f `| Z))) / ((f (#) f) (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((f (#) (((diff (f,Z)) . 2) (#) f)) - ((f (#) (2 (#) (f `| Z))) (#) (f `| Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) ((f (#) (((diff (f,Z)) . 2) (#) f)) - ((f (#) (2 (#) (f `| Z))) (#) (f `| Z)))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((f (#) (2 (#) (f `| Z))) (#) (f `| Z)) - (f (#) (((diff (f,Z)) . 2) (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- (f (#) (((diff (f,Z)) . 2) (#) f)) is V16() V21() V74() set
K38(1) (#) (f (#) (((diff (f,Z)) . 2) (#) f)) is V16() V21() set
((f (#) (2 (#) (f `| Z))) (#) (f `| Z)) + (- (f (#) (((diff (f,Z)) . 2) (#) f))) is V16() V21() set
(((f (#) (2 (#) (f `| Z))) (#) (f `| Z)) - (f (#) (((diff (f,Z)) . 2) (#) f))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) ((2 (#) (f `| Z)) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((2 (#) (f `| Z)) (#) (f `| Z))) - (f (#) (((diff (f,Z)) . 2) (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) ((2 (#) (f `| Z)) (#) (f `| Z))) + (- (f (#) (((diff (f,Z)) . 2) (#) f))) is V16() V21() set
((f (#) ((2 (#) (f `| Z)) (#) (f `| Z))) - (f (#) (((diff (f,Z)) . 2) (#) f))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) (((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f))) / ((f (#) f) (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f (#) (f (#) (f (#) f)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f (#) (((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f))) / (f (#) (f (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f / f is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(f / f) (#) ((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
f " {0} is V84() V85() V86() Element of K6(REAL)
(dom f) \ (f " {0}) is V84() V85() V86() set
((dom f) \ (f " {0})) --> 1 is V16() V19((dom f) \ (f " {0})) V20( NAT ) V20( RAT ) V20( INT ) V21() total V30((dom f) \ (f " {0}), NAT ) V74() V75() V76() V77() Element of K6(K7(((dom f) \ (f " {0})),NAT))
K7(((dom f) \ (f " {0})),NAT) is V20( RAT ) V20( INT ) V74() V75() V76() V77() set
K6(K7(((dom f) \ (f " {0})),NAT)) is set
(((dom f) \ (f " {0})) --> 1) (#) ((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f))) is V16() V21() set
(diff (f,Z)) . (1 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((diff (f,Z)) . (1 + 1)) is V84() V85() V86() Element of K6(REAL)
0 + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (f,Z)) . (0 + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (f,Z)) . (0 + 1)) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (((diff (f,Z)) . (0 + 1)) `| Z) is V84() V85() V86() Element of K6(REAL)
(((diff (f,Z)) . 0) `| Z) `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom ((((diff (f,Z)) . 0) `| Z) `| Z) is V84() V85() V86() Element of K6(REAL)
dom (((diff (f,Z)) . 2) (#) f) is V84() V85() V86() Element of K6(REAL)
dom ((diff (f,Z)) . 2) is V84() V85() V86() Element of K6(REAL)
(dom ((diff (f,Z)) . 2)) /\ (dom f) is V84() V85() V86() set
Z /\ (dom f) is V84() V85() V86() set
dom ((2 (#) (f `| Z)) (#) (f `| Z)) is V84() V85() V86() Element of K6(REAL)
(f `| Z) (#) (f `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((f `| Z) (#) (f `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
dom (2 (#) ((f `| Z) (#) (f `| Z))) is V84() V85() V86() Element of K6(REAL)
dom ((f `| Z) (#) (f `| Z)) is V84() V85() V86() Element of K6(REAL)
dom (f `| Z) is V84() V85() V86() Element of K6(REAL)
(dom (f `| Z)) /\ (dom (f `| Z)) is V84() V85() V86() set
dom (f (#) (f (#) f)) is V84() V85() V86() Element of K6(REAL)
dom (f (#) f) is V84() V85() V86() Element of K6(REAL)
(dom f) /\ (dom (f (#) f)) is V84() V85() V86() set
(dom f) /\ (dom f) is V84() V85() V86() set
(dom f) /\ ((dom f) /\ (dom f)) is V84() V85() V86() set
dom (f / f) is V84() V85() V86() Element of K6(REAL)
dom ((f / f) (#) ((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f)))) is V84() V85() V86() Element of K6(REAL)
dom ((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f))) is V84() V85() V86() Element of K6(REAL)
(dom (f / f)) /\ (dom ((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f)))) is V84() V85() V86() set
x is V11() V12() ext-real Element of REAL
((f / f) (#) ((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f)))) . x is V11() V12() ext-real Element of REAL
