:: INTEGR11 semantic presentation

REAL is non empty V51() V52() V53() V57() V62() set
NAT is non empty V21() V22() V23() V51() V52() V53() V54() V55() V56() V57() Element of K19(REAL)
K19(REAL) is set
COMPLEX is non empty V51() V57() V62() set
K20(NAT,REAL) is Relation-like V34() V35() V36() set
K19(K20(NAT,REAL)) is set
K20(NAT,COMPLEX) is Relation-like V34() set
K19(K20(NAT,COMPLEX)) is set
K20(COMPLEX,COMPLEX) is Relation-like V34() set
K19(K20(COMPLEX,COMPLEX)) is set
K20(REAL,REAL) is Relation-like V34() V35() V36() set
K19(K20(REAL,REAL)) is set
PFuncs (REAL,REAL) is set
K20(NAT,(PFuncs (REAL,REAL))) is Relation-like set
K19(K20(NAT,(PFuncs (REAL,REAL)))) is set
ExtREAL is non empty V52() set
RAT is non empty V51() V52() V53() V54() V57() V62() set
INT is non empty V51() V52() V53() V54() V55() V57() V62() set
NAT is non empty V21() V22() V23() V51() V52() V53() V54() V55() V56() V57() set
K19(NAT) is set
K19(NAT) is set
K20(COMPLEX,REAL) is Relation-like V34() V35() V36() set
K19(K20(COMPLEX,REAL)) is set
{} is set
the Relation-like non-empty empty-yielding RAT -valued empty V21() V22() V23() V25() V26() V27() V29() V30() non negative V34() V35() V36() V37() V51() V52() V53() V54() V55() V56() V57() set is Relation-like non-empty empty-yielding RAT -valued empty V21() V22() V23() V25() V26() V27() V29() V30() non negative V34() V35() V36() V37() V51() V52() V53() V54() V55() V56() V57() set
1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
{{},1} is set
0 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
tan is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin / cos is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom tan is set
cot is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
cos / sin is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom cot is set
K405(REAL,sin) is non empty V51() V52() V53() Element of K19(REAL)
K405(REAL,cos) is non empty V51() V52() V53() Element of K19(REAL)
cos . 0 is V28() V29() ext-real Element of REAL
sin . 0 is V28() V29() ext-real Element of REAL
cos 0 is V28() V29() ext-real Element of REAL
sin 0 is V28() V29() ext-real Element of REAL
PI is V28() V29() ext-real Element of REAL
2 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
PI / 2 is V28() V29() ext-real Element of REAL
cos . (PI / 2) is V28() V29() ext-real Element of REAL
sin . (PI / 2) is V28() V29() ext-real Element of REAL
cos . PI is V28() V29() ext-real Element of REAL
- 1 is V28() V29() V30() ext-real Element of REAL
sin . PI is V28() V29() ext-real Element of REAL
PI + (PI / 2) is V28() V29() ext-real Element of REAL
cos . (PI + (PI / 2)) is V28() V29() ext-real Element of REAL
sin . (PI + (PI / 2)) is V28() V29() ext-real Element of REAL
2 * PI is V28() V29() ext-real Element of REAL
cos . (2 * PI) is V28() V29() ext-real Element of REAL
sin . (2 * PI) is V28() V29() ext-real Element of REAL
cos ^ is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
sin ^ is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
ln is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
ln * sin is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (ln * sin) is set
sinh is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
cosh is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
arcsin is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
#Z 2 is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z 2) * arcsin is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / 2 is V28() V29() ext-real Element of REAL
(1 / 2) (#) ((#Z 2) * arcsin) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
K405(REAL,((1 / 2) (#) ((#Z 2) * arcsin))) is V51() V52() V53() Element of K19(REAL)
].(- 1),1.[ is V51() V52() V53() open Element of K19(REAL)
arccos is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(#Z 2) * arccos is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(1 / 2) (#) ((#Z 2) * arccos) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
K405(REAL,((1 / 2) (#) ((#Z 2) * arccos))) is V51() V52() V53() Element of K19(REAL)
#R (1 / 2) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
K405(REAL,tan) is V51() V52() V53() Element of K19(REAL)
K405(REAL,cot) is V51() V52() V53() Element of K19(REAL)
sec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
K405(REAL,sec) is V51() V52() V53() Element of K19(REAL)
cosec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
K405(REAL,cosec) is V51() V52() V53() Element of K19(REAL)
- cosec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
K98(1) is V28() V29() V30() set
K98(1) (#) cosec is Relation-like V6() V34() V35() V36() set
arctan is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
[.(- 1),1.] is non empty V51() V52() V53() closed Element of K19(REAL)
arctan | [.(- 1),1.] is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
arccot is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
arccot | [.(- 1),1.] is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
[#] REAL is V51() V52() V53() closed open Element of K19(REAL)
AffineMap ((1 / 2),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
dom (AffineMap ((1 / 2),0)) is non empty set
AffineMap (2,0) is Relation-like V6() V7() non empty total V18( REAL , REAL ) V19( REAL ) V20( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (2,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
dom (sin * (AffineMap (2,0))) is non empty set
4 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
1 / 4 is V28() V29() ext-real Element of REAL
(1 / 4) (#) (sin * (AffineMap (2,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
dom ((1 / 4) (#) (sin * (AffineMap (2,0)))) is non empty set
(AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
- ((1 / 4) (#) (sin * (AffineMap (2,0)))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((1 / 4) (#) (sin * (AffineMap (2,0)))) is Relation-like V6() V34() V35() V36() set
(AffineMap ((1 / 2),0)) + (- ((1 / 4) (#) (sin * (AffineMap (2,0))))) is Relation-like V6() V34() V35() V36() set
((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . A is V28() V29() ext-real Element of REAL
2 * A is V28() V29() ext-real Element of REAL
(2 * A) + 0 is V28() V29() ext-real Element of REAL
dom ((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) is non empty set
A is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . A is V28() V29() ext-real Element of REAL
(1 / 2) * A is V28() V29() ext-real Element of REAL
((1 / 2) * A) + 0 is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V28() V29() ext-real Element of REAL
(((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL) . A is V28() V29() ext-real Element of REAL
2 * A is V28() V29() ext-real Element of REAL
cos (2 * A) is V28() V29() ext-real Element of REAL
cos . (2 * A) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos (2 * A)) is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap (2,0))),A) is V28() V29() ext-real Element of REAL
(1 / 4) * (diff ((sin * (AffineMap (2,0))),A)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap (2,0))) `| REAL) . A is V28() V29() ext-real Element of REAL
(1 / 4) * (((sin * (AffineMap (2,0))) `| REAL) . A) is V28() V29() ext-real Element of REAL
(2 * A) + 0 is V28() V29() ext-real Element of REAL
cos . ((2 * A) + 0) is V28() V29() ext-real Element of REAL
2 * (cos . ((2 * A) + 0)) is V28() V29() ext-real Element of REAL
(1 / 4) * (2 * (cos . ((2 * A) + 0))) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) . A is V28() V29() ext-real Element of REAL
sin . A is V28() V29() ext-real Element of REAL
(sin . A) ^2 is V28() V29() ext-real Element of REAL
K97((sin . A),(sin . A)) is set
diff ((AffineMap ((1 / 2),0)),A) is V28() V29() ext-real Element of REAL
diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A) is V28() V29() ext-real Element of REAL
(diff ((AffineMap ((1 / 2),0)),A)) - (diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A)) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap ((1 / 2),0)) `| REAL) . A is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) `| REAL) . A) - (diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A)) is V28() V29() ext-real Element of REAL
(1 / 2) - (diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A)) is V28() V29() ext-real Element of REAL
(((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL) . A is V28() V29() ext-real Element of REAL
(1 / 2) - ((((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL) . A) is V28() V29() ext-real Element of REAL
2 * A is V28() V29() ext-real Element of REAL
cos (2 * A) is V28() V29() ext-real Element of REAL
cos . (2 * A) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos (2 * A)) is V28() V29() ext-real Element of REAL
(1 / 2) - ((1 / 2) * (cos (2 * A))) is V28() V29() ext-real Element of REAL
1 - (cos (2 * A)) is V28() V29() ext-real Element of REAL
(1 - (cos (2 * A))) / 2 is V28() V29() ext-real Element of REAL
sin A is V28() V29() ext-real Element of REAL
(sin A) ^2 is V28() V29() ext-real Element of REAL
K97((sin A),(sin A)) is set
A is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) . A is V28() V29() ext-real Element of REAL
sin . A is V28() V29() ext-real Element of REAL
(sin . A) ^2 is V28() V29() ext-real Element of REAL
K97((sin . A),(sin . A)) is set
(AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . A is V28() V29() ext-real Element of REAL
2 * A is V28() V29() ext-real Element of REAL
(2 * A) + 0 is V28() V29() ext-real Element of REAL
dom ((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) is non empty set
A is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . A is V28() V29() ext-real Element of REAL
(1 / 2) * A is V28() V29() ext-real Element of REAL
((1 / 2) * A) + 0 is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V28() V29() ext-real Element of REAL
(((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL) . A is V28() V29() ext-real Element of REAL
2 * A is V28() V29() ext-real Element of REAL
cos (2 * A) is V28() V29() ext-real Element of REAL
cos . (2 * A) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos (2 * A)) is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap (2,0))),A) is V28() V29() ext-real Element of REAL
(1 / 4) * (diff ((sin * (AffineMap (2,0))),A)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap (2,0))) `| REAL) . A is V28() V29() ext-real Element of REAL
(1 / 4) * (((sin * (AffineMap (2,0))) `| REAL) . A) is V28() V29() ext-real Element of REAL
(2 * A) + 0 is V28() V29() ext-real Element of REAL
cos . ((2 * A) + 0) is V28() V29() ext-real Element of REAL
2 * (cos . ((2 * A) + 0)) is V28() V29() ext-real Element of REAL
(1 / 4) * (2 * (cos . ((2 * A) + 0))) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) . A is V28() V29() ext-real Element of REAL
cos . A is V28() V29() ext-real Element of REAL
(cos . A) ^2 is V28() V29() ext-real Element of REAL
K97((cos . A),(cos . A)) is set
diff ((AffineMap ((1 / 2),0)),A) is V28() V29() ext-real Element of REAL
diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A) is V28() V29() ext-real Element of REAL
(diff ((AffineMap ((1 / 2),0)),A)) + (diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A)) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap ((1 / 2),0)) `| REAL) . A is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) `| REAL) . A) + (diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A)) is V28() V29() ext-real Element of REAL
(1 / 2) + (diff (((1 / 4) (#) (sin * (AffineMap (2,0)))),A)) is V28() V29() ext-real Element of REAL
(((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL) . A is V28() V29() ext-real Element of REAL
(1 / 2) + ((((1 / 4) (#) (sin * (AffineMap (2,0)))) `| REAL) . A) is V28() V29() ext-real Element of REAL
2 * A is V28() V29() ext-real Element of REAL
cos (2 * A) is V28() V29() ext-real Element of REAL
cos . (2 * A) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos (2 * A)) is V28() V29() ext-real Element of REAL
(1 / 2) + ((1 / 2) * (cos (2 * A))) is V28() V29() ext-real Element of REAL
1 + (cos (2 * A)) is V28() V29() ext-real Element of REAL
(1 + (cos (2 * A))) / 2 is V28() V29() ext-real Element of REAL
cos A is V28() V29() ext-real Element of REAL
(cos A) ^2 is V28() V29() ext-real Element of REAL
K97((cos A),(cos A)) is set
A is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) . A is V28() V29() ext-real Element of REAL
cos . A is V28() V29() ext-real Element of REAL
(cos . A) ^2 is V28() V29() ext-real Element of REAL
K97((cos . A),(cos . A)) is set
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) (#) ((#Z (A + 1)) * sin) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) is non empty set
Z is V28() V29() ext-real Element of REAL
dom ((#Z (A + 1)) * sin) is non empty set
Z is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * sin) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(((#Z (A + 1)) * sin) `| REAL) . f2 is V28() V29() ext-real Element of REAL
sin . f2 is V28() V29() ext-real Element of REAL
(sin . f2) #Z A is V28() V29() ext-real Element of REAL
(A + 1) * ((sin . f2) #Z A) is V28() V29() ext-real Element of REAL
cos . f2 is V28() V29() ext-real Element of REAL
((A + 1) * ((sin . f2) #Z A)) * (cos . f2) is V28() V29() ext-real Element of REAL
diff (((#Z (A + 1)) * sin),f2) is V28() V29() ext-real Element of REAL
(A + 1) - 1 is V28() V29() V30() ext-real Element of REAL
(sin . f2) #Z ((A + 1) - 1) is V28() V29() ext-real Element of REAL
(A + 1) * ((sin . f2) #Z ((A + 1) - 1)) is V28() V29() ext-real Element of REAL
diff (sin,f2) is V28() V29() ext-real Element of REAL
((A + 1) * ((sin . f2) #Z ((A + 1) - 1))) * (diff (sin,f2)) is V28() V29() ext-real Element of REAL
((A + 1) * ((sin . f2) #Z ((A + 1) - 1))) * (cos . f2) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) `| REAL) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) #Z A is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
((sin . Z) #Z A) * (cos . Z) is V28() V29() ext-real Element of REAL
diff (((#Z (A + 1)) * sin),Z) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (diff (((#Z (A + 1)) * sin),Z)) is V28() V29() ext-real Element of REAL
(((#Z (A + 1)) * sin) `| REAL) . Z is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * ((((#Z (A + 1)) * sin) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(A + 1) * ((sin . Z) #Z A) is V28() V29() ext-real Element of REAL
((A + 1) * ((sin . Z) #Z A)) * (cos . Z) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (((A + 1) * ((sin . Z) #Z A)) * (cos . Z)) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (A + 1) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * (A + 1)) * ((sin . Z) #Z A) is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) * (A + 1)) * ((sin . Z) #Z A)) * (cos . Z) is V28() V29() ext-real Element of REAL
(A + 1) / (A + 1) is V28() V29() ext-real Element of REAL
((A + 1) / (A + 1)) * ((sin . Z) #Z A) is V28() V29() ext-real Element of REAL
(((A + 1) / (A + 1)) * ((sin . Z) #Z A)) * (cos . Z) is V28() V29() ext-real Element of REAL
1 * ((sin . Z) #Z A) is V28() V29() ext-real Element of REAL
(1 * ((sin . Z) #Z A)) * (cos . Z) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) `| REAL) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) #Z A is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
((sin . Z) #Z A) * (cos . Z) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
- (1 / (A + 1)) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) is non empty set
Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
dom (#Z (A + 1)) is non empty set
dom ((#Z (A + 1)) * cos) is non empty set
((#Z (A + 1)) * cos) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- (A + 1) is V28() V29() V30() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(((#Z (A + 1)) * cos) `| REAL) . f2 is V28() V29() ext-real Element of REAL
cos . f2 is V28() V29() ext-real Element of REAL
(cos . f2) #Z A is V28() V29() ext-real Element of REAL
(- (A + 1)) * ((cos . f2) #Z A) is V28() V29() ext-real Element of REAL
sin . f2 is V28() V29() ext-real Element of REAL
((- (A + 1)) * ((cos . f2) #Z A)) * (sin . f2) is V28() V29() ext-real Element of REAL
diff (((#Z (A + 1)) * cos),f2) is V28() V29() ext-real Element of REAL
(A + 1) - 1 is V28() V29() V30() ext-real Element of REAL
(cos . f2) #Z ((A + 1) - 1) is V28() V29() ext-real Element of REAL
(A + 1) * ((cos . f2) #Z ((A + 1) - 1)) is V28() V29() ext-real Element of REAL
diff (cos,f2) is V28() V29() ext-real Element of REAL
((A + 1) * ((cos . f2) #Z ((A + 1) - 1))) * (diff (cos,f2)) is V28() V29() ext-real Element of REAL
- (sin . f2) is V28() V29() ext-real Element of REAL
((A + 1) * ((cos . f2) #Z ((A + 1) - 1))) * (- (sin . f2)) is V28() V29() ext-real Element of REAL
(- (A + 1)) * ((cos . f2) #Z ((A + 1) - 1)) is V28() V29() ext-real Element of REAL
((- (A + 1)) * ((cos . f2) #Z ((A + 1) - 1))) * (sin . f2) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) `| REAL) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) #Z A is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
((cos . Z) #Z A) * (sin . Z) is V28() V29() ext-real Element of REAL
diff (((#Z (A + 1)) * cos),Z) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * (diff (((#Z (A + 1)) * cos),Z)) is V28() V29() ext-real Element of REAL
(((#Z (A + 1)) * cos) `| REAL) . Z is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * ((((#Z (A + 1)) * cos) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(- (A + 1)) * ((cos . Z) #Z A) is V28() V29() ext-real Element of REAL
((- (A + 1)) * ((cos . Z) #Z A)) * (sin . Z) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * (((- (A + 1)) * ((cos . Z) #Z A)) * (sin . Z)) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (A + 1) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * (A + 1)) * ((cos . Z) #Z A) is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) * (A + 1)) * ((cos . Z) #Z A)) * (sin . Z) is V28() V29() ext-real Element of REAL
(A + 1) / (A + 1) is V28() V29() ext-real Element of REAL
((A + 1) / (A + 1)) * ((cos . Z) #Z A) is V28() V29() ext-real Element of REAL
(((A + 1) / (A + 1)) * ((cos . Z) #Z A)) * (sin . Z) is V28() V29() ext-real Element of REAL
1 * ((cos . Z) #Z A) is V28() V29() ext-real Element of REAL
(1 * ((cos . Z) #Z A)) * (sin . Z) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) `| REAL) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) #Z A is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
((cos . Z) #Z A) * (sin . Z) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A - Z is V28() V29() V30() ext-real Element of REAL
AffineMap ((A + Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A + Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
AffineMap ((A - Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A - Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A - Z) is V28() V29() V30() ext-real Element of REAL
1 / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (sin * (AffineMap ((A - Z),0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap ((A - Z),0)) . f2 is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
((A - Z) * f2) + 0 is V28() V29() ext-real Element of REAL
dom ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) is non empty set
((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A - Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap ((A - Z),0))),f2) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * (diff ((sin * (AffineMap ((A - Z),0))),f2)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap ((A - Z),0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap ((A - Z),0))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * (((sin * (AffineMap ((A - Z),0))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
((A - Z) * f2) + 0 is V28() V29() ext-real Element of REAL
cos . (((A - Z) * f2) + 0) is V28() V29() ext-real Element of REAL
(A - Z) * (cos . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * ((A - Z) * (cos . (((A - Z) * f2) + 0))) is V28() V29() ext-real Element of REAL
(A - Z) * (1 / (2 * (A - Z))) is V28() V29() ext-real Element of REAL
((A - Z) * (1 / (2 * (A - Z)))) * (cos . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
1 * (A - Z) is V28() V29() V30() ext-real Element of REAL
(1 * (A - Z)) / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
((1 * (A - Z)) / (2 * (A - Z))) * (cos . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
dom (((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) is non empty set
dom (sin * (AffineMap ((A + Z),0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap ((A + Z),0)) . f2 is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
((A + Z) * f2) + 0 is V28() V29() ext-real Element of REAL
dom ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is non empty set
((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A + Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A + Z) * f2)) is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap ((A + Z),0))),f2) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) * (diff ((sin * (AffineMap ((A + Z),0))),f2)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap ((A + Z),0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap ((A + Z),0))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) * (((sin * (AffineMap ((A + Z),0))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
((A + Z) * f2) + 0 is V28() V29() ext-real Element of REAL
cos . (((A + Z) * f2) + 0) is V28() V29() ext-real Element of REAL
(A + Z) * (cos . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) * ((A + Z) * (cos . (((A + Z) * f2) + 0))) is V28() V29() ext-real Element of REAL
(A + Z) * (1 / (2 * (A + Z))) is V28() V29() ext-real Element of REAL
((A + Z) * (1 / (2 * (A + Z)))) * (cos . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
1 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
(1 * (A + Z)) / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
((1 * (A + Z)) / (2 * (A + Z))) * (cos . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
cos . (A * f2) is V28() V29() ext-real Element of REAL
Z * f2 is V28() V29() ext-real Element of REAL
cos . (Z * f2) is V28() V29() ext-real Element of REAL
(cos . (A * f2)) * (cos . (Z * f2)) is V28() V29() ext-real Element of REAL
diff (((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))),f2) is V28() V29() ext-real Element of REAL
diff (((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))),f2) is V28() V29() ext-real Element of REAL
(diff (((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))),f2)) + (diff (((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))),f2)) is V28() V29() ext-real Element of REAL