((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f))) . x is V11() V12() ext-real Element of REAL
(f / f) . x is V11() V12() ext-real Element of REAL
((f / f) . x) * (((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f))) . x) is V11() V12() ext-real Element of REAL
1 * (((((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) / (f (#) (f (#) f))) . x) is V11() V12() ext-real Element of REAL
dom (((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f)) is V84() V85() V86() Element of K6(REAL)
(f (#) (f (#) f)) " {0} is V84() V85() V86() Element of K6(REAL)
(dom (f (#) (f (#) f))) \ ((f (#) (f (#) f)) " {0}) is V84() V85() V86() set
(dom (((2 (#) (f `| Z)) (#) (f `| Z)) - (((diff (f,Z)) . 2) (#) f))) /\ ((dom (f (#) (f (#) f))) \ ((f (#) (f (#) f)) " {0})) is V84() V85() V86() set
(dom ((2 (#) (f `| Z)) (#) (f `| Z))) /\ (dom (((diff (f,Z)) . 2) (#) f)) is V84() V85() V86() set
((dom ((2 (#) (f `| Z)) (#) (f `| Z))) /\ (dom (((diff (f,Z)) . 2) (#) f))) /\ ((dom (f (#) (f (#) f))) \ ((f (#) (f (#) f)) " {0})) is V84() V85() V86() set
Z /\ (dom (((diff (f,Z)) . 2) (#) f)) is V84() V85() V86() set
(Z /\ (dom (((diff (f,Z)) . 2) (#) f))) /\ ((dom (f (#) (f (#) f))) \ ((f (#) (f (#) f)) " {0})) is V84() V85() V86() set
Z /\ (Z /\ (dom f)) is V84() V85() V86() set
(Z /\ (Z /\ (dom f))) /\ ((dom (f (#) (f (#) f))) \ ((f (#) (f (#) f)) " {0})) is V84() V85() V86() set
Z /\ Z is V84() V85() V86() set
(Z /\ Z) /\ (dom f) is V84() V85() V86() set
((Z /\ Z) /\ (dom f)) /\ ((dom (f (#) (f (#) f))) \ ((f (#) (f (#) f)) " {0})) is V84() V85() V86() set
(Z /\ (dom f)) /\ ((dom (f (#) (f (#) f))) \ ((f (#) (f (#) f)) " {0})) is V84() V85() V86() set
(dom f) \ ((f (#) (f (#) f)) " {0}) is V84() V85() V86() set
(Z /\ (dom f)) /\ ((dom f) \ ((f (#) (f (#) f)) " {0})) is V84() V85() V86() set
(Z /\ (dom f)) /\ (dom f) is V84() V85() V86() set
((Z /\ (dom f)) /\ (dom f)) \ ((f (#) (f (#) f)) " {0}) is V84() V85() V86() set
Z /\ ((dom f) /\ (dom f)) is V84() V85() V86() set
(Z /\ ((dom f) /\ (dom f))) \ ((f (#) (f (#) f)) " {0}) is V84() V85() V86() set
(Z /\ (dom f)) \ ((f (#) (f (#) f)) " {0}) is V84() V85() V86() set
Z \ ((f (#) (f (#) f)) " {0}) is V84() V85() V86() set
Z \ (f " {0}) is V84() V85() V86() set
(- sin) + cos is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((- sin) + cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (exp_R (#) ((- sin) + cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
Z is open V84() V85() V86() Element of K6(REAL)
diff ((exp_R (#) sin),Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff ((exp_R (#) sin),Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (exp_R (#) ((- sin) + cos))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (exp_R,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (exp_R,Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (exp_R,Z)) . 3) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (exp_R,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((diff (exp_R,Z)) . 2) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) (((diff (exp_R,Z)) . 2) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R `| Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
diff (sin,Z) is V16() V19( NAT ) V20( PFuncs (REAL,REAL)) V21() V30( NAT , PFuncs (REAL,REAL)) Element of K6(K7(NAT,(PFuncs (REAL,REAL))))
(diff (sin,Z)) . 2 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R `| Z) (#) ((diff (sin,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) (((diff (exp_R,Z)) . 2) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((diff (exp_R,Z)) . 3) (#) sin) + ((3 (#) (((diff (exp_R,Z)) . 2) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(diff (sin,Z)) . 3 is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((diff (sin,Z)) . 3) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((diff (exp_R,Z)) . 3) (#) sin) + ((3 (#) (((diff (exp_R,Z)) . 2) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2))))) + (exp_R (#) ((diff (sin,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + ((3 (#) (((diff (exp_R,Z)) . 2) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) (((diff (exp_R,Z)) . 2) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2))))) + (exp_R (#) ((diff (sin,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) (sin `| Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R | Z) (#) (sin `| Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R | Z) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (sin `| Z))) + (3 (#) ((exp_R `| Z) (#) ((diff (sin,Z)) . 