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2) + (diff (((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))),f2)) is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2) + ((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A + Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A + Z) * f2)) is V28() V29() ext-real Element of REAL
((1 / 2) * (cos ((A + Z) * f2))) + ((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A - Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
((1 / 2) * (cos ((A + Z) * f2))) + ((1 / 2) * (cos ((A - Z) * f2))) is V28() V29() ext-real Element of REAL
(cos ((A + Z) * f2)) + (cos ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
(1 / 2) * ((cos ((A + Z) * f2)) + (cos ((A - Z) * f2))) is V28() V29() ext-real Element of REAL
((A + Z) * f2) + ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(((A + Z) * f2) + ((A - Z) * f2)) / 2 is V28() V29() ext-real Element of REAL
cos ((((A + Z) * f2) + ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
cos . ((((A + Z) * f2) + ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
((A + Z) * f2) - ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(((A + Z) * f2) - ((A - Z) * f2)) / 2 is V28() V29() ext-real Element of REAL
cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
cos . ((((A + Z) * f2) - ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
(cos ((((A + Z) * f2) + ((A - Z) * f2)) / 2)) * (cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2)) is V28() V29() ext-real Element of REAL
2 * ((cos ((((A + Z) * f2) + ((A - Z) * f2)) / 2)) * (cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2))) is V28() V29() ext-real Element of REAL
(1 / 2) * (2 * ((cos ((((A + Z) * f2) + ((A - Z) * f2)) / 2)) * (cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2)))) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
cos . (A * f2) is V28() V29() ext-real Element of REAL
Z * f2 is V28() V29() ext-real Element of REAL
cos . (Z * f2) is V28() V29() ext-real Element of REAL
(cos . (A * f2)) * (cos . (Z * f2)) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A - Z is V28() V29() V30() ext-real Element of REAL
AffineMap ((A - Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A - Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A - Z) is V28() V29() V30() ext-real Element of REAL
1 / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
AffineMap ((A + Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A + Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
- ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is Relation-like V6() V34() V35() V36() set
((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) + (- ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) is Relation-like V6() V34() V35() V36() set
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) is non empty set
dom (sin * (AffineMap ((A - Z),0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap ((A - Z),0)) . f2 is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
((A - Z) * f2) + 0 is V28() V29() ext-real Element of REAL
((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A - Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap ((A - Z),0))),f2) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * (diff ((sin * (AffineMap ((A - Z),0))),f2)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap ((A - Z),0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap ((A - Z),0))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * (((sin * (AffineMap ((A - Z),0))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
((A - Z) * f2) + 0 is V28() V29() ext-real Element of REAL
cos . (((A - Z) * f2) + 0) is V28() V29() ext-real Element of REAL
(A - Z) * (cos . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * ((A - Z) * (cos . (((A - Z) * f2) + 0))) is V28() V29() ext-real Element of REAL
(A - Z) * (1 / (2 * (A - Z))) is V28() V29() ext-real Element of REAL
((A - Z) * (1 / (2 * (A - Z)))) * (cos . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
1 * (A - Z) is V28() V29() V30() ext-real Element of REAL
(1 * (A - Z)) / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
((1 * (A - Z)) / (2 * (A - Z))) * (cos . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
dom (((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) is non empty set
dom (sin * (AffineMap ((A + Z),0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap ((A + Z),0)) . f2 is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
((A + Z) * f2) + 0 is V28() V29() ext-real Element of REAL
dom ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is non empty set
((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A + Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A + Z) * f2)) is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap ((A + Z),0))),f2) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) * (diff ((sin * (AffineMap ((A + Z),0))),f2)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap ((A + Z),0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap ((A + Z),0))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) * (((sin * (AffineMap ((A + Z),0))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
((A + Z) * f2) + 0 is V28() V29() ext-real Element of REAL
cos . (((A + Z) * f2) + 0) is V28() V29() ext-real Element of REAL
(A + Z) * (cos . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) * ((A + Z) * (cos . (((A + Z) * f2) + 0))) is V28() V29() ext-real Element of REAL
(A + Z) * (1 / (2 * (A + Z))) is V28() V29() ext-real Element of REAL
((A + Z) * (1 / (2 * (A + Z)))) * (cos . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
1 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
(1 * (A + Z)) / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
((1 * (A + Z)) / (2 * (A + Z))) * (cos . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
sin . (A * f2) is V28() V29() ext-real Element of REAL
Z * f2 is V28() V29() ext-real Element of REAL
sin . (Z * f2) is V28() V29() ext-real Element of REAL
(sin . (A * f2)) * (sin . (Z * f2)) is V28() V29() ext-real Element of REAL
diff (((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))),f2) is V28() V29() ext-real Element of REAL
diff (((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))),f2) is V28() V29() ext-real Element of REAL
(diff (((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))),f2)) - (diff (((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))),f2)) is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2) - (diff (((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))),f2)) is V28() V29() ext-real Element of REAL
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) `| REAL) . f2) - ((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A - Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
((1 / 2) * (cos ((A - Z) * f2))) - ((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
cos ((A + Z) * f2) is V28() V29() ext-real Element of REAL
cos . ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (cos ((A + Z) * f2)) is V28() V29() ext-real Element of REAL
((1 / 2) * (cos ((A - Z) * f2))) - ((1 / 2) * (cos ((A + Z) * f2))) is V28() V29() ext-real Element of REAL
(cos ((A - Z) * f2)) - (cos ((A + Z) * f2)) is V28() V29() ext-real Element of REAL
(1 / 2) * ((cos ((A - Z) * f2)) - (cos ((A + Z) * f2))) is V28() V29() ext-real Element of REAL
((A - Z) * f2) + ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(((A - Z) * f2) + ((A + Z) * f2)) / 2 is V28() V29() ext-real Element of REAL
sin ((((A - Z) * f2) + ((A + Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
sin . ((((A - Z) * f2) + ((A + Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
((A - Z) * f2) - ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(((A - Z) * f2) - ((A + Z) * f2)) / 2 is V28() V29() ext-real Element of REAL
sin ((((A - Z) * f2) - ((A + Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
sin . ((((A - Z) * f2) - ((A + Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
(sin ((((A - Z) * f2) + ((A + Z) * f2)) / 2)) * (sin ((((A - Z) * f2) - ((A + Z) * f2)) / 2)) is V28() V29() ext-real Element of REAL
2 * ((sin ((((A - Z) * f2) + ((A + Z) * f2)) / 2)) * (sin ((((A - Z) * f2) - ((A + Z) * f2)) / 2))) is V28() V29() ext-real Element of REAL
- (2 * ((sin ((((A - Z) * f2) + ((A + Z) * f2)) / 2)) * (sin ((((A - Z) * f2) - ((A + Z) * f2)) / 2)))) is V28() V29() ext-real Element of REAL
(1 / 2) * (- (2 * ((sin ((((A - Z) * f2) + ((A + Z) * f2)) / 2)) * (sin ((((A - Z) * f2) - ((A + Z) * f2)) / 2))))) is V28() V29() ext-real Element of REAL
sin (A * f2) is V28() V29() ext-real Element of REAL
- (Z * f2) is V28() V29() ext-real Element of REAL
sin (- (Z * f2)) is V28() V29() ext-real Element of REAL
sin . (- (Z * f2)) is V28() V29() ext-real Element of REAL
(sin (A * f2)) * (sin (- (Z * f2))) is V28() V29() ext-real Element of REAL
2 * ((sin (A * f2)) * (sin (- (Z * f2)))) is V28() V29() ext-real Element of REAL
- (2 * ((sin (A * f2)) * (sin (- (Z * f2))))) is V28() V29() ext-real Element of REAL
(1 / 2) * (- (2 * ((sin (A * f2)) * (sin (- (Z * f2)))))) is V28() V29() ext-real Element of REAL
sin (Z * f2) is V28() V29() ext-real Element of REAL
- (sin (Z * f2)) is V28() V29() ext-real Element of REAL
(sin (A * f2)) * (- (sin (Z * f2))) is V28() V29() ext-real Element of REAL
2 * ((sin (A * f2)) * (- (sin (Z * f2)))) is V28() V29() ext-real Element of REAL
- (2 * ((sin (A * f2)) * (- (sin (Z * f2))))) is V28() V29() ext-real Element of REAL
(1 / 2) * (- (2 * ((sin (A * f2)) * (- (sin (Z * f2)))))) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
sin . (A * f2) is V28() V29() ext-real Element of REAL
Z * f2 is V28() V29() ext-real Element of REAL
sin . (Z * f2) is V28() V29() ext-real Element of REAL
(sin . (A * f2)) * (sin . (Z * f2)) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A - Z is V28() V29() V30() ext-real Element of REAL
AffineMap ((A + Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap ((A + Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
K98(1) (#) ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) is Relation-like V6() V34() V35() V36() set
AffineMap ((A - Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap ((A - Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A - Z) is V28() V29() V30() ext-real Element of REAL
1 / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
- ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) is Relation-like V6() V34() V35() V36() set
(- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) + (- ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) is Relation-like V6() V34() V35() V36() set
((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (cos * (AffineMap ((A + Z),0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap ((A + Z),0)) . f2 is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
((A + Z) * f2) + 0 is V28() V29() ext-real Element of REAL
(- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
sin ((A + Z) * f2) is V28() V29() ext-real Element of REAL
sin . ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (sin ((A + Z) * f2)) is V28() V29() ext-real Element of REAL
(- 1) / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
((- 1) / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
dom (((- 1) / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) is non empty set
(- 1) * (1 / (2 * (A + Z))) is V28() V29() ext-real Element of REAL
((- 1) * (1 / (2 * (A + Z)))) (#) (cos * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(((- 1) * (1 / (2 * (A + Z)))) (#) (cos * (AffineMap ((A + Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((((- 1) * (1 / (2 * (A + Z)))) (#) (cos * (AffineMap ((A + Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
- (1 / (2 * (A + Z))) is V28() V29() ext-real Element of REAL
(- (1 / (2 * (A + Z)))) (#) (cos * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((- (1 / (2 * (A + Z)))) (#) (cos * (AffineMap ((A + Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((- (1 / (2 * (A + Z)))) (#) (cos * (AffineMap ((A + Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(((- 1) / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((((- 1) / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
diff ((cos * (AffineMap ((A + Z),0))),f2) is V28() V29() ext-real Element of REAL
((- 1) / (2 * (A + Z))) * (diff ((cos * (AffineMap ((A + Z),0))),f2)) is V28() V29() ext-real Element of REAL
(cos * (AffineMap ((A + Z),0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((cos * (AffineMap ((A + Z),0))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
((- 1) / (2 * (A + Z))) * (((cos * (AffineMap ((A + Z),0))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
((A + Z) * f2) + 0 is V28() V29() ext-real Element of REAL
sin . (((A + Z) * f2) + 0) is V28() V29() ext-real Element of REAL
(A + Z) * (sin . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
- ((A + Z) * (sin . (((A + Z) * f2) + 0))) is V28() V29() ext-real Element of REAL
((- 1) / (2 * (A + Z))) * (- ((A + Z) * (sin . (((A + Z) * f2) + 0)))) is V28() V29() ext-real Element of REAL
- ((- 1) / (2 * (A + Z))) is V28() V29() ext-real Element of REAL
(- ((- 1) / (2 * (A + Z)))) * (A + Z) is V28() V29() ext-real Element of REAL
((- ((- 1) / (2 * (A + Z)))) * (A + Z)) * (sin . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) * (A + Z) is V28() V29() ext-real Element of REAL
((1 / (2 * (A + Z))) * (A + Z)) * (sin . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
1 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
(1 * (A + Z)) / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
((1 * (A + Z)) / (2 * (A + Z))) * (sin . (((A + Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
dom (- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) is non empty set
dom ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) is non empty set
(- 1) (#) ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
dom ((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) is non empty set
dom (cos * (AffineMap ((A - Z),0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap ((A - Z),0)) . f2 is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
((A - Z) * f2) + 0 is V28() V29() ext-real Element of REAL
dom ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) is non empty set
((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
sin ((A - Z) * f2) is V28() V29() ext-real Element of REAL
sin . ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (sin ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
- ((1 / 2) * (sin ((A - Z) * f2))) is V28() V29() ext-real Element of REAL
diff ((cos * (AffineMap ((A - Z),0))),f2) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * (diff ((cos * (AffineMap ((A - Z),0))),f2)) is V28() V29() ext-real Element of REAL
(cos * (AffineMap ((A - Z),0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((cos * (AffineMap ((A - Z),0))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * (((cos * (AffineMap ((A - Z),0))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
((A - Z) * f2) + 0 is V28() V29() ext-real Element of REAL
sin . (((A - Z) * f2) + 0) is V28() V29() ext-real Element of REAL
(A - Z) * (sin . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
- ((A - Z) * (sin . (((A - Z) * f2) + 0))) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) * (- ((A - Z) * (sin . (((A - Z) * f2) + 0)))) is V28() V29() ext-real Element of REAL
- (1 / (2 * (A - Z))) is V28() V29() ext-real Element of REAL
(- (1 / (2 * (A - Z)))) * (A - Z) is V28() V29() ext-real Element of REAL
((- (1 / (2 * (A - Z)))) * (A - Z)) * (sin . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(- 1) / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
((- 1) / (2 * (A - Z))) * (A - Z) is V28() V29() ext-real Element of REAL
(((- 1) / (2 * (A - Z))) * (A - Z)) * (sin . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(- 1) * (A - Z) is V28() V29() V30() ext-real Element of REAL
((- 1) * (A - Z)) / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
(((- 1) * (A - Z)) / (2 * (A - Z))) * (sin . (((A - Z) * f2) + 0)) is V28() V29() ext-real Element of REAL
(- 1) / 2 is V28() V29() ext-real Element of REAL
((- 1) / 2) * (sin ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
sin . (A * f2) is V28() V29() ext-real Element of REAL
Z * f2 is V28() V29() ext-real Element of REAL
cos . (Z * f2) is V28() V29() ext-real Element of REAL
(sin . (A * f2)) * (cos . (Z * f2)) is V28() V29() ext-real Element of REAL
diff ((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))),f2) is V28() V29() ext-real Element of REAL
diff (((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))),f2) is V28() V29() ext-real Element of REAL
(diff ((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))),f2)) - (diff (((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))),f2)) is V28() V29() ext-real Element of REAL
((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) `| REAL) . f2) - (diff (((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))),f2)) is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) `| REAL) . f2) - ((((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
(A + Z) * f2 is V28() V29() ext-real Element of REAL
sin ((A + Z) * f2) is V28() V29() ext-real Element of REAL
sin . ((A + Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (sin ((A + Z) * f2)) is V28() V29() ext-real Element of REAL
((1 / 2) * (sin ((A + Z) * f2))) - ((((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) `| REAL) . f2) is V28() V29() ext-real Element of REAL
(A - Z) * f2 is V28() V29() ext-real Element of REAL
sin ((A - Z) * f2) is V28() V29() ext-real Element of REAL
sin . ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (sin ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
- ((1 / 2) * (sin ((A - Z) * f2))) is V28() V29() ext-real Element of REAL
((1 / 2) * (sin ((A + Z) * f2))) - (- ((1 / 2) * (sin ((A - Z) * f2)))) is V28() V29() ext-real Element of REAL
(sin ((A + Z) * f2)) + (sin ((A - Z) * f2)) is V28() V29() ext-real Element of REAL
(1 / 2) * ((sin ((A + Z) * f2)) + (sin ((A - Z) * f2))) is V28() V29() ext-real Element of REAL
((A + Z) * f2) - ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(((A + Z) * f2) - ((A - Z) * f2)) / 2 is V28() V29() ext-real Element of REAL
cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
cos . ((((A + Z) * f2) - ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
((A + Z) * f2) + ((A - Z) * f2) is V28() V29() ext-real Element of REAL
(((A + Z) * f2) + ((A - Z) * f2)) / 2 is V28() V29() ext-real Element of REAL
sin ((((A + Z) * f2) + ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
sin . ((((A + Z) * f2) + ((A - Z) * f2)) / 2) is V28() V29() ext-real Element of REAL
(cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2)) * (sin ((((A + Z) * f2) + ((A - Z) * f2)) / 2)) is V28() V29() ext-real Element of REAL
2 * ((cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2)) * (sin ((((A + Z) * f2) + ((A - Z) * f2)) / 2))) is V28() V29() ext-real Element of REAL
(1 / 2) * (2 * ((cos ((((A + Z) * f2) - ((A - Z) * f2)) / 2)) * (sin ((((A + Z) * f2) + ((A - Z) * f2)) / 2)))) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
sin . (A * f2) is V28() V29() ext-real Element of REAL
Z * f2 is V28() V29() ext-real Element of REAL
cos . (Z * f2) is V28() V29() ext-real Element of REAL
(sin . (A * f2)) * (cos . (Z * f2)) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
AffineMap (A,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A ^2 is V28() V29() ext-real Element of REAL
K97(A,A) is V21() V22() V23() V27() V29() V30() non negative set
1 / (A ^2) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) (#) (sin * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
1 / A is V28() V29() ext-real Element of REAL
AffineMap ((1 / A),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
- ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) is Relation-like V6() V34() V35() V36() set
((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) + (- ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) is Relation-like V6() V34() V35() V36() set
(((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) is non empty set
dom (AffineMap ((1 / A),0)) is non empty set
Z is V28() V29() ext-real Element of REAL
(AffineMap ((1 / A),0)) . Z is V28() V29() ext-real Element of REAL
(1 / A) * Z is V28() V29() ext-real Element of REAL
((1 / A) * Z) + 0 is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
(A * Z) + 0 is V28() V29() ext-real Element of REAL
dom (sin * (AffineMap (A,0))) is non empty set
dom ((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) is non empty set
((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
cos (A * Z) is V28() V29() ext-real Element of REAL
cos . (A * Z) is V28() V29() ext-real Element of REAL
(1 / A) * (cos (A * Z)) is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap (A,0))),Z) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) * (diff ((sin * (AffineMap (A,0))),Z)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (A,0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap (A,0))) `| REAL) . Z is V28() V29() ext-real Element of REAL
(1 / (A ^2)) * (((sin * (AffineMap (A,0))) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(A * Z) + 0 is V28() V29() ext-real Element of REAL
cos . ((A * Z) + 0) is V28() V29() ext-real Element of REAL
A * (cos . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) * (A * (cos . ((A * Z) + 0))) is V28() V29() ext-real Element of REAL
A * A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (A * A) is V28() V29() ext-real Element of REAL
A * (1 / (A * A)) is V28() V29() ext-real Element of REAL
(A * (1 / (A * A))) * (cos . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
A * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
(A * 1) / (A * A) is V28() V29() ext-real Element of REAL
((A * 1) / (A * A)) * (cos . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
(1 / A) * (cos . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
dom (cos * (AffineMap (A,0))) is non empty set
dom ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) is non empty set
((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
cos . (A * Z) is V28() V29() ext-real Element of REAL
(1 / A) * (cos . (A * Z)) is V28() V29() ext-real Element of REAL
sin . (A * Z) is V28() V29() ext-real Element of REAL
Z * (sin . (A * Z)) is V28() V29() ext-real Element of REAL
((1 / A) * (cos . (A * Z))) - (Z * (sin . (A * Z))) is V28() V29() ext-real Element of REAL
(cos * (AffineMap (A,0))) . Z is V28() V29() ext-real Element of REAL
diff ((AffineMap ((1 / A),0)),Z) is V28() V29() ext-real Element of REAL
((cos * (AffineMap (A,0))) . Z) * (diff ((AffineMap ((1 / A),0)),Z)) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / A),0)) . Z is V28() V29() ext-real Element of REAL
diff ((cos * (AffineMap (A,0))),Z) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / A),0)) . Z) * (diff ((cos * (AffineMap (A,0))),Z)) is V28() V29() ext-real Element of REAL
(((cos * (AffineMap (A,0))) . Z) * (diff ((AffineMap ((1 / A),0)),Z))) + (((AffineMap ((1 / A),0)) . Z) * (diff ((cos * (AffineMap (A,0))),Z))) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / A),0)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap ((1 / A),0)) `| REAL) . Z is V28() V29() ext-real Element of REAL
((cos * (AffineMap (A,0))) . Z) * (((AffineMap ((1 / A),0)) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(((cos * (AffineMap (A,0))) . Z) * (((AffineMap ((1 / A),0)) `| REAL) . Z)) + (((AffineMap ((1 / A),0)) . Z) * (diff ((cos * (AffineMap (A,0))),Z))) is V28() V29() ext-real Element of REAL
((cos * (AffineMap (A,0))) . Z) * (1 / A) is V28() V29() ext-real Element of REAL
(((cos * (AffineMap (A,0))) . Z) * (1 / A)) + (((AffineMap ((1 / A),0)) . Z) * (diff ((cos * (AffineMap (A,0))),Z))) is V28() V29() ext-real Element of REAL
(cos * (AffineMap (A,0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((cos * (AffineMap (A,0))) `| REAL) . Z is V28() V29() ext-real Element of REAL
((AffineMap ((1 / A),0)) . Z) * (((cos * (AffineMap (A,0))) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(((cos * (AffineMap (A,0))) . Z) * (1 / A)) + (((AffineMap ((1 / A),0)) . Z) * (((cos * (AffineMap (A,0))) `| REAL) . Z)) is V28() V29() ext-real Element of REAL
(A * Z) + 0 is V28() V29() ext-real Element of REAL
sin . ((A * Z) + 0) is V28() V29() ext-real Element of REAL
A * (sin . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
- (A * (sin . ((A * Z) + 0))) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / A),0)) . Z) * (- (A * (sin . ((A * Z) + 0)))) is V28() V29() ext-real Element of REAL
(((cos * (AffineMap (A,0))) . Z) * (1 / A)) + (((AffineMap ((1 / A),0)) . Z) * (- (A * (sin . ((A * Z) + 0))))) is V28() V29() ext-real Element of REAL
(1 / A) * Z is V28() V29() ext-real Element of REAL
((1 / A) * Z) + 0 is V28() V29() ext-real Element of REAL
(((1 / A) * Z) + 0) * (- (A * (sin . ((A * Z) + 0)))) is V28() V29() ext-real Element of REAL
(((cos * (AffineMap (A,0))) . Z) * (1 / A)) + ((((1 / A) * Z) + 0) * (- (A * (sin . ((A * Z) + 0))))) is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . Z is V28() V29() ext-real Element of REAL
cos . ((AffineMap (A,0)) . Z) is V28() V29() ext-real Element of REAL
(cos . ((AffineMap (A,0)) . Z)) * (1 / A) is V28() V29() ext-real Element of REAL
((1 / A) * Z) * (- (A * (sin . ((A * Z) + 0)))) is V28() V29() ext-real Element of REAL
((cos . ((AffineMap (A,0)) . Z)) * (1 / A)) + (((1 / A) * Z) * (- (A * (sin . ((A * Z) + 0))))) is V28() V29() ext-real Element of REAL
(1 / A) * A is V28() V29() ext-real Element of REAL
((1 / A) * A) * Z is V28() V29() ext-real Element of REAL
(((1 / A) * A) * Z) * (sin . (A * Z)) is V28() V29() ext-real Element of REAL
- ((((1 / A) * A) * Z) * (sin . (A * Z))) is V28() V29() ext-real Element of REAL
((1 / A) * (cos . (A * Z))) + (- ((((1 / A) * A) * Z) * (sin . (A * Z)))) is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) * (sin . (A * Z)) is V28() V29() ext-real Element of REAL
- ((1 * Z) * (sin . (A * Z))) is V28() V29() ext-real Element of REAL
((1 / A) * (cos . (A * Z))) + (- ((1 * Z) * (sin . (A * Z)))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
sin . (A * Z) is V28() V29() ext-real Element of REAL
Z * (sin . (A * Z)) is V28() V29() ext-real Element of REAL
diff (((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))),Z) is V28() V29() ext-real Element of REAL
diff (((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))),Z) is V28() V29() ext-real Element of REAL
(diff (((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))),Z)) - (diff (((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))),Z)) is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) `| REAL) . Z) - (diff (((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))),Z)) is V28() V29() ext-real Element of REAL
cos (A * Z) is V28() V29() ext-real Element of REAL
cos . (A * Z) is V28() V29() ext-real Element of REAL
(1 / A) * (cos (A * Z)) is V28() V29() ext-real Element of REAL
((1 / A) * (cos (A * Z))) - (diff (((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))),Z)) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
((1 / A) * (cos (A * Z))) - ((((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(1 / A) * (cos . (A * Z)) is V28() V29() ext-real Element of REAL
((1 / A) * (cos . (A * Z))) - (Z * (sin . (A * Z))) is V28() V29() ext-real Element of REAL
((1 / A) * (cos (A * Z))) - (((1 / A) * (cos . (A * Z))) - (Z * (sin . (A * Z)))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
sin . (A * Z) is V28() V29() ext-real Element of REAL
Z * (sin . (A * Z)) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
AffineMap (A,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A ^2 is V28() V29() ext-real Element of REAL
K97(A,A) is V21() V22() V23() V27() V29() V30() non negative set
1 / (A ^2) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) (#) (cos * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
1 / A is V28() V29() ext-real Element of REAL
AffineMap ((1 / A),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) is non empty set
dom (AffineMap ((1 / A),0)) is non empty set
Z is V28() V29() ext-real Element of REAL
(AffineMap ((1 / A),0)) . Z is V28() V29() ext-real Element of REAL
(1 / A) * Z is V28() V29() ext-real Element of REAL
((1 / A) * Z) + 0 is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
(A * Z) + 0 is V28() V29() ext-real Element of REAL
dom (cos * (AffineMap (A,0))) is non empty set
dom ((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) is non empty set
((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
sin (A * Z) is V28() V29() ext-real Element of REAL
sin . (A * Z) is V28() V29() ext-real Element of REAL
(1 / A) * (sin (A * Z)) is V28() V29() ext-real Element of REAL
- ((1 / A) * (sin (A * Z))) is V28() V29() ext-real Element of REAL
diff ((cos * (AffineMap (A,0))),Z) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) * (diff ((cos * (AffineMap (A,0))),Z)) is V28() V29() ext-real Element of REAL
(cos * (AffineMap (A,0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((cos * (AffineMap (A,0))) `| REAL) . Z is V28() V29() ext-real Element of REAL
(1 / (A ^2)) * (((cos * (AffineMap (A,0))) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(A * Z) + 0 is V28() V29() ext-real Element of REAL
sin . ((A * Z) + 0) is V28() V29() ext-real Element of REAL
A * (sin . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
- (A * (sin . ((A * Z) + 0))) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) * (- (A * (sin . ((A * Z) + 0)))) is V28() V29() ext-real Element of REAL
A * A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (A * A) is V28() V29() ext-real Element of REAL
A * (1 / (A * A)) is V28() V29() ext-real Element of REAL
(- 1) * (A * (1 / (A * A))) is V28() V29() ext-real Element of REAL
((- 1) * (A * (1 / (A * A)))) * (sin . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
(A * A) / 1 is V28() V29() ext-real Element of REAL
A / ((A * A) / 1) is V28() V29() ext-real Element of REAL
(- 1) * (A / ((A * A) / 1)) is V28() V29() ext-real Element of REAL
((- 1) * (A / ((A * A) / 1))) * (sin . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
A * 1 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
(A * 1) / (A * A) is V28() V29() ext-real Element of REAL
(- 1) * ((A * 1) / (A * A)) is V28() V29() ext-real Element of REAL
((- 1) * ((A * 1) / (A * A))) * (sin . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
(- 1) * (1 / A) is V28() V29() ext-real Element of REAL
((- 1) * (1 / A)) * (sin . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
dom (sin * (AffineMap (A,0))) is non empty set
dom ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))) is non empty set
((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
sin . (A * Z) is V28() V29() ext-real Element of REAL
(1 / A) * (sin . (A * Z)) is V28() V29() ext-real Element of REAL
cos . (A * Z) is V28() V29() ext-real Element of REAL
Z * (cos . (A * Z)) is V28() V29() ext-real Element of REAL
((1 / A) * (sin . (A * Z))) + (Z * (cos . (A * Z))) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (A,0))) . Z is V28() V29() ext-real Element of REAL
diff ((AffineMap ((1 / A),0)),Z) is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) . Z) * (diff ((AffineMap ((1 / A),0)),Z)) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / A),0)) . Z is V28() V29() ext-real Element of REAL
diff ((sin * (AffineMap (A,0))),Z) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / A),0)) . Z) * (diff ((sin * (AffineMap (A,0))),Z)) is V28() V29() ext-real Element of REAL
(((sin * (AffineMap (A,0))) . Z) * (diff ((AffineMap ((1 / A),0)),Z))) + (((AffineMap ((1 / A),0)) . Z) * (diff ((sin * (AffineMap (A,0))),Z))) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / A),0)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap ((1 / A),0)) `| REAL) . Z is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) . Z) * (((AffineMap ((1 / A),0)) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(((sin * (AffineMap (A,0))) . Z) * (((AffineMap ((1 / A),0)) `| REAL) . Z)) + (((AffineMap ((1 / A),0)) . Z) * (diff ((sin * (AffineMap (A,0))),Z))) is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) . Z) * (1 / A) is V28() V29() ext-real Element of REAL
(((sin * (AffineMap (A,0))) . Z) * (1 / A)) + (((AffineMap ((1 / A),0)) . Z) * (diff ((sin * (AffineMap (A,0))),Z))) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (A,0))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin * (AffineMap (A,0))) `| REAL) . Z is V28() V29() ext-real Element of REAL
((AffineMap ((1 / A),0)) . Z) * (((sin * (AffineMap (A,0))) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(((sin * (AffineMap (A,0))) . Z) * (1 / A)) + (((AffineMap ((1 / A),0)) . Z) * (((sin * (AffineMap (A,0))) `| REAL) . Z)) is V28() V29() ext-real Element of REAL
(A * Z) + 0 is V28() V29() ext-real Element of REAL
cos . ((A * Z) + 0) is V28() V29() ext-real Element of REAL
A * (cos . ((A * Z) + 0)) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / A),0)) . Z) * (A * (cos . ((A * Z) + 0))) is V28() V29() ext-real Element of REAL
(((sin * (AffineMap (A,0))) . Z) * (1 / A)) + (((AffineMap ((1 / A),0)) . Z) * (A * (cos . ((A * Z) + 0)))) is V28() V29() ext-real Element of REAL
(1 / A) * Z is V28() V29() ext-real Element of REAL
((1 / A) * Z) + 0 is V28() V29() ext-real Element of REAL
(((1 / A) * Z) + 0) * (A * (cos . ((A * Z) + 0))) is V28() V29() ext-real Element of REAL
(((sin * (AffineMap (A,0))) . Z) * (1 / A)) + ((((1 / A) * Z) + 0) * (A * (cos . ((A * Z) + 0)))) is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . Z is V28() V29() ext-real Element of REAL
sin . ((AffineMap (A,0)) . Z) is V28() V29() ext-real Element of REAL
(sin . ((AffineMap (A,0)) . Z)) * (1 / A) is V28() V29() ext-real Element of REAL
((1 / A) * Z) * (A * (cos . ((A * Z) + 0))) is V28() V29() ext-real Element of REAL
((sin . ((AffineMap (A,0)) . Z)) * (1 / A)) + (((1 / A) * Z) * (A * (cos . ((A * Z) + 0)))) is V28() V29() ext-real Element of REAL
(1 / A) * A is V28() V29() ext-real Element of REAL
((1 / A) * A) * Z is V28() V29() ext-real Element of REAL
(((1 / A) * A) * Z) * (cos . (A * Z)) is V28() V29() ext-real Element of REAL
((1 / A) * (sin . (A * Z))) + ((((1 / A) * A) * Z) * (cos . (A * Z))) is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) * (cos . (A * Z)) is V28() V29() ext-real Element of REAL
((1 / A) * (sin . (A * Z))) + ((1 * Z) * (cos . (A * Z))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
cos . (A * Z) is V28() V29() ext-real Element of REAL
Z * (cos . (A * Z)) is V28() V29() ext-real Element of REAL
diff (((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))),Z) is V28() V29() ext-real Element of REAL
diff (((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))),Z) is V28() V29() ext-real Element of REAL
(diff (((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))),Z)) + (diff (((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))),Z)) is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) `| REAL) . Z) + (diff (((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))),Z)) is V28() V29() ext-real Element of REAL
sin (A * Z) is V28() V29() ext-real Element of REAL
sin . (A * Z) is V28() V29() ext-real Element of REAL
(1 / A) * (sin (A * Z)) is V28() V29() ext-real Element of REAL
- ((1 / A) * (sin (A * Z))) is V28() V29() ext-real Element of REAL
(- ((1 / A) * (sin (A * Z)))) + (diff (((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))),Z)) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))) `| REAL) . Z is V28() V29() ext-real Element of REAL
(- ((1 / A) * (sin (A * Z)))) + ((((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))) `| REAL) . Z) is V28() V29() ext-real Element of REAL
(1 / A) * (sin . (A * Z)) is V28() V29() ext-real Element of REAL
((1 / A) * (sin . (A * Z))) + (Z * (cos . (A * Z))) is V28() V29() ext-real Element of REAL
(- ((1 / A) * (sin (A * Z)))) + (((1 / A) * (sin . (A * Z))) + (Z * (cos . (A * Z)))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) `| REAL) . Z is V28() V29() ext-real Element of REAL
A * Z is V28() V29() ext-real Element of REAL
cos . (A * Z) is V28() V29() ext-real Element of REAL
Z * (cos . (A * Z)) is V28() V29() ext-real Element of REAL
AffineMap (1,0) is Relation-like V6() V7() non empty total V18( REAL , REAL ) V19( REAL ) V20( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(AffineMap (1,0)) (#) cosh is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap (1,0)) (#) cosh) - sinh is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
- sinh is Relation-like V6() V34() V35() V36() set
K98(1) (#) sinh is Relation-like V6() V34() V35() V36() set
((AffineMap (1,0)) (#) cosh) + (- sinh) is Relation-like V6() V34() V35() V36() set
(((AffineMap (1,0)) (#) cosh) - sinh) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((AffineMap (1,0)) (#) cosh) - sinh) is non empty set
dom (AffineMap (1,0)) is non empty set
A is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . A is V28() V29() ext-real Element of REAL
1 * A is V28() V29() ext-real Element of REAL
(1 * A) + 0 is V28() V29() ext-real Element of REAL
dom ((AffineMap (1,0)) (#) cosh) is non empty set
((AffineMap (1,0)) (#) cosh) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) cosh) `| REAL) . A is V28() V29() ext-real Element of REAL
cosh . A is V28() V29() ext-real Element of REAL
sinh . A is V28() V29() ext-real Element of REAL
A * (sinh . A) is V28() V29() ext-real Element of REAL
(cosh . A) + (A * (sinh . A)) is V28() V29() ext-real Element of REAL
diff ((AffineMap (1,0)),A) is V28() V29() ext-real Element of REAL
(cosh . A) * (diff ((AffineMap (1,0)),A)) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . A is V28() V29() ext-real Element of REAL
diff (cosh,A) is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . A) * (diff (cosh,A)) is V28() V29() ext-real Element of REAL
((cosh . A) * (diff ((AffineMap (1,0)),A))) + (((AffineMap (1,0)) . A) * (diff (cosh,A))) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap (1,0)) `| REAL) . A is V28() V29() ext-real Element of REAL
(cosh . A) * (((AffineMap (1,0)) `| REAL) . A) is V28() V29() ext-real Element of REAL
((cosh . A) * (((AffineMap (1,0)) `| REAL) . A)) + (((AffineMap (1,0)) . A) * (diff (cosh,A))) is V28() V29() ext-real Element of REAL
(cosh . A) * 1 is V28() V29() ext-real Element of REAL
((cosh . A) * 1) + (((AffineMap (1,0)) . A) * (diff (cosh,A))) is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . A) * (sinh . A) is V28() V29() ext-real Element of REAL
(cosh . A) + (((AffineMap (1,0)) . A) * (sinh . A)) is V28() V29() ext-real Element of REAL
1 * A is V28() V29() ext-real Element of REAL
(1 * A) + 0 is V28() V29() ext-real Element of REAL
((1 * A) + 0) * (sinh . A) is V28() V29() ext-real Element of REAL
(cosh . A) + (((1 * A) + 0) * (sinh . A)) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) cosh) - sinh) `| REAL) . A is V28() V29() ext-real Element of REAL
sinh . A is V28() V29() ext-real Element of REAL
A * (sinh . A) is V28() V29() ext-real Element of REAL
diff (((AffineMap (1,0)) (#) cosh),A) is V28() V29() ext-real Element of REAL
diff (sinh,A) is V28() V29() ext-real Element of REAL
(diff (((AffineMap (1,0)) (#) cosh),A)) - (diff (sinh,A)) is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) cosh) `| REAL) . A is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) cosh) `| REAL) . A) - (diff (sinh,A)) is V28() V29() ext-real Element of REAL
cosh . A is V28() V29() ext-real Element of REAL
(cosh . A) + (A * (sinh . A)) is V28() V29() ext-real Element of REAL
((cosh . A) + (A * (sinh . A))) - (diff (sinh,A)) is V28() V29() ext-real Element of REAL
((cosh . A) + (A * (sinh . A))) - (cosh . A) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) cosh) - sinh) `| REAL) . A is V28() V29() ext-real Element of REAL
sinh . A is V28() V29() ext-real Element of REAL
A * (sinh . A) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) (#) sinh is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap (1,0)) (#) sinh) - cosh is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
- cosh is Relation-like V6() V34() V35() V36() set
K98(1) (#) cosh is Relation-like V6() V34() V35() V36() set
((AffineMap (1,0)) (#) sinh) + (- cosh) is Relation-like V6() V34() V35() V36() set
(((AffineMap (1,0)) (#) sinh) - cosh) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((AffineMap (1,0)) (#) sinh) - cosh) is non empty set
dom (AffineMap (1,0)) is non empty set
A is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . A is V28() V29() ext-real Element of REAL
1 * A is V28() V29() ext-real Element of REAL
(1 * A) + 0 is V28() V29() ext-real Element of REAL
dom ((AffineMap (1,0)) (#) sinh) is non empty set
((AffineMap (1,0)) (#) sinh) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) sinh) `| REAL) . A is V28() V29() ext-real Element of REAL
sinh . A is V28() V29() ext-real Element of REAL
cosh . A is V28() V29() ext-real Element of REAL
A * (cosh . A) is V28() V29() ext-real Element of REAL
(sinh . A) + (A * (cosh . A)) is V28() V29() ext-real Element of REAL
diff ((AffineMap (1,0)),A) is V28() V29() ext-real Element of REAL
(sinh . A) * (diff ((AffineMap (1,0)),A)) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . A is V28() V29() ext-real Element of REAL
diff (sinh,A) is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . A) * (diff (sinh,A)) is V28() V29() ext-real Element of REAL
((sinh . A) * (diff ((AffineMap (1,0)),A))) + (((AffineMap (1,0)) . A) * (diff (sinh,A))) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap (1,0)) `| REAL) . A is V28() V29() ext-real Element of REAL
(sinh . A) * (((AffineMap (1,0)) `| REAL) . A) is V28() V29() ext-real Element of REAL
((sinh . A) * (((AffineMap (1,0)) `| REAL) . A)) + (((AffineMap (1,0)) . A) * (diff (sinh,A))) is V28() V29() ext-real Element of REAL
(sinh . A) * 1 is V28() V29() ext-real Element of REAL
((sinh . A) * 1) + (((AffineMap (1,0)) . A) * (diff (sinh,A))) is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . A) * (cosh . A) is V28() V29() ext-real Element of REAL
(sinh . A) + (((AffineMap (1,0)) . A) * (cosh . A)) is V28() V29() ext-real Element of REAL
1 * A is V28() V29() ext-real Element of REAL
(1 * A) + 0 is V28() V29() ext-real Element of REAL
((1 * A) + 0) * (cosh . A) is V28() V29() ext-real Element of REAL
(sinh . A) + (((1 * A) + 0) * (cosh . A)) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) sinh) - cosh) `| REAL) . A is V28() V29() ext-real Element of REAL
cosh . A is V28() V29() ext-real Element of REAL
A * (cosh . A) is V28() V29() ext-real Element of REAL
diff (((AffineMap (1,0)) (#) sinh),A) is V28() V29() ext-real Element of REAL
diff (cosh,A) is V28() V29() ext-real Element of REAL
(diff (((AffineMap (1,0)) (#) sinh),A)) - (diff (cosh,A)) is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) sinh) `| REAL) . A is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) sinh) `| REAL) . A) - (diff (cosh,A)) is V28() V29() ext-real Element of REAL
sinh . A is V28() V29() ext-real Element of REAL
(sinh . A) + (A * (cosh . A)) is V28() V29() ext-real Element of REAL
((sinh . A) + (A * (cosh . A))) - (diff (cosh,A)) is V28() V29() ext-real Element of REAL
((sinh . A) + (A * (cosh . A))) - (sinh . A) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) sinh) - cosh) `| REAL) . A is V28() V29() ext-real Element of REAL
cosh . A is V28() V29() ext-real Element of REAL
A * (cosh . A) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
AffineMap (A,Z) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
f2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
f2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A * (f2 + 1) is V28() V29() ext-real Element of REAL
#Z (f2 + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (f2 + 1)) * (AffineMap (A,Z)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A * (f2 + 1)) is V28() V29() ext-real Element of REAL
(1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) is non empty set
dom (AffineMap (A,Z)) is non empty set
f1 is V28() V29() ext-real Element of REAL
(AffineMap (A,Z)) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
(A * f1) + Z is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
dom ((#Z (f2 + 1)) * (AffineMap (A,Z))) is non empty set
f1 is V28() V29() ext-real Element of REAL
((#Z (f2 + 1)) * (AffineMap (A,Z))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
x is V28() V29() ext-real Element of REAL
(((#Z (f2 + 1)) * (AffineMap (A,Z))) `| REAL) . x is V28() V29() ext-real Element of REAL
(AffineMap (A,Z)) . x is V28() V29() ext-real Element of REAL
((AffineMap (A,Z)) . x) #Z f2 is V28() V29() ext-real Element of REAL
(A * (f2 + 1)) * (((AffineMap (A,Z)) . x) #Z f2) is V28() V29() ext-real Element of REAL
diff (((#Z (f2 + 1)) * (AffineMap (A,Z))),x) is V28() V29() ext-real Element of REAL
(f2 + 1) - 1 is V28() V29() V30() ext-real Element of REAL
((AffineMap (A,Z)) . x) #Z ((f2 + 1) - 1) is V28() V29() ext-real Element of REAL
(f2 + 1) * (((AffineMap (A,Z)) . x) #Z ((f2 + 1) - 1)) is V28() V29() ext-real Element of REAL
diff ((AffineMap (A,Z)),x) is V28() V29() ext-real Element of REAL
((f2 + 1) * (((AffineMap (A,Z)) . x) #Z ((f2 + 1) - 1))) * (diff ((AffineMap (A,Z)),x)) is V28() V29() ext-real Element of REAL
(AffineMap (A,Z)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap (A,Z)) `| REAL) . x is V28() V29() ext-real Element of REAL
((f2 + 1) * (((AffineMap (A,Z)) . x) #Z ((f2 + 1) - 1))) * (((AffineMap (A,Z)) `| REAL) . x) is V28() V29() ext-real Element of REAL