2))))) + (exp_R (#) ((diff (sin,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) ((diff (sin,Z)) . 2) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . 2)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R | Z) (#) (sin `| Z))) + (3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . 2))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (sin `| Z))) + (3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . 2)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (sin `| Z))) + (3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . 2))))) + (exp_R (#) ((diff (sin,Z)) . 3)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
cos | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R | Z) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 * 1 is V4() V5() V6() V10() V11() V12() ext-real non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,Z)) . (2 * 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) ((diff (sin,Z)) . (2 * 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . (2 * 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . (2 * 1)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . (2 * 1))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 * 1) + 1 is non empty V4() V5() V6() V10() V11() V12() ext-real positive non negative V48() V84() V85() V86() V87() V88() V89() V91() Element of NAT
(diff (sin,Z)) . ((2 * 1) + 1) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((diff (sin,Z)) . ((2 * 1) + 1)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((diff (sin,Z)) . (2 * 1)))))) + (exp_R (#) ((diff (sin,Z)) . ((2 * 1) + 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
sin | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) |^ 1 is V11() V12() ext-real Element of REAL
((- 1) |^ 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) (((- 1) |^ 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R | Z) (#) (((- 1) |^ 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) (((- 1) |^ 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) (((- 1) |^ 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) (((- 1) |^ 1) (#) (sin | Z)))))) + (exp_R (#) ((diff (sin,Z)) . ((2 * 1) + 1))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) |^ 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) (((- 1) |^ 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) (((- 1) |^ 1) (#) (sin | Z)))))) + (exp_R (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) ((- 1) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z)))))) + (exp_R (#) (((- 1) |^ 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((- 1) (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R | Z) (#) sin) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z)))))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R (#) sin) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((3 (#) ((exp_R | Z) (#) (cos | Z))) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z)))))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R (#) cos) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + (3 (#) ((exp_R | Z) (#) ((- 1) (#) (sin | Z)))))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R | Z) (#) (sin | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((exp_R | Z) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 (#) ((- 1) (#) ((exp_R | Z) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + (3 (#) ((- 1) (#) ((exp_R | Z) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + (3 (#) ((- 1) (#) ((exp_R | Z) (#) (sin | Z))))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + (3 (#) ((- 1) (#) ((exp_R | Z) (#) (sin | Z)))))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 * (- 1) is V11() V12() ext-real V48() Element of REAL
(3 * (- 1)) (#) ((exp_R | Z) (#) (sin | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + ((3 * (- 1)) (#) ((exp_R | Z) (#) (sin | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + ((3 * (- 1)) (#) ((exp_R | Z) (#) (sin | Z)))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + ((3 * (- 1)) (#) ((exp_R | Z) (#) (sin | Z))))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
- 3 is V11() V12() ext-real V48() Element of REAL