((f2 + 1) * (((AffineMap (A,Z)) . x) #Z ((f2 + 1) - 1))) * A is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
(((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) `| REAL) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
(A * f1) + Z is V28() V29() ext-real Element of REAL
((A * f1) + Z) #Z f2 is V28() V29() ext-real Element of REAL
diff (((#Z (f2 + 1)) * (AffineMap (A,Z))),f1) is V28() V29() ext-real Element of REAL
(1 / (A * (f2 + 1))) * (diff (((#Z (f2 + 1)) * (AffineMap (A,Z))),f1)) is V28() V29() ext-real Element of REAL
(((#Z (f2 + 1)) * (AffineMap (A,Z))) `| REAL) . f1 is V28() V29() ext-real Element of REAL
(1 / (A * (f2 + 1))) * ((((#Z (f2 + 1)) * (AffineMap (A,Z))) `| REAL) . f1) is V28() V29() ext-real Element of REAL
(AffineMap (A,Z)) . f1 is V28() V29() ext-real Element of REAL
((AffineMap (A,Z)) . f1) #Z f2 is V28() V29() ext-real Element of REAL
(A * (f2 + 1)) * (((AffineMap (A,Z)) . f1) #Z f2) is V28() V29() ext-real Element of REAL
(1 / (A * (f2 + 1))) * ((A * (f2 + 1)) * (((AffineMap (A,Z)) . f1) #Z f2)) is V28() V29() ext-real Element of REAL
(1 / (A * (f2 + 1))) * (A * (f2 + 1)) is V28() V29() ext-real Element of REAL
((1 / (A * (f2 + 1))) * (A * (f2 + 1))) * (((AffineMap (A,Z)) . f1) #Z f2) is V28() V29() ext-real Element of REAL
(A * (f2 + 1)) / (A * (f2 + 1)) is V28() V29() ext-real Element of REAL
((A * (f2 + 1)) / (A * (f2 + 1))) * (((AffineMap (A,Z)) . f1) #Z f2) is V28() V29() ext-real Element of REAL
1 * (((AffineMap (A,Z)) . f1) #Z f2) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
(((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) `| REAL) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
(A * f1) + Z is V28() V29() ext-real Element of REAL
((A * f1) + Z) #Z f2 is V28() V29() ext-real Element of REAL
sin ^2 is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
sin (#) sin is Relation-like V6() V34() V35() V36() set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((sin ^2),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (upper_bound A)) - (((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (lower_bound A)) is V28() V29() ext-real Element of REAL
dom (((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) is set
Z is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) . Z is V28() V29() ext-real Element of REAL
(sin ^2) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
dom (sin ^2) is non empty set
(sin ^2) | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (AffineMap (2,0)) is non empty set
dom ((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) is non empty set
[.0,PI.] is V51() V52() V53() closed Element of K19(REAL)
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((sin ^2),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . PI is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0 is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . PI) - (((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . PI is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . PI) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . PI) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI)) - (((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . 0 is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0 is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . PI) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI)) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(1 / 2) * PI is V28() V29() ext-real Element of REAL
((1 / 2) * PI) + 0 is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI) is V28() V29() ext-real Element of REAL
((((1 / 2) * PI) + 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI)) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . PI is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . PI) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) - ((1 / 4) * ((sin * (AffineMap (2,0))) . PI)) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * ((sin * (AffineMap (2,0))) . PI))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . PI is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . PI) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . PI)) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) - ((1 / 4) * (sin . ((AffineMap (2,0)) . PI))) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . ((AffineMap (2,0)) . PI)))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(2 * PI) + 0 is V28() V29() ext-real Element of REAL
sin . ((2 * PI) + 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((2 * PI) + 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) - ((1 / 4) * (sin . ((2 * PI) + 0))) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . ((2 * PI) + 0)))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
0 - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . ((2 * PI) + 0)))) - (0 - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . ((2 * PI) + 0)))) - 0 is V28() V29() ext-real Element of REAL
((((1 / 2) * PI) - ((1 / 4) * (sin . ((2 * PI) + 0)))) - 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . 0 is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . ((2 * PI) + 0)))) + ((1 / 4) * ((sin * (AffineMap (2,0))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . 0 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . ((2 * PI) + 0)))) + ((1 / 4) * (sin . ((AffineMap (2,0)) . 0))) is V28() V29() ext-real Element of REAL
(2 * PI) * 1 is V28() V29() ext-real Element of REAL
0 + ((2 * PI) * 1) is V28() V29() ext-real Element of REAL
sin . (0 + ((2 * PI) * 1)) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . (0 + ((2 * PI) * 1))) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) - ((1 / 4) * (sin . (0 + ((2 * PI) * 1)))) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . (0 + ((2 * PI) * 1))))) + ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) - ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) - ((1 / 4) * (sin . 0))) + ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
[.0,(2 * PI).] is V51() V52() V53() closed Element of K19(REAL)
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((sin ^2),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (2 * PI) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0 is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (2 * PI)) - (((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . (2 * PI) is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . (2 * PI)) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI)) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . (2 * PI)) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI))) - (((AffineMap ((1 / 2),0)) - ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . 0 is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0 is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . (2 * PI)) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(1 / 2) * (2 * PI) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + 0 is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI)) is V28() V29() ext-real Element of REAL
((((1 / 2) * (2 * PI)) + 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . (2 * PI) is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . (2 * PI)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) - ((1 / 4) * ((sin * (AffineMap (2,0))) . (2 * PI))) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * ((sin * (AffineMap (2,0))) . (2 * PI)))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . (2 * PI) is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . (2 * PI)) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . (2 * PI))) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . ((AffineMap (2,0)) . (2 * PI)))) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . ((AffineMap (2,0)) . (2 * PI))))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
2 * (2 * PI) is V28() V29() ext-real Element of REAL
(2 * (2 * PI)) + 0 is V28() V29() ext-real Element of REAL
sin . ((2 * (2 * PI)) + 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((2 * (2 * PI)) + 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . ((2 * (2 * PI)) + 0))) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . ((2 * (2 * PI)) + 0)))) - (((AffineMap ((1 / 2),0)) . 0) - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
2 * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
(2 * 2) * PI is V28() V29() ext-real Element of REAL
((2 * 2) * PI) + 0 is V28() V29() ext-real Element of REAL
sin . (((2 * 2) * PI) + 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . (((2 * 2) * PI) + 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (((2 * 2) * PI) + 0))) is V28() V29() ext-real Element of REAL
0 - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) - (0 - (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) - 0 is V28() V29() ext-real Element of REAL
((((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) - 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . 0 is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) + ((1 / 4) * ((sin * (AffineMap (2,0))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . 0 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) + ((1 / 4) * (sin . ((AffineMap (2,0)) . 0))) is V28() V29() ext-real Element of REAL
(2 * PI) * 2 is V28() V29() ext-real Element of REAL
0 + ((2 * PI) * 2) is V28() V29() ext-real Element of REAL
sin . (0 + ((2 * PI) * 2)) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . (0 + ((2 * PI) * 2))) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (0 + ((2 * PI) * 2)))) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . (0 + ((2 * PI) * 2))))) + ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) - ((1 / 4) * (sin . 0))) + ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
cos ^2 is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
cos (#) cos is Relation-like V6() V34() V35() V36() set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((cos ^2),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (upper_bound A)) - (((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (lower_bound A)) is V28() V29() ext-real Element of REAL
dom (((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) is set
Z is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) `| REAL) . Z is V28() V29() ext-real Element of REAL
(cos ^2) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
dom (cos ^2) is non empty set
(cos ^2) | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((cos ^2),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . PI is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0 is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . PI) - (((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . PI is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . PI) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . PI) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI)) - (((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . 0 is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0 is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . PI) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI)) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(1 / 2) * PI is V28() V29() ext-real Element of REAL
((1 / 2) * PI) + 0 is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI) is V28() V29() ext-real Element of REAL
((((1 / 2) * PI) + 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . PI)) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . PI is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . PI) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) + ((1 / 4) * ((sin * (AffineMap (2,0))) . PI)) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * ((sin * (AffineMap (2,0))) . PI))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . PI is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . PI) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . PI)) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) + ((1 / 4) * (sin . ((AffineMap (2,0)) . PI))) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * (sin . ((AffineMap (2,0)) . PI)))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(2 * PI) + 0 is V28() V29() ext-real Element of REAL
sin . ((2 * PI) + 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((2 * PI) + 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) + ((1 / 4) * (sin . ((2 * PI) + 0))) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * (sin . ((2 * PI) + 0)))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
0 + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * (sin . ((2 * PI) + 0)))) - (0 + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . 0 is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * (sin . ((2 * PI) + 0)))) - ((1 / 4) * ((sin * (AffineMap (2,0))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . 0 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * (sin . ((2 * PI) + 0)))) - ((1 / 4) * (sin . ((AffineMap (2,0)) . 0))) is V28() V29() ext-real Element of REAL
(2 * PI) * 1 is V28() V29() ext-real Element of REAL
0 + ((2 * PI) * 1) is V28() V29() ext-real Element of REAL
sin . (0 + ((2 * PI) * 1)) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . (0 + ((2 * PI) * 1))) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) + ((1 / 4) * (sin . (0 + ((2 * PI) * 1)))) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * (sin . (0 + ((2 * PI) * 1))))) - ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * PI) + ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * PI) + ((1 / 4) * (sin . 0))) - ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((cos ^2),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (2 * PI) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0 is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . (2 * PI)) - (((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . (2 * PI) is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI) is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . (2 * PI)) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI)) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . (2 * PI)) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI))) - (((AffineMap ((1 / 2),0)) + ((1 / 4) (#) (sin * (AffineMap (2,0))))) . 0) is V28() V29() ext-real Element of REAL
(AffineMap ((1 / 2),0)) . 0 is V28() V29() ext-real Element of REAL
((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0 is V28() V29() ext-real Element of REAL
((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((AffineMap ((1 / 2),0)) . (2 * PI)) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(1 / 2) * (2 * PI) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + 0 is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI)) is V28() V29() ext-real Element of REAL
((((1 / 2) * (2 * PI)) + 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . (2 * PI))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . (2 * PI) is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . (2 * PI)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + ((1 / 4) * ((sin * (AffineMap (2,0))) . (2 * PI))) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * ((sin * (AffineMap (2,0))) . (2 * PI)))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . (2 * PI) is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . (2 * PI)) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . (2 * PI))) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . ((AffineMap (2,0)) . (2 * PI)))) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . ((AffineMap (2,0)) . (2 * PI))))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
2 * (2 * PI) is V28() V29() ext-real Element of REAL
(2 * (2 * PI)) + 0 is V28() V29() ext-real Element of REAL
sin . ((2 * (2 * PI)) + 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((2 * (2 * PI)) + 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . ((2 * (2 * PI)) + 0))) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . ((2 * (2 * PI)) + 0)))) - (((AffineMap ((1 / 2),0)) . 0) + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
2 * 2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
(2 * 2) * PI is V28() V29() ext-real Element of REAL
((2 * 2) * PI) + 0 is V28() V29() ext-real Element of REAL
sin . (((2 * 2) * PI) + 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . (((2 * 2) * PI) + 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . (((2 * 2) * PI) + 0))) is V28() V29() ext-real Element of REAL
0 + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) - (0 + (((1 / 4) (#) (sin * (AffineMap (2,0)))) . 0)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (2,0))) . 0 is V28() V29() ext-real Element of REAL
(1 / 4) * ((sin * (AffineMap (2,0))) . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) - ((1 / 4) * ((sin * (AffineMap (2,0))) . 0)) is V28() V29() ext-real Element of REAL
(AffineMap (2,0)) . 0 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (2,0)) . 0) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . ((AffineMap (2,0)) . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . (((2 * 2) * PI) + 0)))) - ((1 / 4) * (sin . ((AffineMap (2,0)) . 0))) is V28() V29() ext-real Element of REAL
(2 * PI) * 2 is V28() V29() ext-real Element of REAL
0 + ((2 * PI) * 2) is V28() V29() ext-real Element of REAL
sin . (0 + ((2 * PI) * 2)) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . (0 + ((2 * PI) * 2))) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . (0 + ((2 * PI) * 2)))) is V28() V29() ext-real Element of REAL
(1 / 4) * (sin . 0) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . (0 + ((2 * PI) * 2))))) - ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
(((1 / 2) * (2 * PI)) + ((1 / 4) * (sin . 0))) - ((1 / 4) * (sin . 0)) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
#Z A is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z A) * sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((#Z A) * sin) (#) cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) (#) ((#Z (A + 1)) * sin) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((((#Z A) * sin) (#) cos),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . (upper_bound Z) is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . (lower_bound Z) is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . (upper_bound Z)) - (((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
dom (((#Z A) * sin) (#) cos) is non empty set
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) `| REAL) is set
f2 is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(((#Z A) * sin) (#) cos) . f2 is V28() V29() ext-real Element of REAL
sin . f2 is V28() V29() ext-real Element of REAL
(sin . f2) #Z A is V28() V29() ext-real Element of REAL
cos . f2 is V28() V29() ext-real Element of REAL
((sin . f2) #Z A) * (cos . f2) is V28() V29() ext-real Element of REAL
(#Z A) . (sin . f2) is V28() V29() ext-real Element of REAL
((#Z A) . (sin . f2)) * (cos . f2) is V28() V29() ext-real Element of REAL
((#Z A) * sin) . f2 is V28() V29() ext-real Element of REAL
(((#Z A) * sin) . f2) * (cos . f2) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
dom ((#Z A) * sin) is non empty set
f2 is V28() V29() ext-real Element of REAL
(((#Z A) * sin) (#) cos) | REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((#Z A) * sin) (#) cos) | Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
#Z A is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z A) * sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((#Z A) * sin) (#) cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((((#Z A) * sin) (#) cos),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) (#) ((#Z (A + 1)) * sin) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . PI is V28() V29() ext-real Element of REAL
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . 0 is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . PI) - (((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . 0) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * sin) . PI is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (((#Z (A + 1)) * sin) . PI) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * (((#Z (A + 1)) * sin) . PI)) - (((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . 0) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * sin) . 0 is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (((#Z (A + 1)) * sin) . 0) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * (((#Z (A + 1)) * sin) . PI)) - ((1 / (A + 1)) * (((#Z (A + 1)) * sin) . 0)) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (sin . PI) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * ((#Z (A + 1)) . (sin . PI)) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * ((#Z (A + 1)) . (sin . PI))) - ((1 / (A + 1)) * (((#Z (A + 1)) * sin) . 0)) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (sin . 0) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * ((#Z (A + 1)) . (sin . 0)) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * ((#Z (A + 1)) . (sin . PI))) - ((1 / (A + 1)) * ((#Z (A + 1)) . (sin . 0))) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
#Z A is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z A) * sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((#Z A) * sin) (#) cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((((#Z A) * sin) (#) cos),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) (#) ((#Z (A + 1)) * sin) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . (2 * PI) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . 0 is V28() V29() ext-real Element of REAL
(((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . (2 * PI)) - (((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . 0) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * sin) . (2 * PI) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (((#Z (A + 1)) * sin) . (2 * PI)) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * (((#Z (A + 1)) * sin) . (2 * PI))) - (((1 / (A + 1)) (#) ((#Z (A + 1)) * sin)) . 0) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * sin) . 0 is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * (((#Z (A + 1)) * sin) . 0) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * (((#Z (A + 1)) * sin) . (2 * PI))) - ((1 / (A + 1)) * (((#Z (A + 1)) * sin) . 0)) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (sin . (2 * PI)) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * ((#Z (A + 1)) . (sin . (2 * PI))) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * ((#Z (A + 1)) . (sin . (2 * PI)))) - ((1 / (A + 1)) * (((#Z (A + 1)) * sin) . 0)) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (sin . 0) is V28() V29() ext-real Element of REAL
(1 / (A + 1)) * ((#Z (A + 1)) . (sin . 0)) is V28() V29() ext-real Element of REAL
((1 / (A + 1)) * ((#Z (A + 1)) . (sin . (2 * PI)))) - ((1 / (A + 1)) * ((#Z (A + 1)) . (sin . 0))) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
#Z A is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z A) * cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((#Z A) * cos) (#) sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
- (1 / (A + 1)) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((((#Z A) * cos) (#) sin),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (upper_bound Z) is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (lower_bound Z) is V28() V29() ext-real Element of REAL
(((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (upper_bound Z)) - (((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
dom (((#Z A) * cos) (#) sin) is non empty set
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) `| REAL) is set
f2 is V28() V29() ext-real Element of REAL
(((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) `| REAL) . f2 is V28() V29() ext-real Element of REAL
(((#Z A) * cos) (#) sin) . f2 is V28() V29() ext-real Element of REAL
cos . f2 is V28() V29() ext-real Element of REAL
(cos . f2) #Z A is V28() V29() ext-real Element of REAL
sin . f2 is V28() V29() ext-real Element of REAL
((cos . f2) #Z A) * (sin . f2) is V28() V29() ext-real Element of REAL
(#Z A) . (cos . f2) is V28() V29() ext-real Element of REAL
((#Z A) . (cos . f2)) * (sin . f2) is V28() V29() ext-real Element of REAL
((#Z A) * cos) . f2 is V28() V29() ext-real Element of REAL
(((#Z A) * cos) . f2) * (sin . f2) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
dom ((#Z A) * cos) is non empty set
f2 is V28() V29() ext-real Element of REAL
(((#Z A) * cos) (#) sin) | REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((#Z A) * cos) (#) sin) | Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
#Z A is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z A) * cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((#Z A) * cos) (#) sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((((#Z A) * cos) (#) sin),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
- (1 / (A + 1)) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (2 * PI) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . 0 is V28() V29() ext-real Element of REAL
(((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (2 * PI)) - (((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . 0) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * cos) . (2 * PI) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (2 * PI)) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (2 * PI))) - (((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . 0) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * cos) . 0 is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . 0) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (2 * PI))) - ((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . 0)) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (cos . (2 * PI)) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (2 * PI))) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (2 * PI)))) - ((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . 0)) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (cos . 0) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . 0)) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (2 * PI)))) - ((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . 0))) is V28() V29() ext-real Element of REAL
- (PI / 2) is V28() V29() ext-real Element of REAL
[.(- (PI / 2)),(PI / 2).] is V51() V52() V53() closed Element of K19(REAL)
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
#Z A is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z A) * cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((#Z A) * cos) (#) sin is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral ((((#Z A) * cos) (#) sin),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
A + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
#Z (A + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (A + 1)) * cos is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A + 1) is V28() V29() ext-real Element of REAL
- (1 / (A + 1)) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (PI / 2) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (- (PI / 2)) is V28() V29() ext-real Element of REAL
(((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (PI / 2)) - (((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (- (PI / 2))) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * cos) . (PI / 2) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (PI / 2)) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (PI / 2))) - (((- (1 / (A + 1))) (#) ((#Z (A + 1)) * cos)) . (- (PI / 2))) is V28() V29() ext-real Element of REAL
((#Z (A + 1)) * cos) . (- (PI / 2)) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (- (PI / 2))) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (PI / 2))) - ((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (- (PI / 2)))) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (cos . (PI / 2)) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (PI / 2))) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (PI / 2)))) - ((- (1 / (A + 1))) * (((#Z (A + 1)) * cos) . (- (PI / 2)))) is V28() V29() ext-real Element of REAL
cos . (- (PI / 2)) is V28() V29() ext-real Element of REAL
(#Z (A + 1)) . (cos . (- (PI / 2))) is V28() V29() ext-real Element of REAL
(- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (- (PI / 2)))) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (PI / 2)))) - ((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (- (PI / 2))))) is V28() V29() ext-real Element of REAL
((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (PI / 2)))) - ((- (1 / (A + 1))) * ((#Z (A + 1)) . (cos . (PI / 2)))) is V28() V29() ext-real Element of REAL
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
AffineMap (A,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A - Z is V28() V29() V30() ext-real Element of REAL
AffineMap (Z,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap (Z,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(cos * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
AffineMap ((A + Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A + Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
AffineMap ((A - Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A - Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A - Z) is V28() V29() V30() ext-real Element of REAL
1 / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
f2 is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((cos * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))),f2) is V28() V29() ext-real Element of REAL
upper_bound f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) . (upper_bound f2) is V28() V29() ext-real Element of REAL
lower_bound f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) . (lower_bound f2) is V28() V29() ext-real Element of REAL
((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) . (upper_bound f2)) - ((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) . (lower_bound f2)) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
(AffineMap (Z,0)) . f1 is V28() V29() ext-real Element of REAL
Z * f1 is V28() V29() ext-real Element of REAL
(Z * f1) + 0 is V28() V29() ext-real Element of REAL
dom (cos * (AffineMap (Z,0))) is non empty set
dom (cos * (AffineMap (A,0))) is non empty set
f1 is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
(A * f1) + 0 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) `| REAL) is set
f1 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) + ((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))))) `| REAL) . f1 is V28() V29() ext-real Element of REAL
((cos * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
cos . (A * f1) is V28() V29() ext-real Element of REAL
Z * f1 is V28() V29() ext-real Element of REAL
cos . (Z * f1) is V28() V29() ext-real Element of REAL
(cos . (A * f1)) * (cos . (Z * f1)) is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f1 is V28() V29() ext-real Element of REAL
cos . ((AffineMap (A,0)) . f1) is V28() V29() ext-real Element of REAL
(cos . ((AffineMap (A,0)) . f1)) * (cos . (Z * f1)) is V28() V29() ext-real Element of REAL
(AffineMap (Z,0)) . f1 is V28() V29() ext-real Element of REAL
cos . ((AffineMap (Z,0)) . f1) is V28() V29() ext-real Element of REAL
(cos . ((AffineMap (A,0)) . f1)) * (cos . ((AffineMap (Z,0)) . f1)) is V28() V29() ext-real Element of REAL
(cos * (AffineMap (A,0))) . f1 is V28() V29() ext-real Element of REAL
((cos * (AffineMap (A,0))) . f1) * (cos . ((AffineMap (Z,0)) . f1)) is V28() V29() ext-real Element of REAL
(cos * (AffineMap (Z,0))) . f1 is V28() V29() ext-real Element of REAL
((cos * (AffineMap (A,0))) . f1) * ((cos * (AffineMap (Z,0))) . f1) is V28() V29() ext-real Element of REAL
dom ((cos * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))) is non empty set
((cos * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))) | f2 is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
AffineMap (A,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A - Z is V28() V29() V30() ext-real Element of REAL
AffineMap (Z,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (Z,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(sin * (AffineMap (A,0))) (#) (sin * (AffineMap (Z,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
AffineMap ((A - Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A - Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A - Z) is V28() V29() V30() ext-real Element of REAL
1 / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
AffineMap ((A + Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap ((A + Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
- ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0)))) is Relation-like V6() V34() V35() V36() set
((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) + (- ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) is Relation-like V6() V34() V35() V36() set
f2 is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((sin * (AffineMap (A,0))) (#) (sin * (AffineMap (Z,0)))),f2) is V28() V29() ext-real Element of REAL
upper_bound f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) . (upper_bound f2) is V28() V29() ext-real Element of REAL
lower_bound f2 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) . (lower_bound f2) is V28() V29() ext-real Element of REAL
((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) . (upper_bound f2)) - ((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) . (lower_bound f2)) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
(AffineMap (Z,0)) . f1 is V28() V29() ext-real Element of REAL
Z * f1 is V28() V29() ext-real Element of REAL
(Z * f1) + 0 is V28() V29() ext-real Element of REAL
dom (sin * (AffineMap (Z,0))) is non empty set
dom (sin * (AffineMap (A,0))) is non empty set
f1 is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
(A * f1) + 0 is V28() V29() ext-real Element of REAL
(((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) `| REAL) is set
f1 is V28() V29() ext-real Element of REAL
((((1 / (2 * (A - Z))) (#) (sin * (AffineMap ((A - Z),0)))) - ((1 / (2 * (A + Z))) (#) (sin * (AffineMap ((A + Z),0))))) `| REAL) . f1 is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) (#) (sin * (AffineMap (Z,0)))) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
sin . (A * f1) is V28() V29() ext-real Element of REAL
Z * f1 is V28() V29() ext-real Element of REAL
sin . (Z * f1) is V28() V29() ext-real Element of REAL
(sin . (A * f1)) * (sin . (Z * f1)) is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f1 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (A,0)) . f1) is V28() V29() ext-real Element of REAL
(sin . ((AffineMap (A,0)) . f1)) * (sin . (Z * f1)) is V28() V29() ext-real Element of REAL
(AffineMap (Z,0)) . f1 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (Z,0)) . f1) is V28() V29() ext-real Element of REAL
(sin . ((AffineMap (A,0)) . f1)) * (sin . ((AffineMap (Z,0)) . f1)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (A,0))) . f1 is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) . f1) * (sin . ((AffineMap (Z,0)) . f1)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (Z,0))) . f1 is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) . f1) * ((sin * (AffineMap (Z,0))) . f1) is V28() V29() ext-real Element of REAL
dom ((sin * (AffineMap (A,0))) (#) (sin * (AffineMap (Z,0)))) is non empty set
((sin * (AffineMap (A,0))) (#) (sin * (AffineMap (Z,0)))) | f2 is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
AffineMap (A,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
A + Z is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A - Z is V28() V29() V30() ext-real Element of REAL
AffineMap (Z,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap (Z,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(sin * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
AffineMap ((A + Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap ((A + Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A + Z) is V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
1 / (2 * (A + Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
K98(1) (#) ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0)))) is Relation-like V6() V34() V35() V36() set
AffineMap ((A - Z),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap ((A - Z),0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
2 * (A - Z) is V28() V29() V30() ext-real Element of REAL
1 / (2 * (A - Z)) is V28() V29() ext-real Element of REAL
(1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
- ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0)))) is Relation-like V6() V34() V35() V36() set
(- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) + (- ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) is Relation-like V6() V34() V35() V36() set
f2 is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((sin * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))),f2) is V28() V29() ext-real Element of REAL
upper_bound f2 is V28() V29() ext-real Element of REAL
((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) . (upper_bound f2) is V28() V29() ext-real Element of REAL
lower_bound f2 is V28() V29() ext-real Element of REAL
((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) . (lower_bound f2) is V28() V29() ext-real Element of REAL
(((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) . (upper_bound f2)) - (((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) . (lower_bound f2)) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
(AffineMap (Z,0)) . f1 is V28() V29() ext-real Element of REAL
Z * f1 is V28() V29() ext-real Element of REAL
(Z * f1) + 0 is V28() V29() ext-real Element of REAL
dom (cos * (AffineMap (Z,0))) is non empty set
dom (sin * (AffineMap (A,0))) is non empty set
f1 is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
(A * f1) + 0 is V28() V29() ext-real Element of REAL
((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) `| REAL) is set
f1 is V28() V29() ext-real Element of REAL
(((- ((1 / (2 * (A + Z))) (#) (cos * (AffineMap ((A + Z),0))))) - ((1 / (2 * (A - Z))) (#) (cos * (AffineMap ((A - Z),0))))) `| REAL) . f1 is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))) . f1 is V28() V29() ext-real Element of REAL
A * f1 is V28() V29() ext-real Element of REAL
sin . (A * f1) is V28() V29() ext-real Element of REAL
Z * f1 is V28() V29() ext-real Element of REAL
cos . (Z * f1) is V28() V29() ext-real Element of REAL
(sin . (A * f1)) * (cos . (Z * f1)) is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f1 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (A,0)) . f1) is V28() V29() ext-real Element of REAL
(sin . ((AffineMap (A,0)) . f1)) * (cos . (Z * f1)) is V28() V29() ext-real Element of REAL
(AffineMap (Z,0)) . f1 is V28() V29() ext-real Element of REAL
cos . ((AffineMap (Z,0)) . f1) is V28() V29() ext-real Element of REAL
(sin . ((AffineMap (A,0)) . f1)) * (cos . ((AffineMap (Z,0)) . f1)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (A,0))) . f1 is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) . f1) * (cos . ((AffineMap (Z,0)) . f1)) is V28() V29() ext-real Element of REAL
(cos * (AffineMap (Z,0))) . f1 is V28() V29() ext-real Element of REAL
((sin * (AffineMap (A,0))) . f1) * ((cos * (AffineMap (Z,0))) . f1) is V28() V29() ext-real Element of REAL
dom ((sin * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))) is non empty set
((sin * (AffineMap (A,0))) (#) (cos * (AffineMap (Z,0)))) | f2 is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
AffineMap (A,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(AffineMap (1,0)) (#) (sin * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A ^2 is V28() V29() ext-real Element of REAL
K97(A,A) is V21() V22() V23() V27() V29() V30() non negative set
1 / (A ^2) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) (#) (sin * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
1 / A is V28() V29() ext-real Element of REAL
AffineMap ((1 / A),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
- ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0)))) is Relation-like V6() V34() V35() V36() set
((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) + (- ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) is Relation-like V6() V34() V35() V36() set
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((AffineMap (1,0)) (#) (sin * (AffineMap (A,0)))),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) . (upper_bound Z) is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) . (lower_bound Z) is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) . (upper_bound Z)) - ((((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
(A * f2) + 0 is V28() V29() ext-real Element of REAL
dom (sin * (AffineMap (A,0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . f2 is V28() V29() ext-real Element of REAL
1 * f2 is V28() V29() ext-real Element of REAL
(1 * f2) + 0 is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) `| REAL) is set
f2 is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (sin * (AffineMap (A,0)))) - ((AffineMap ((1 / A),0)) (#) (cos * (AffineMap (A,0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) (#) (sin * (AffineMap (A,0)))) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
sin . (A * f2) is V28() V29() ext-real Element of REAL
f2 * (sin . (A * f2)) is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f2 is V28() V29() ext-real Element of REAL
sin . ((AffineMap (A,0)) . f2) is V28() V29() ext-real Element of REAL
f2 * (sin . ((AffineMap (A,0)) . f2)) is V28() V29() ext-real Element of REAL
(sin * (AffineMap (A,0))) . f2 is V28() V29() ext-real Element of REAL
f2 * ((sin * (AffineMap (A,0))) . f2) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . f2 is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . f2) * ((sin * (AffineMap (A,0))) . f2) is V28() V29() ext-real Element of REAL
dom ((AffineMap (1,0)) (#) (sin * (AffineMap (A,0)))) is non empty set
((AffineMap (1,0)) (#) (sin * (AffineMap (A,0)))) | Z is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
AffineMap (A,0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
cos * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(AffineMap (1,0)) (#) (cos * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A ^2 is V28() V29() ext-real Element of REAL
K97(A,A) is V21() V22() V23() V27() V29() V30() non negative set
1 / (A ^2) is V28() V29() ext-real Element of REAL
(1 / (A ^2)) (#) (cos * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
1 / A is V28() V29() ext-real Element of REAL
AffineMap ((1 / A),0) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
sin * (AffineMap (A,0)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0)))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((AffineMap (1,0)) (#) (cos * (AffineMap (A,0)))),Z) is V28() V29() ext-real Element of REAL
upper_bound Z is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) . (upper_bound Z) is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) . (lower_bound Z) is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) . (upper_bound Z)) - ((((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
(A * f2) + 0 is V28() V29() ext-real Element of REAL
dom (cos * (AffineMap (A,0))) is non empty set
f2 is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . f2 is V28() V29() ext-real Element of REAL
1 * f2 is V28() V29() ext-real Element of REAL
(1 * f2) + 0 is V28() V29() ext-real Element of REAL
(((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) `| REAL) is set
f2 is V28() V29() ext-real Element of REAL
((((1 / (A ^2)) (#) (cos * (AffineMap (A,0)))) + ((AffineMap ((1 / A),0)) (#) (sin * (AffineMap (A,0))))) `| REAL) . f2 is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) (#) (cos * (AffineMap (A,0)))) . f2 is V28() V29() ext-real Element of REAL
A * f2 is V28() V29() ext-real Element of REAL
cos . (A * f2) is V28() V29() ext-real Element of REAL
f2 * (cos . (A * f2)) is V28() V29() ext-real Element of REAL
(AffineMap (A,0)) . f2 is V28() V29() ext-real Element of REAL
cos . ((AffineMap (A,0)) . f2) is V28() V29() ext-real Element of REAL
f2 * (cos . ((AffineMap (A,0)) . f2)) is V28() V29() ext-real Element of REAL
(cos * (AffineMap (A,0))) . f2 is V28() V29() ext-real Element of REAL
f2 * ((cos * (AffineMap (A,0))) . f2) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . f2 is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . f2) * ((cos * (AffineMap (A,0))) . f2) is V28() V29() ext-real Element of REAL
dom ((AffineMap (1,0)) (#) (cos * (AffineMap (A,0)))) is non empty set
((AffineMap (1,0)) (#) (cos * (AffineMap (A,0)))) | Z is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((AffineMap (1,0)) (#) sinh),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) cosh) - sinh) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) cosh) - sinh) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) cosh) - sinh) . (upper_bound A)) - ((((AffineMap (1,0)) (#) cosh) - sinh) . (lower_bound A)) is V28() V29() ext-real Element of REAL
dom ((((AffineMap (1,0)) (#) cosh) - sinh) `| REAL) is set
Z is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) cosh) - sinh) `| REAL) . Z is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) (#) sinh) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
sinh . Z is V28() V29() ext-real Element of REAL
((1 * Z) + 0) * (sinh . Z) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . Z is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . Z) * (sinh . Z) is V28() V29() ext-real Element of REAL