(- 3) (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z)))) + (exp_R (#) ((- 1) (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) (cos | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (exp_R (#) (cos | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z)))) + ((- 1) (#) (exp_R (#) (cos | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + ((3 (#) ((exp_R (#) cos) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z)))) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((exp_R (#) sin) | Z) + (3 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((exp_R (#) sin) | Z) + (3 (#) ((exp_R (#) cos) | Z))) + ((- 3) (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((((exp_R (#) sin) | Z) + (3 (#) ((exp_R (#) cos) | Z))) + ((- 3) (#) ((exp_R (#) sin) | Z))) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + (1 (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((3 (#) ((exp_R (#) cos) | Z)) + (1 (#) ((exp_R (#) sin) | Z))) + ((- 3) (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((3 (#) ((exp_R (#) cos) | Z)) + (1 (#) ((exp_R (#) sin) | Z))) + ((- 3) (#) ((exp_R (#) sin) | Z))) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(1 (#) ((exp_R (#) sin) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + ((1 (#) ((exp_R (#) sin) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((3 (#) ((exp_R (#) cos) | Z)) + ((1 (#) ((exp_R (#) sin) | Z)) + ((- 3) (#) ((exp_R (#) sin) | Z)))) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
1 + (- 3) is V11() V12() ext-real V48() Element of REAL
(1 + (- 3)) (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + ((1 + (- 3)) (#) ((exp_R (#) sin) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((3 (#) ((exp_R (#) cos) | Z)) + ((1 + (- 3)) (#) ((exp_R (#) sin) | Z))) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) (#) ((exp_R (#) sin) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(3 (#) ((exp_R (#) cos) | Z)) + ((- 1) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 2) (#) ((exp_R (#) sin) | Z)) + ((3 (#) ((exp_R (#) cos) | Z)) + ((- 1) (#) ((exp_R (#) cos) | Z))) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
3 + (- 1) is V11() V12() ext-real V48() Element of REAL
(3 + (- 1)) (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 2) (#) ((exp_R (#) sin) | Z)) + ((3 + (- 1)) (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 2) (#) (exp_R (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 2) (#) (exp_R (#) sin)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R (#) cos) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 2) (#) (exp_R (#) sin)) | Z) + (2 (#) ((exp_R (#) cos) | Z)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (exp_R (#) cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (exp_R (#) cos)) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((- 2) (#) (exp_R (#) sin)) | Z) + ((2 (#) (exp_R (#) cos)) | Z) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 * (- 1) is V11() V12() ext-real V48() Element of REAL
(2 * (- 1)) (#) (exp_R (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((2 * (- 1)) (#) (exp_R (#) sin)) + (2 (#) (exp_R (#) cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(((2 * (- 1)) (#) (exp_R (#) sin)) + (2 (#) (exp_R (#) cos))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) (exp_R (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((- 1) (#) (exp_R (#) sin)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((- 1) (#) (exp_R (#) sin))) + (2 (#) (exp_R (#) cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((2 (#) ((- 1) (#) (exp_R (#) sin))) + (2 (#) (exp_R (#) cos))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
((- 1) (#) (exp_R (#) sin)) + (exp_R (#) cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) (((- 1) (#) (exp_R (#) sin)) + (exp_R (#) cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) (((- 1) (#) (exp_R (#) sin)) + (exp_R (#) cos))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(- 1) (#) sin is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
exp_R (#) ((- 1) (#) sin) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(exp_R (#) ((- 1) (#) sin)) + (exp_R (#) cos) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
2 (#) ((exp_R (#) ((- 1) (#) sin)) + (exp_R (#) cos)) is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))
(2 (#) ((exp_R (#) ((- 1) (#) sin)) + (exp_R (#) cos))) | Z is V16() V19( REAL ) V20( REAL ) V21() V74() V75() V76() Element of K6(K7(REAL,REAL))