dom ((AffineMap (1,0)) (#) sinh) is non empty set
dom (AffineMap (1,0)) is non empty set
Z is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) (#) sinh) | REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap (1,0)) (#) sinh) | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((AffineMap (1,0)) (#) cosh),A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) sinh) - cosh) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
(((AffineMap (1,0)) (#) sinh) - cosh) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) sinh) - cosh) . (upper_bound A)) - ((((AffineMap (1,0)) (#) sinh) - cosh) . (lower_bound A)) is V28() V29() ext-real Element of REAL
dom ((((AffineMap (1,0)) (#) sinh) - cosh) `| REAL) is set
Z is V28() V29() ext-real Element of REAL
((((AffineMap (1,0)) (#) sinh) - cosh) `| REAL) . Z is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) (#) cosh) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
cosh . Z is V28() V29() ext-real Element of REAL
((1 * Z) + 0) * (cosh . Z) is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . Z is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) . Z) * (cosh . Z) is V28() V29() ext-real Element of REAL
dom ((AffineMap (1,0)) (#) cosh) is non empty set
dom (AffineMap (1,0)) is non empty set
Z is V28() V29() ext-real Element of REAL
(AffineMap (1,0)) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
((AffineMap (1,0)) (#) cosh) | REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((AffineMap (1,0)) (#) cosh) | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
AffineMap (A,Z) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
f2 is V21() V22() V23() V27() V28() V29() V30() ext-real non negative V50() V51() V52() V53() V54() V55() V56() Element of NAT
f2 + 1 is non empty V21() V22() V23() V27() V28() V29() V30() ext-real non negative Element of REAL
A * (f2 + 1) is V28() V29() ext-real Element of REAL
#Z f2 is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z f2) * (AffineMap (A,Z)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
#Z (f2 + 1) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
(#Z (f2 + 1)) * (AffineMap (A,Z)) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
1 / (A * (f2 + 1)) is V28() V29() ext-real Element of REAL
(1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z))) is Relation-like V6() non empty total V18( REAL , REAL ) V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (((#Z f2) * (AffineMap (A,Z))),f1) is V28() V29() ext-real Element of REAL
upper_bound f1 is V28() V29() ext-real Element of REAL
((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) . (upper_bound f1) is V28() V29() ext-real Element of REAL
lower_bound f1 is V28() V29() ext-real Element of REAL
((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) . (lower_bound f1) is V28() V29() ext-real Element of REAL
(((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) . (upper_bound f1)) - (((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) . (lower_bound f1)) is V28() V29() ext-real Element of REAL
dom (AffineMap (A,Z)) is non empty set
((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) `| REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) `| REAL) is set
x is V28() V29() ext-real Element of REAL
(((1 / (A * (f2 + 1))) (#) ((#Z (f2 + 1)) * (AffineMap (A,Z)))) `| REAL) . x is V28() V29() ext-real Element of REAL
((#Z f2) * (AffineMap (A,Z))) . x is V28() V29() ext-real Element of REAL
A * x is V28() V29() ext-real Element of REAL
(A * x) + Z is V28() V29() ext-real Element of REAL
((A * x) + Z) #Z f2 is V28() V29() ext-real Element of REAL
(AffineMap (A,Z)) . x is V28() V29() ext-real Element of REAL
((AffineMap (A,Z)) . x) #Z f2 is V28() V29() ext-real Element of REAL
(#Z f2) . ((AffineMap (A,Z)) . x) is V28() V29() ext-real Element of REAL
dom ((#Z f2) * (AffineMap (A,Z))) is non empty set
x is V28() V29() ext-real Element of REAL
(AffineMap (A,Z)) . x is V28() V29() ext-real Element of REAL
A * x is V28() V29() ext-real Element of REAL
(A * x) + Z is V28() V29() ext-real Element of REAL
x is V28() V29() ext-real Element of REAL
x is V28() V29() ext-real Element of REAL
((#Z f2) * (AffineMap (A,Z))) | REAL is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((#Z f2) * (AffineMap (A,Z))) | f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
A is V51() V52() V53() open Element of K19(REAL)
Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(1 / 2) (#) Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((1 / 2) (#) Z) is set
((1 / 2) (#) Z) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom Z is set
f2 is V28() V29() ext-real Element of REAL
Z `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(Z `| A) . f2 is V28() V29() ext-real Element of REAL
2 * f2 is V28() V29() ext-real Element of REAL
2 - 1 is V28() V29() V30() ext-real Element of REAL
f2 #Z (2 - 1) is V28() V29() ext-real Element of REAL
2 * (f2 #Z (2 - 1)) is V28() V29() ext-real Element of REAL
diff (Z,f2) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(((1 / 2) (#) Z) `| A) . f2 is V28() V29() ext-real Element of REAL
diff (Z,f2) is V28() V29() ext-real Element of REAL
(1 / 2) * (diff (Z,f2)) is V28() V29() ext-real Element of REAL
(Z `| A) . f2 is V28() V29() ext-real Element of REAL
(1 / 2) * ((Z `| A) . f2) is V28() V29() ext-real Element of REAL
2 * f2 is V28() V29() ext-real Element of REAL
(1 / 2) * (2 * f2) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(((1 / 2) (#) Z) `| A) . f2 is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
integral ((id Z),A) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(1 / 2) (#) f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((1 / 2) (#) f2) is set
((1 / 2) (#) f2) . (upper_bound A) is V28() V29() ext-real Element of REAL
((1 / 2) (#) f2) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((1 / 2) (#) f2) . (upper_bound A)) - (((1 / 2) (#) f2) . (lower_bound A)) is V28() V29() ext-real Element of REAL
dom (id Z) is set
(id Z) | A is Relation-like A -defined Z -defined Z -valued V6() V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
((1 / 2) (#) f2) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((1 / 2) (#) f2) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(((1 / 2) (#) f2) `| Z) . f1 is V28() V29() ext-real Element of REAL
(id Z) . f1 is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) ^ is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) ^) . (upper_bound A) is V28() V29() ext-real Element of REAL
((id Z) ^) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((id Z) ^) . (upper_bound A)) - (((id Z) ^) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
((id Z) ^) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id Z) ^) `| Z) is set
x is V28() V29() ext-real Element of REAL
(((id Z) ^) `| Z) . x is V28() V29() ext-real Element of REAL
f2 . x is V28() V29() ext-real Element of REAL
x ^2 is V28() V29() ext-real Element of REAL
K97(x,x) is set
1 / (x ^2) is V28() V29() ext-real Element of REAL
- (1 / (x ^2)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 + f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 / (f1 + f2) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (f2 / (f1 + f2)) is set
(f2 / (f1 + f2)) . (upper_bound A) is V28() V29() ext-real Element of REAL
(f2 / (f1 + f2)) . (lower_bound A) is V28() V29() ext-real Element of REAL
((f2 / (f1 + f2)) . (upper_bound A)) - ((f2 / (f1 + f2)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
x is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom x is set
x | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (x,A) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
f1 . f2 is V28() V29() ext-real Element of REAL
(f2 / (f1 + f2)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((f2 / (f1 + f2)) `| Z) is set
f2 is V28() V29() ext-real Element of REAL
((f2 / (f1 + f2)) `| Z) . f2 is V28() V29() ext-real Element of REAL
x . f2 is V28() V29() ext-real Element of REAL
2 * f2 is V28() V29() ext-real Element of REAL
f2 ^2 is V28() V29() ext-real Element of REAL
K97(f2,f2) is set
1 + (f2 ^2) is V28() V29() ext-real Element of REAL
(1 + (f2 ^2)) ^2 is V28() V29() ext-real Element of REAL
K97((1 + (f2 ^2)),(1 + (f2 ^2))) is set
(2 * f2) / ((1 + (f2 ^2)) ^2) is V28() V29() ext-real Element of REAL
tan + sec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (tan + sec) is set
A is V51() V52() V53() open Element of K19(REAL)
(tan + sec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (cos ^) is set
(dom tan) /\ (dom (cos ^)) is set
Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((tan + sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
1 - (sin . Z) is V28() V29() ext-real Element of REAL
1 / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 + (sin . Z) is V28() V29() ext-real Element of REAL
diff (tan,Z) is V28() V29() ext-real Element of REAL
diff ((cos ^),Z) is V28() V29() ext-real Element of REAL
(diff (tan,Z)) + (diff ((cos ^),Z)) is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
1 / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) + (diff ((cos ^),Z)) is V28() V29() ext-real Element of REAL
(cos ^) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((cos ^) `| A) . Z is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) + (((cos ^) `| A) . Z) is V28() V29() ext-real Element of REAL
(sin . Z) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) + ((sin . Z) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
((cos . Z) ^2) + ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) / ((((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) / (1 - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) * (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) / ((1 + (sin . Z)) * (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
((1 + (sin . Z)) / (1 + (sin . Z))) / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((tan + sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
1 - (sin . Z) is V28() V29() ext-real Element of REAL
1 / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
(tan + sec) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
(tan + sec) . (lower_bound A) is V28() V29() ext-real Element of REAL
((tan + sec) . (upper_bound A)) - ((tan + sec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
1 + (sin . f1) is V28() V29() ext-real Element of REAL
1 - (sin . f1) is V28() V29() ext-real Element of REAL
(tan + sec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((tan + sec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((tan + sec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
1 - (sin . f1) is V28() V29() ext-real Element of REAL
1 / (1 - (sin . f1)) is V28() V29() ext-real Element of REAL
tan - sec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- sec is Relation-like V6() V34() V35() V36() set
K98(1) (#) sec is Relation-like V6() V34() V35() V36() set
tan + (- sec) is Relation-like V6() V34() V35() V36() set
dom (tan - sec) is set
A is V51() V52() V53() open Element of K19(REAL)
(tan - sec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (cos ^) is set
(dom tan) /\ (dom (cos ^)) is set
Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((tan - sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
1 + (sin . Z) is V28() V29() ext-real Element of REAL
1 / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 - (sin . Z) is V28() V29() ext-real Element of REAL
diff (tan,Z) is V28() V29() ext-real Element of REAL
diff ((cos ^),Z) is V28() V29() ext-real Element of REAL
(diff (tan,Z)) - (diff ((cos ^),Z)) is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
1 / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) - (diff ((cos ^),Z)) is V28() V29() ext-real Element of REAL
(cos ^) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((cos ^) `| A) . Z is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) - (((cos ^) `| A) . Z) is V28() V29() ext-real Element of REAL
(sin . Z) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) - ((sin . Z) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
((cos . Z) ^2) + ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(1 - (sin . Z)) / ((((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(1 - (sin . Z)) / (1 - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) * (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
(1 - (sin . Z)) / ((1 + (sin . Z)) * (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
(1 - (sin . Z)) / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
((1 - (sin . Z)) / (1 - (sin . Z))) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((tan - sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
1 + (sin . Z) is V28() V29() ext-real Element of REAL
1 / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
(tan - sec) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
(tan - sec) . (lower_bound A) is V28() V29() ext-real Element of REAL
((tan - sec) . (upper_bound A)) - ((tan - sec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
1 + (sin . f1) is V28() V29() ext-real Element of REAL
1 - (sin . f1) is V28() V29() ext-real Element of REAL
(tan - sec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((tan - sec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((tan - sec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
1 + (sin . f1) is V28() V29() ext-real Element of REAL
1 / (1 + (sin . f1)) is V28() V29() ext-real Element of REAL
- cot is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
K98(1) (#) cot is Relation-like V6() V34() V35() V36() set
(- cot) + cosec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((- cot) + cosec) is set
A is V51() V52() V53() open Element of K19(REAL)
((- cot) + cosec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (- cot) is set
dom (sin ^) is set
(dom (- cot)) /\ (dom (sin ^)) is set
Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(- 1) (#) cot is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((- cot) + cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 + (cos . Z) is V28() V29() ext-real Element of REAL
1 / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
1 - (cos . Z) is V28() V29() ext-real Element of REAL
diff ((- cot),Z) is V28() V29() ext-real Element of REAL
diff ((sin ^),Z) is V28() V29() ext-real Element of REAL
(diff ((- cot),Z)) + (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
((- 1) (#) cot) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((- 1) (#) cot) `| A) . Z is V28() V29() ext-real Element of REAL
((((- 1) (#) cot) `| A) . Z) + (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
diff (cot,Z) is V28() V29() ext-real Element of REAL
(- 1) * (diff (cot,Z)) is V28() V29() ext-real Element of REAL
((- 1) * (diff (cot,Z))) + (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
1 / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(- 1) * (- (1 / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
((- 1) * (- (1 / ((sin . Z) ^2)))) + (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
(sin ^) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin ^) `| A) . Z is V28() V29() ext-real Element of REAL
(1 / ((sin . Z) ^2)) + (((sin ^) `| A) . Z) is V28() V29() ext-real Element of REAL
(cos . Z) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- ((cos . Z) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(1 / ((sin . Z) ^2)) + (- ((cos . Z) / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
(1 / ((sin . Z) ^2)) - ((cos . Z) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
((sin . Z) ^2) + ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 - (cos . Z)) / ((((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 - (cos . Z)) / (1 - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(1 - (cos . Z)) * (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
(1 - (cos . Z)) / ((1 - (cos . Z)) * (1 + (cos . Z))) is V28() V29() ext-real Element of REAL
(1 - (cos . Z)) / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
((1 - (cos . Z)) / (1 - (cos . Z))) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((- cot) + cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 + (cos . Z) is V28() V29() ext-real Element of REAL
1 / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
((- cot) + cosec) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((- cot) + cosec) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((- cot) + cosec) . (upper_bound A)) - (((- cot) + cosec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
1 + (cos . f1) is V28() V29() ext-real Element of REAL
1 - (cos . f1) is V28() V29() ext-real Element of REAL
((- cot) + cosec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((- cot) + cosec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(((- cot) + cosec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
1 + (cos . f1) is V28() V29() ext-real Element of REAL
1 / (1 + (cos . f1)) is V28() V29() ext-real Element of REAL
(- cot) - cosec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- cosec is Relation-like V6() V34() V35() V36() set
(- cot) + (- cosec) is Relation-like V6() V34() V35() V36() set
dom ((- cot) - cosec) is set
A is V51() V52() V53() open Element of K19(REAL)
((- cot) - cosec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (- cot) is set
dom (sin ^) is set
(dom (- cot)) /\ (dom (sin ^)) is set
Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(- 1) (#) cot is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((- cot) - cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 - (cos . Z) is V28() V29() ext-real Element of REAL
1 / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
1 + (cos . Z) is V28() V29() ext-real Element of REAL
diff ((- cot),Z) is V28() V29() ext-real Element of REAL
diff ((sin ^),Z) is V28() V29() ext-real Element of REAL
(diff ((- cot),Z)) - (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
((- 1) (#) cot) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((- 1) (#) cot) `| A) . Z is V28() V29() ext-real Element of REAL
((((- 1) (#) cot) `| A) . Z) - (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
diff (cot,Z) is V28() V29() ext-real Element of REAL
(- 1) * (diff (cot,Z)) is V28() V29() ext-real Element of REAL
((- 1) * (diff (cot,Z))) - (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
1 / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(- 1) * (- (1 / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
((- 1) * (- (1 / ((sin . Z) ^2)))) - (diff ((sin ^),Z)) is V28() V29() ext-real Element of REAL
(sin ^) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((sin ^) `| A) . Z is V28() V29() ext-real Element of REAL
(1 / ((sin . Z) ^2)) - (((sin ^) `| A) . Z) is V28() V29() ext-real Element of REAL
(cos . Z) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- ((cos . Z) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(1 / ((sin . Z) ^2)) - (- ((cos . Z) / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
(1 / ((sin . Z) ^2)) + ((cos . Z) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
((sin . Z) ^2) + ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 + (cos . Z)) / ((((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 + (cos . Z)) / (1 - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(1 + (cos . Z)) * (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
(1 + (cos . Z)) / ((1 + (cos . Z)) * (1 - (cos . Z))) is V28() V29() ext-real Element of REAL
(1 + (cos . Z)) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
((1 + (cos . Z)) / (1 + (cos . Z))) / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
(((- cot) - cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 - (cos . Z) is V28() V29() ext-real Element of REAL
1 / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
((- cot) - cosec) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((- cot) - cosec) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((- cot) - cosec) . (upper_bound A)) - (((- cot) - cosec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
1 + (cos . f1) is V28() V29() ext-real Element of REAL
1 - (cos . f1) is V28() V29() ext-real Element of REAL
((- cot) - cosec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((- cot) - cosec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(((- cot) - cosec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
1 - (cos . f1) is V28() V29() ext-real Element of REAL
1 / (1 - (cos . f1)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
arctan . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
arctan . (lower_bound A) is V28() V29() ext-real Element of REAL
(arctan . (upper_bound A)) - (arctan . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
arctan `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (arctan `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(arctan `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
f1 ^2 is V28() V29() ext-real Element of REAL
K97(f1,f1) is set
1 + (f1 ^2) is V28() V29() ext-real Element of REAL
1 / (1 + (f1 ^2)) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
A (#) arctan is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound Z is V28() V29() ext-real Element of REAL
(A (#) arctan) . (upper_bound Z) is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
(A (#) arctan) . (lower_bound Z) is V28() V29() ext-real Element of REAL
((A (#) arctan) . (upper_bound Z)) - ((A (#) arctan) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
f2 is V51() V52() V53() open Element of K19(REAL)
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f1 is set
f1 | Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f1,Z) is V28() V29() ext-real Element of REAL
(A (#) arctan) `| f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((A (#) arctan) `| f2) is set
x is V28() V29() ext-real Element of REAL
((A (#) arctan) `| f2) . x is V28() V29() ext-real Element of REAL
f1 . x is V28() V29() ext-real Element of REAL
x ^2 is V28() V29() ext-real Element of REAL
K97(x,x) is set
1 + (x ^2) is V28() V29() ext-real Element of REAL
A / (1 + (x ^2)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
arccot . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
arccot . (lower_bound A) is V28() V29() ext-real Element of REAL
(arccot . (upper_bound A)) - (arccot . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
arccot `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (arccot `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(arccot `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
f1 ^2 is V28() V29() ext-real Element of REAL
K97(f1,f1) is set
1 + (f1 ^2) is V28() V29() ext-real Element of REAL
1 / (1 + (f1 ^2)) is V28() V29() ext-real Element of REAL
- (1 / (1 + (f1 ^2))) is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
A (#) arccot is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound Z is V28() V29() ext-real Element of REAL
(A (#) arccot) . (upper_bound Z) is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
(A (#) arccot) . (lower_bound Z) is V28() V29() ext-real Element of REAL
((A (#) arccot) . (upper_bound Z)) - ((A (#) arccot) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
f2 is V51() V52() V53() open Element of K19(REAL)
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f1 is set
f1 | Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f1,Z) is V28() V29() ext-real Element of REAL
(A (#) arccot) `| f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((A (#) arccot) `| f2) is set
x is V28() V29() ext-real Element of REAL
((A (#) arccot) `| f2) . x is V28() V29() ext-real Element of REAL
f1 . x is V28() V29() ext-real Element of REAL
x ^2 is V28() V29() ext-real Element of REAL
K97(x,x) is set
1 + (x ^2) is V28() V29() ext-real Element of REAL
A / (1 + (x ^2)) is V28() V29() ext-real Element of REAL
- (A / (1 + (x ^2))) is V28() V29() ext-real Element of REAL
A is V51() V52() V53() open Element of K19(REAL)
id A is Relation-like A -defined A -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id A) + cot is Relation-like A -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) + cot) - cosec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) + cot) + (- cosec) is Relation-like A -defined V6() V34() V35() V36() set
dom (((id A) + cot) - cosec) is set
(((id A) + cot) - cosec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((id A) + cot) is set
dom cosec is set
(dom ((id A) + cot)) /\ (dom cosec) is set
dom (id A) is set
(dom (id A)) /\ (dom cot) is set
Z is V28() V29() ext-real Element of REAL
(id A) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
((id A) + cot) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((id A) + cot) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
((cos . Z) ^2) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (((cos . Z) ^2) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
diff ((id A),Z) is V28() V29() ext-real Element of REAL
diff (cot,Z) is V28() V29() ext-real Element of REAL
(diff ((id A),Z)) + (diff (cot,Z)) is V28() V29() ext-real Element of REAL
(id A) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) `| A) . Z is V28() V29() ext-real Element of REAL
(((id A) `| A) . Z) + (diff (cot,Z)) is V28() V29() ext-real Element of REAL
1 + (diff (cot,Z)) is V28() V29() ext-real Element of REAL
1 / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
1 + (- (1 / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
1 - (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) / ((sin . Z) ^2)) - (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) - 1 is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) - 1) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) + ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) - (((sin . Z) ^2) + ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) - (((sin . Z) ^2) + ((cos . Z) ^2))) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(- ((cos . Z) ^2)) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) + cot) - cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 + (cos . Z) is V28() V29() ext-real Element of REAL
(cos . Z) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
1 - (cos . Z) is V28() V29() ext-real Element of REAL
diff (((id A) + cot),Z) is V28() V29() ext-real Element of REAL
diff (cosec,Z) is V28() V29() ext-real Element of REAL
(diff (((id A) + cot),Z)) - (diff (cosec,Z)) is V28() V29() ext-real Element of REAL
(((id A) + cot) `| A) . Z is V28() V29() ext-real Element of REAL
((((id A) + cot) `| A) . Z) - (diff (cosec,Z)) is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
((cos . Z) ^2) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (((cos . Z) ^2) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(- (((cos . Z) ^2) / ((sin . Z) ^2))) - (diff (cosec,Z)) is V28() V29() ext-real Element of REAL
cosec `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(cosec `| A) . Z is V28() V29() ext-real Element of REAL
(- (((cos . Z) ^2) / ((sin . Z) ^2))) - ((cosec `| A) . Z) is V28() V29() ext-real Element of REAL
(cos . Z) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- ((cos . Z) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(- (((cos . Z) ^2) / ((sin . Z) ^2))) - (- ((cos . Z) / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
((cos . Z) / ((sin . Z) ^2)) - (((cos . Z) ^2) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(cos . Z) * (cos . Z) is V28() V29() ext-real Element of REAL
(cos . Z) - ((cos . Z) * (cos . Z)) is V28() V29() ext-real Element of REAL
((cos . Z) - ((cos . Z) * (cos . Z))) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(cos . Z) * (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) + ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
((cos . Z) * (1 - (cos . Z))) / ((((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
((cos . Z) * (1 - (cos . Z))) / (1 - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(1 - (cos . Z)) * (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
((cos . Z) * (1 - (cos . Z))) / ((1 - (cos . Z)) * (1 + (cos . Z))) is V28() V29() ext-real Element of REAL
((cos . Z) * (1 - (cos . Z))) / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
(((cos . Z) * (1 - (cos . Z))) / (1 - (cos . Z))) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
(1 - (cos . Z)) / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
(cos . Z) * ((1 - (cos . Z)) / (1 - (cos . Z))) is V28() V29() ext-real Element of REAL
((cos . Z) * ((1 - (cos . Z)) / (1 - (cos . Z)))) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
(cos . Z) * 1 is V28() V29() ext-real Element of REAL
((cos . Z) * 1) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) + cot) - cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
1 + (cos . Z) is V28() V29() ext-real Element of REAL
(cos . Z) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) + cot is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) + cot) - cosec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) + cot) + (- cosec) is Relation-like Z -defined V6() V34() V35() V36() set
dom (((id Z) + cot) - cosec) is set
(((id Z) + cot) - cosec) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) + cot) - cosec) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) + cot) - cosec) . (upper_bound A)) - ((((id Z) + cot) - cosec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
1 + (cos . f1) is V28() V29() ext-real Element of REAL
1 - (cos . f1) is V28() V29() ext-real Element of REAL
(((id Z) + cot) - cosec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) + cot) - cosec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((((id Z) + cot) - cosec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
1 + (cos . f1) is V28() V29() ext-real Element of REAL
(cos . f1) / (1 + (cos . f1)) is V28() V29() ext-real Element of REAL
A is V51() V52() V53() open Element of K19(REAL)
id A is Relation-like A -defined A -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id A) + cot is Relation-like A -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) + cot) + cosec is Relation-like A -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id A) + cot) + cosec) is set
(((id A) + cot) + cosec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((id A) + cot) is set
dom cosec is set
(dom ((id A) + cot)) /\ (dom cosec) is set
dom (id A) is set
(dom (id A)) /\ (dom cot) is set
Z is V28() V29() ext-real Element of REAL
(id A) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
((id A) + cot) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((id A) + cot) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
((cos . Z) ^2) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (((cos . Z) ^2) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
diff ((id A),Z) is V28() V29() ext-real Element of REAL
diff (cot,Z) is V28() V29() ext-real Element of REAL
(diff ((id A),Z)) + (diff (cot,Z)) is V28() V29() ext-real Element of REAL
(id A) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) `| A) . Z is V28() V29() ext-real Element of REAL
(((id A) `| A) . Z) + (diff (cot,Z)) is V28() V29() ext-real Element of REAL
1 + (diff (cot,Z)) is V28() V29() ext-real Element of REAL
1 / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
1 + (- (1 / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
1 - (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) / ((sin . Z) ^2)) - (1 / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) - 1 is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) - 1) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) + ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) - (((sin . Z) ^2) + ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) - (((sin . Z) ^2) + ((cos . Z) ^2))) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(- ((cos . Z) ^2)) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) + cot) + cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) - 1 is V28() V29() ext-real Element of REAL
(cos . Z) / ((cos . Z) - 1) is V28() V29() ext-real Element of REAL
1 + (cos . Z) is V28() V29() ext-real Element of REAL
diff (((id A) + cot),Z) is V28() V29() ext-real Element of REAL
diff (cosec,Z) is V28() V29() ext-real Element of REAL
(diff (((id A) + cot),Z)) + (diff (cosec,Z)) is V28() V29() ext-real Element of REAL
(((id A) + cot) `| A) . Z is V28() V29() ext-real Element of REAL
((((id A) + cot) `| A) . Z) + (diff (cosec,Z)) is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
((cos . Z) ^2) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- (((cos . Z) ^2) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(- (((cos . Z) ^2) / ((sin . Z) ^2))) + (diff (cosec,Z)) is V28() V29() ext-real Element of REAL
cosec `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(cosec `| A) . Z is V28() V29() ext-real Element of REAL
(- (((cos . Z) ^2) / ((sin . Z) ^2))) + ((cosec `| A) . Z) is V28() V29() ext-real Element of REAL
(cos . Z) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- ((cos . Z) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(- (((cos . Z) ^2) / ((sin . Z) ^2))) + (- ((cos . Z) / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) / ((sin . Z) ^2)) + ((cos . Z) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
- ((((cos . Z) ^2) / ((sin . Z) ^2)) + ((cos . Z) / ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
(cos . Z) * (cos . Z) is V28() V29() ext-real Element of REAL
((cos . Z) * (cos . Z)) + (cos . Z) is V28() V29() ext-real Element of REAL
(((cos . Z) * (cos . Z)) + (cos . Z)) / ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
- ((((cos . Z) * (cos . Z)) + (cos . Z)) / ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
(cos . Z) + 1 is V28() V29() ext-real Element of REAL
(cos . Z) * ((cos . Z) + 1) is V28() V29() ext-real Element of REAL
((sin . Z) ^2) + ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
((cos . Z) * ((cos . Z) + 1)) / ((((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
- (((cos . Z) * ((cos . Z) + 1)) / ((((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2))) is V28() V29() ext-real Element of REAL
1 - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
((cos . Z) * ((cos . Z) + 1)) / (1 - ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
- (((cos . Z) * ((cos . Z) + 1)) / (1 - ((cos . Z) ^2))) is V28() V29() ext-real Element of REAL
1 - (cos . Z) is V28() V29() ext-real Element of REAL
(1 + (cos . Z)) * (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
((cos . Z) * ((cos . Z) + 1)) / ((1 + (cos . Z)) * (1 - (cos . Z))) is V28() V29() ext-real Element of REAL
- (((cos . Z) * ((cos . Z) + 1)) / ((1 + (cos . Z)) * (1 - (cos . Z)))) is V28() V29() ext-real Element of REAL
((cos . Z) * ((cos . Z) + 1)) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
(((cos . Z) * ((cos . Z) + 1)) / (1 + (cos . Z))) / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
- ((((cos . Z) * ((cos . Z) + 1)) / (1 + (cos . Z))) / (1 - (cos . Z))) is V28() V29() ext-real Element of REAL
(1 + (cos . Z)) / (1 + (cos . Z)) is V28() V29() ext-real Element of REAL
(cos . Z) * ((1 + (cos . Z)) / (1 + (cos . Z))) is V28() V29() ext-real Element of REAL
((cos . Z) * ((1 + (cos . Z)) / (1 + (cos . Z)))) / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
- (((cos . Z) * ((1 + (cos . Z)) / (1 + (cos . Z)))) / (1 - (cos . Z))) is V28() V29() ext-real Element of REAL
(cos . Z) * 1 is V28() V29() ext-real Element of REAL
((cos . Z) * 1) / (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
- (((cos . Z) * 1) / (1 - (cos . Z))) is V28() V29() ext-real Element of REAL
- (1 - (cos . Z)) is V28() V29() ext-real Element of REAL
(cos . Z) / (- (1 - (cos . Z))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) + cot) + cosec) `| A) . Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) - 1 is V28() V29() ext-real Element of REAL
(cos . Z) / ((cos . Z) - 1) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) + cot is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) + cot) + cosec is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id Z) + cot) + cosec) is set
(((id Z) + cot) + cosec) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) + cot) + cosec) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) + cot) + cosec) . (upper_bound A)) - ((((id Z) + cot) + cosec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
1 + (cos . f1) is V28() V29() ext-real Element of REAL
1 - (cos . f1) is V28() V29() ext-real Element of REAL
(((id Z) + cot) + cosec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) + cot) + cosec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((((id Z) + cot) + cosec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
(cos . f1) - 1 is V28() V29() ext-real Element of REAL
(cos . f1) / ((cos . f1) - 1) is V28() V29() ext-real Element of REAL
A is V51() V52() V53() open Element of K19(REAL)
id A is Relation-like A -defined A -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id A) - tan is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- tan is Relation-like V6() V34() V35() V36() set
K98(1) (#) tan is Relation-like V6() V34() V35() V36() set
(id A) + (- tan) is Relation-like A -defined V6() V34() V35() V36() set
((id A) - tan) + sec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id A) - tan) + sec) is set
(((id A) - tan) + sec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((id A) - tan) is set
dom sec is set
(dom ((id A) - tan)) /\ (dom sec) is set
dom (id A) is set
(dom (id A)) /\ (dom tan) is set
Z is V28() V29() ext-real Element of REAL
(id A) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
((id A) - tan) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((id A) - tan) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
((sin . Z) ^2) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
- (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
diff ((id A),Z) is V28() V29() ext-real Element of REAL
diff (tan,Z) is V28() V29() ext-real Element of REAL
(diff ((id A),Z)) - (diff (tan,Z)) is V28() V29() ext-real Element of REAL
(id A) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) `| A) . Z is V28() V29() ext-real Element of REAL
(((id A) `| A) . Z) - (diff (tan,Z)) is V28() V29() ext-real Element of REAL
1 - (diff (tan,Z)) is V28() V29() ext-real Element of REAL
1 / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
1 - (1 / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
((cos . Z) ^2) + ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) + ((sin . Z) ^2)) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
1 - ((((cos . Z) ^2) + ((sin . Z) ^2)) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
((cos . Z) ^2) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) / ((cos . Z) ^2)) + (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((((cos . Z) ^2) / ((cos . Z) ^2)) + (((sin . Z) ^2) / ((cos . Z) ^2))) is V28() V29() ext-real Element of REAL
1 + (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - (1 + (((sin . Z) ^2) / ((cos . Z) ^2))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) - tan) + sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) + 1 is V28() V29() ext-real Element of REAL
(sin . Z) / ((sin . Z) + 1) is V28() V29() ext-real Element of REAL
1 - (sin . Z) is V28() V29() ext-real Element of REAL
diff (((id A) - tan),Z) is V28() V29() ext-real Element of REAL
diff (sec,Z) is V28() V29() ext-real Element of REAL
(diff (((id A) - tan),Z)) + (diff (sec,Z)) is V28() V29() ext-real Element of REAL
(((id A) - tan) `| A) . Z is V28() V29() ext-real Element of REAL
((((id A) - tan) `| A) . Z) + (diff (sec,Z)) is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
((sin . Z) ^2) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
- (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(- (((sin . Z) ^2) / ((cos . Z) ^2))) + (diff (sec,Z)) is V28() V29() ext-real Element of REAL
sec `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(sec `| A) . Z is V28() V29() ext-real Element of REAL
(- (((sin . Z) ^2) / ((cos . Z) ^2))) + ((sec `| A) . Z) is V28() V29() ext-real Element of REAL
(sin . Z) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(- (((sin . Z) ^2) / ((cos . Z) ^2))) + ((sin . Z) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
((sin . Z) / ((cos . Z) ^2)) - (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(sin . Z) * (sin . Z) is V28() V29() ext-real Element of REAL
(sin . Z) - ((sin . Z) * (sin . Z)) is V28() V29() ext-real Element of REAL
((sin . Z) - ((sin . Z) * (sin . Z))) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(sin . Z) * (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
((cos . Z) ^2) + ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 - (sin . Z))) / ((((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 - (sin . Z))) / (1 - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
1 + (sin . Z) is V28() V29() ext-real Element of REAL
(1 - (sin . Z)) * (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 - (sin . Z))) / ((1 - (sin . Z)) * (1 + (sin . Z))) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 - (sin . Z))) / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
(((sin . Z) * (1 - (sin . Z))) / (1 - (sin . Z))) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
(1 - (sin . Z)) / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
(sin . Z) * ((1 - (sin . Z)) / (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
((sin . Z) * ((1 - (sin . Z)) / (1 - (sin . Z)))) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
(sin . Z) * 1 is V28() V29() ext-real Element of REAL
((sin . Z) * 1) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
(sin . Z) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) - tan) + sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) + 1 is V28() V29() ext-real Element of REAL
(sin . Z) / ((sin . Z) + 1) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) - tan is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- tan is Relation-like V6() V34() V35() V36() set
K98(1) (#) tan is Relation-like V6() V34() V35() V36() set
(id Z) + (- tan) is Relation-like Z -defined V6() V34() V35() V36() set
((id Z) - tan) + sec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id Z) - tan) + sec) is set
(((id Z) - tan) + sec) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) - tan) + sec) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) - tan) + sec) . (upper_bound A)) - ((((id Z) - tan) + sec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
1 + (sin . f1) is V28() V29() ext-real Element of REAL
1 - (sin . f1) is V28() V29() ext-real Element of REAL
(((id Z) - tan) + sec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) - tan) + sec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((((id Z) - tan) + sec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
1 + (sin . f1) is V28() V29() ext-real Element of REAL
(sin . f1) / (1 + (sin . f1)) is V28() V29() ext-real Element of REAL
A is V51() V52() V53() open Element of K19(REAL)
id A is Relation-like A -defined A -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id A) - tan is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- tan is Relation-like V6() V34() V35() V36() set
K98(1) (#) tan is Relation-like V6() V34() V35() V36() set
(id A) + (- tan) is Relation-like A -defined V6() V34() V35() V36() set
((id A) - tan) - sec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) - tan) + (- sec) is Relation-like V6() V34() V35() V36() set
dom (((id A) - tan) - sec) is set
(((id A) - tan) - sec) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((id A) - tan) is set
dom sec is set
(dom ((id A) - tan)) /\ (dom sec) is set
dom (id A) is set
(dom (id A)) /\ (dom tan) is set
Z is V28() V29() ext-real Element of REAL
(id A) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
((id A) - tan) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(((id A) - tan) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
((sin . Z) ^2) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
- (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
diff ((id A),Z) is V28() V29() ext-real Element of REAL
diff (tan,Z) is V28() V29() ext-real Element of REAL
(diff ((id A),Z)) - (diff (tan,Z)) is V28() V29() ext-real Element of REAL
(id A) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) `| A) . Z is V28() V29() ext-real Element of REAL
(((id A) `| A) . Z) - (diff (tan,Z)) is V28() V29() ext-real Element of REAL
1 - (diff (tan,Z)) is V28() V29() ext-real Element of REAL
1 / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
1 - (1 / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
((cos . Z) ^2) + ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) + ((sin . Z) ^2)) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
1 - ((((cos . Z) ^2) + ((sin . Z) ^2)) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
((cos . Z) ^2) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) / ((cos . Z) ^2)) + (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((((cos . Z) ^2) / ((cos . Z) ^2)) + (((sin . Z) ^2) / ((cos . Z) ^2))) is V28() V29() ext-real Element of REAL
1 + (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - (1 + (((sin . Z) ^2) / ((cos . Z) ^2))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) - tan) - sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) - 1 is V28() V29() ext-real Element of REAL
(sin . Z) / ((sin . Z) - 1) is V28() V29() ext-real Element of REAL
1 + (sin . Z) is V28() V29() ext-real Element of REAL
diff (((id A) - tan),Z) is V28() V29() ext-real Element of REAL
diff (sec,Z) is V28() V29() ext-real Element of REAL
(diff (((id A) - tan),Z)) - (diff (sec,Z)) is V28() V29() ext-real Element of REAL
(((id A) - tan) `| A) . Z is V28() V29() ext-real Element of REAL
((((id A) - tan) `| A) . Z) - (diff (sec,Z)) is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
((sin . Z) ^2) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
- (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(- (((sin . Z) ^2) / ((cos . Z) ^2))) - (diff (sec,Z)) is V28() V29() ext-real Element of REAL
sec `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(sec `| A) . Z is V28() V29() ext-real Element of REAL
(- (((sin . Z) ^2) / ((cos . Z) ^2))) - ((sec `| A) . Z) is V28() V29() ext-real Element of REAL
(sin . Z) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(- (((sin . Z) ^2) / ((cos . Z) ^2))) - ((sin . Z) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
((sin . Z) / ((cos . Z) ^2)) + (((sin . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
- (((sin . Z) / ((cos . Z) ^2)) + (((sin . Z) ^2) / ((cos . Z) ^2))) is V28() V29() ext-real Element of REAL
(sin . Z) + ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) + ((sin . Z) ^2)) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
- (((sin . Z) + ((sin . Z) ^2)) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
(sin . Z) * (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
((cos . Z) ^2) + ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
(((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 + (sin . Z))) / ((((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
- (((sin . Z) * (1 + (sin . Z))) / ((((cos . Z) ^2) + ((sin . Z) ^2)) - ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
1 - ((sin . Z) ^2) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 + (sin . Z))) / (1 - ((sin . Z) ^2)) is V28() V29() ext-real Element of REAL
- (((sin . Z) * (1 + (sin . Z))) / (1 - ((sin . Z) ^2))) is V28() V29() ext-real Element of REAL
1 - (sin . Z) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) * (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 + (sin . Z))) / ((1 + (sin . Z)) * (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
- (((sin . Z) * (1 + (sin . Z))) / ((1 + (sin . Z)) * (1 - (sin . Z)))) is V28() V29() ext-real Element of REAL
((sin . Z) * (1 + (sin . Z))) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
(((sin . Z) * (1 + (sin . Z))) / (1 + (sin . Z))) / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
- ((((sin . Z) * (1 + (sin . Z))) / (1 + (sin . Z))) / (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
(1 + (sin . Z)) / (1 + (sin . Z)) is V28() V29() ext-real Element of REAL
(sin . Z) * ((1 + (sin . Z)) / (1 + (sin . Z))) is V28() V29() ext-real Element of REAL
((sin . Z) * ((1 + (sin . Z)) / (1 + (sin . Z)))) / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
- (((sin . Z) * ((1 + (sin . Z)) / (1 + (sin . Z)))) / (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
(sin . Z) * 1 is V28() V29() ext-real Element of REAL
((sin . Z) * 1) / (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
- (((sin . Z) * 1) / (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
- (1 - (sin . Z)) is V28() V29() ext-real Element of REAL
(sin . Z) / (- (1 - (sin . Z))) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((((id A) - tan) - sec) `| A) . Z is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) - 1 is V28() V29() ext-real Element of REAL
(sin . Z) / ((sin . Z) - 1) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) - tan is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- tan is Relation-like V6() V34() V35() V36() set
K98(1) (#) tan is Relation-like V6() V34() V35() V36() set
(id Z) + (- tan) is Relation-like Z -defined V6() V34() V35() V36() set
((id Z) - tan) - sec is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) - tan) + (- sec) is Relation-like V6() V34() V35() V36() set
dom (((id Z) - tan) - sec) is set
(((id Z) - tan) - sec) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) - tan) - sec) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) - tan) - sec) . (upper_bound A)) - ((((id Z) - tan) - sec) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
1 + (sin . f1) is V28() V29() ext-real Element of REAL
1 - (sin . f1) is V28() V29() ext-real Element of REAL
(((id Z) - tan) - sec) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) - tan) - sec) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((((id Z) - tan) - sec) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
(sin . f1) - 1 is V28() V29() ext-real Element of REAL
(sin . f1) / ((sin . f1) - 1) is V28() V29() ext-real Element of REAL
A is V51() V52() V53() open Element of K19(REAL)
id A is Relation-like A -defined A -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
tan - (id A) is Relation-like A -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- (id A) is Relation-like A -defined V6() total V34() V35() V36() set
K98(1) (#) (id A) is Relation-like A -defined V6() total V34() V35() V36() set
tan + (- (id A)) is Relation-like A -defined V6() V34() V35() V36() set
dom (tan - (id A)) is set
(tan - (id A)) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
Z is V28() V29() ext-real Element of REAL
(id A) . Z is V28() V29() ext-real Element of REAL
1 * Z is V28() V29() ext-real Element of REAL
(1 * Z) + 0 is V28() V29() ext-real Element of REAL
dom (id A) is set
(dom tan) /\ (dom (id A)) is set
Z is V28() V29() ext-real Element of REAL
cos . Z is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((tan - (id A)) `| A) . Z is V28() V29() ext-real Element of REAL
tan . Z is V28() V29() ext-real Element of REAL
(tan . Z) ^2 is V28() V29() ext-real Element of REAL
K97((tan . Z),(tan . Z)) is set
cos . Z is V28() V29() ext-real Element of REAL
(cos . Z) ^2 is V28() V29() ext-real Element of REAL
K97((cos . Z),(cos . Z)) is set
diff (tan,Z) is V28() V29() ext-real Element of REAL
diff ((id A),Z) is V28() V29() ext-real Element of REAL
(diff (tan,Z)) - (diff ((id A),Z)) is V28() V29() ext-real Element of REAL
1 / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) - (diff ((id A),Z)) is V28() V29() ext-real Element of REAL
(id A) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) `| A) . Z is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) - (((id A) `| A) . Z) is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) - 1 is V28() V29() ext-real Element of REAL
((cos . Z) ^2) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 / ((cos . Z) ^2)) - (((cos . Z) ^2) / ((cos . Z) ^2)) is V28() V29() ext-real Element of REAL
1 - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(1 - ((cos . Z) ^2)) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
sin . Z is V28() V29() ext-real Element of REAL
(sin . Z) ^2 is V28() V29() ext-real Element of REAL
K97((sin . Z),(sin . Z)) is set
((sin . Z) ^2) + ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
(((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
((((sin . Z) ^2) + ((cos . Z) ^2)) - ((cos . Z) ^2)) / ((cos . Z) ^2) is V28() V29() ext-real Element of REAL
sin Z is V28() V29() ext-real Element of REAL
cos Z is V28() V29() ext-real Element of REAL
(sin Z) / (cos Z) is V28() V29() ext-real Element of REAL
(sin . Z) / (cos . Z) is V28() V29() ext-real Element of REAL
((sin Z) / (cos Z)) * ((sin . Z) / (cos . Z)) is V28() V29() ext-real Element of REAL
tan Z is V28() V29() ext-real Element of REAL
sin Z is set
cos Z is set
K101((sin Z),(cos Z)) is set
(tan . Z) * (tan Z) is V28() V29() ext-real Element of REAL
Z is V28() V29() ext-real Element of REAL
((tan - (id A)) `| A) . Z is V28() V29() ext-real Element of REAL
tan . Z is V28() V29() ext-real Element of REAL
(tan . Z) ^2 is V28() V29() ext-real Element of REAL
K97((tan . Z),(tan . Z)) is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
tan - (id Z) is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
K98(1) (#) (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
tan + (- (id Z)) is Relation-like Z -defined V6() V34() V35() V36() set
dom (tan - (id Z)) is set
(tan - (id Z)) . (upper_bound A) is V28() V29() ext-real Element of REAL
(tan - (id Z)) . (lower_bound A) is V28() V29() ext-real Element of REAL
((tan - (id Z)) . (upper_bound A)) - ((tan - (id Z)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
(tan - (id Z)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((tan - (id Z)) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((tan - (id Z)) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
tan . f1 is V28() V29() ext-real Element of REAL
(tan . f1) ^2 is V28() V29() ext-real Element of REAL
K97((tan . f1),(tan . f1)) is set
A is V51() V52() V53() open Element of K19(REAL)
id A is Relation-like A -defined A -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(- cot) - (id A) is Relation-like A -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- (id A) is Relation-like A -defined V6() total V34() V35() V36() set
K98(1) (#) (id A) is Relation-like A -defined V6() total V34() V35() V36() set
(- cot) + (- (id A)) is Relation-like A -defined V6() V34() V35() V36() set
dom ((- cot) - (id A)) is set
((- cot) - (id A)) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(id A) . f2 is V28() V29() ext-real Element of REAL
1 * f2 is V28() V29() ext-real Element of REAL
(1 * f2) + 0 is V28() V29() ext-real Element of REAL
dom (- cot) is set
dom (id A) is set
(dom (- cot)) /\ (dom (id A)) is set
f2 is V28() V29() ext-real Element of REAL
sin . f2 is V28() V29() ext-real Element of REAL
(- 1) (#) cot is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is V28() V29() ext-real Element of REAL
(((- cot) - (id A)) `| A) . f2 is V28() V29() ext-real Element of REAL
cot . f2 is V28() V29() ext-real Element of REAL
(cot . f2) ^2 is V28() V29() ext-real Element of REAL
K97((cot . f2),(cot . f2)) is set
sin . f2 is V28() V29() ext-real Element of REAL
(sin . f2) ^2 is V28() V29() ext-real Element of REAL
K97((sin . f2),(sin . f2)) is set
diff ((- cot),f2) is V28() V29() ext-real Element of REAL
diff ((id A),f2) is V28() V29() ext-real Element of REAL
(diff ((- cot),f2)) - (diff ((id A),f2)) is V28() V29() ext-real Element of REAL
((- 1) (#) cot) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((- 1) (#) cot) `| A) . f2 is V28() V29() ext-real Element of REAL
((((- 1) (#) cot) `| A) . f2) - (diff ((id A),f2)) is V28() V29() ext-real Element of REAL
diff (cot,f2) is V28() V29() ext-real Element of REAL
(- 1) * (diff (cot,f2)) is V28() V29() ext-real Element of REAL
((- 1) * (diff (cot,f2))) - (diff ((id A),f2)) is V28() V29() ext-real Element of REAL
1 / ((sin . f2) ^2) is V28() V29() ext-real Element of REAL
- (1 / ((sin . f2) ^2)) is V28() V29() ext-real Element of REAL
(- 1) * (- (1 / ((sin . f2) ^2))) is V28() V29() ext-real Element of REAL
((- 1) * (- (1 / ((sin . f2) ^2)))) - (diff ((id A),f2)) is V28() V29() ext-real Element of REAL
(id A) `| A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id A) `| A) . f2 is V28() V29() ext-real Element of REAL
(1 / ((sin . f2) ^2)) - (((id A) `| A) . f2) is V28() V29() ext-real Element of REAL
(1 / ((sin . f2) ^2)) - 1 is V28() V29() ext-real Element of REAL
((sin . f2) ^2) / ((sin . f2) ^2) is V28() V29() ext-real Element of REAL
(1 / ((sin . f2) ^2)) - (((sin . f2) ^2) / ((sin . f2) ^2)) is V28() V29() ext-real Element of REAL
1 - ((sin . f2) ^2) is V28() V29() ext-real Element of REAL
(1 - ((sin . f2) ^2)) / ((sin . f2) ^2) is V28() V29() ext-real Element of REAL
cos . f2 is V28() V29() ext-real Element of REAL
(cos . f2) ^2 is V28() V29() ext-real Element of REAL
K97((cos . f2),(cos . f2)) is set
((cos . f2) ^2) + ((sin . f2) ^2) is V28() V29() ext-real Element of REAL
(((cos . f2) ^2) + ((sin . f2) ^2)) - ((sin . f2) ^2) is V28() V29() ext-real Element of REAL
((((cos . f2) ^2) + ((sin . f2) ^2)) - ((sin . f2) ^2)) / ((sin . f2) ^2) is V28() V29() ext-real Element of REAL
cos f2 is V28() V29() ext-real Element of REAL
sin f2 is V28() V29() ext-real Element of REAL
(cos f2) / (sin f2) is V28() V29() ext-real Element of REAL
(cos . f2) / (sin . f2) is V28() V29() ext-real Element of REAL
((cos f2) / (sin f2)) * ((cos . f2) / (sin . f2)) is V28() V29() ext-real Element of REAL
cot f2 is V28() V29() ext-real Element of REAL
cos f2 is set
sin f2 is set
K101((cos f2),(sin f2)) is set
(cot . f2) * (cot f2) is V28() V29() ext-real Element of REAL
f2 is V28() V29() ext-real Element of REAL
(((- cot) - (id A)) `| A) . f2 is V28() V29() ext-real Element of REAL
cot . f2 is V28() V29() ext-real Element of REAL
(cot . f2) ^2 is V28() V29() ext-real Element of REAL
K97((cot . f2),(cot . f2)) is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(- cot) - (id Z) is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
K98(1) (#) (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
(- cot) + (- (id Z)) is Relation-like Z -defined V6() V34() V35() V36() set
dom ((- cot) - (id Z)) is set
((- cot) - (id Z)) . (upper_bound A) is V28() V29() ext-real Element of REAL
((- cot) - (id Z)) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((- cot) - (id Z)) . (upper_bound A)) - (((- cot) - (id Z)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
((- cot) - (id Z)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((- cot) - (id Z)) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(((- cot) - (id Z)) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
cot . f1 is V28() V29() ext-real Element of REAL
(cot . f1) ^2 is V28() V29() ext-real Element of REAL
K97((cot . f1),(cot . f1)) is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
tan . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
tan . (lower_bound A) is V28() V29() ext-real Element of REAL
(tan . (upper_bound A)) - (tan . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
tan `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (tan `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(tan `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
(cos . f1) ^2 is V28() V29() ext-real Element of REAL
K97((cos . f1),(cos . f1)) is set
1 / ((cos . f1) ^2) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
cot . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
cot . (lower_bound A) is V28() V29() ext-real Element of REAL
(cot . (upper_bound A)) - (cot . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
cot `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (cot `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(cot `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
(sin . f1) ^2 is V28() V29() ext-real Element of REAL
K97((sin . f1),(sin . f1)) is set
1 / ((sin . f1) ^2) is V28() V29() ext-real Element of REAL
- (1 / ((sin . f1) ^2)) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
sec - (id Z) is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
K98(1) (#) (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
sec + (- (id Z)) is Relation-like Z -defined V6() V34() V35() V36() set
dom (sec - (id Z)) is set
(sec - (id Z)) . (upper_bound A) is V28() V29() ext-real Element of REAL
(sec - (id Z)) . (lower_bound A) is V28() V29() ext-real Element of REAL
((sec - (id Z)) . (upper_bound A)) - ((sec - (id Z)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
(sec - (id Z)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((sec - (id Z)) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((sec - (id Z)) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
(cos . f1) ^2 is V28() V29() ext-real Element of REAL
K97((cos . f1),(cos . f1)) is set
(sin . f1) - ((cos . f1) ^2) is V28() V29() ext-real Element of REAL
((sin . f1) - ((cos . f1) ^2)) / ((cos . f1) ^2) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(- cosec) - (id Z) is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
K98(1) (#) (id Z) is Relation-like Z -defined V6() total V34() V35() V36() set
(- cosec) + (- (id Z)) is Relation-like Z -defined V6() V34() V35() V36() set
dom ((- cosec) - (id Z)) is set
((- cosec) - (id Z)) . (upper_bound A) is V28() V29() ext-real Element of REAL
((- cosec) - (id Z)) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((- cosec) - (id Z)) . (upper_bound A)) - (((- cosec) - (id Z)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
((- cosec) - (id Z)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((- cosec) - (id Z)) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(((- cosec) - (id Z)) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
cos . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
(sin . f1) ^2 is V28() V29() ext-real Element of REAL
K97((sin . f1),(sin . f1)) is set
(cos . f1) - ((sin . f1) ^2) is V28() V29() ext-real Element of REAL
((cos . f1) - ((sin . f1) ^2)) / ((sin . f1) ^2) is V28() V29() ext-real Element of REAL
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
cot | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (cot,A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
(ln * sin) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
(ln * sin) . (lower_bound A) is V28() V29() ext-real Element of REAL
((ln * sin) . (upper_bound A)) - ((ln * sin) . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
(ln * sin) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((ln * sin) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
((ln * sin) `| Z) . f1 is V28() V29() ext-real Element of REAL
cot . f1 is V28() V29() ext-real Element of REAL
sin . f1 is V28() V29() ext-real Element of REAL
cot f1 is V28() V29() ext-real Element of REAL
cos f1 is set
cos . f1 is V28() V29() ext-real Element of REAL
sin f1 is set
K101((cos f1),(sin f1)) is set
dom ((1 / 2) (#) ((#Z 2) * arcsin)) is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
((1 / 2) (#) ((#Z 2) * arcsin)) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((1 / 2) (#) ((#Z 2) * arcsin)) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((1 / 2) (#) ((#Z 2) * arcsin)) . (upper_bound A)) - (((1 / 2) (#) ((#Z 2) * arcsin)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
((1 / 2) (#) ((#Z 2) * arcsin)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((1 / 2) (#) ((#Z 2) * arcsin)) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(((1 / 2) (#) ((#Z 2) * arcsin)) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
arcsin . f1 is V28() V29() ext-real Element of REAL
f1 ^2 is V28() V29() ext-real Element of REAL
K97(f1,f1) is set
1 - (f1 ^2) is V28() V29() ext-real Element of REAL
sqrt (1 - (f1 ^2)) is V28() V29() ext-real Element of REAL
(arcsin . f1) / (sqrt (1 - (f1 ^2))) is V28() V29() ext-real Element of REAL
dom ((1 / 2) (#) ((#Z 2) * arccos)) is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound A is V28() V29() ext-real Element of REAL
((1 / 2) (#) ((#Z 2) * arccos)) . (upper_bound A) is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
((1 / 2) (#) ((#Z 2) * arccos)) . (lower_bound A) is V28() V29() ext-real Element of REAL
(((1 / 2) (#) ((#Z 2) * arccos)) . (upper_bound A)) - (((1 / 2) (#) ((#Z 2) * arccos)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom f2 is set
f2 | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral (f2,A) is V28() V29() ext-real Element of REAL
((1 / 2) (#) ((#Z 2) * arccos)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((1 / 2) (#) ((#Z 2) * arccos)) `| Z) is set
f1 is V28() V29() ext-real Element of REAL
(((1 / 2) (#) ((#Z 2) * arccos)) `| Z) . f1 is V28() V29() ext-real Element of REAL
f2 . f1 is V28() V29() ext-real Element of REAL
arccos . f1 is V28() V29() ext-real Element of REAL
f1 ^2 is V28() V29() ext-real Element of REAL
K97(f1,f1) is set
1 - (f1 ^2) is V28() V29() ext-real Element of REAL
sqrt (1 - (f1 ^2)) is V28() V29() ext-real Element of REAL
(arccos . f1) / (sqrt (1 - (f1 ^2))) is V28() V29() ext-real Element of REAL
- ((arccos . f1) / (sqrt (1 - (f1 ^2)))) is V28() V29() ext-real Element of REAL
dom arcsin is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (arcsin,A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) (#) arcsin is Relation-like Z -defined V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(#R (1 / 2)) * f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) (#) arcsin) + ((#R (1 / 2)) * f2) is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) is set
(((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) . (upper_bound A)) - ((((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
x is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 - x is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- x is Relation-like V6() V34() V35() V36() set
K98(1) (#) x is Relation-like V6() V34() V35() V36() set
f1 + (- x) is Relation-like V6() V34() V35() V36() set
arcsin | A is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) `| Z) is set
f2 is V28() V29() ext-real Element of REAL
((((id Z) (#) arcsin) + ((#R (1 / 2)) * f2)) `| Z) . f2 is V28() V29() ext-real Element of REAL
arcsin . f2 is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
A ^2 is V28() V29() ext-real Element of REAL
K97(A,A) is set
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound Z is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
f2 is V51() V52() V53() open Element of K19(REAL)
id f2 is Relation-like f2 -defined f2 -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(#R (1 / 2)) * f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
x is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
x - f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- f2 is Relation-like V6() V34() V35() V36() set
K98(1) (#) f2 is Relation-like V6() V34() V35() V36() set
x + (- f2) is Relation-like V6() V34() V35() V36() set
f3 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
arcsin * f3 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (arcsin * f3) is set
(id f2) (#) (arcsin * f3) is Relation-like f2 -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1) is Relation-like f2 -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) is set
(arcsin * f3) | Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral ((arcsin * f3),Z) is V28() V29() ext-real Element of REAL
(((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) . (upper_bound Z) is V28() V29() ext-real Element of REAL
(((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) . (lower_bound Z) is V28() V29() ext-real Element of REAL
((((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) . (upper_bound Z)) - ((((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
(((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) `| f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) `| f2) is set
x is V28() V29() ext-real Element of REAL
((((id f2) (#) (arcsin * f3)) + ((#R (1 / 2)) * f1)) `| f2) . x is V28() V29() ext-real Element of REAL
(arcsin * f3) . x is V28() V29() ext-real Element of REAL
x / A is V28() V29() ext-real Element of REAL
arcsin . (x / A) is V28() V29() ext-real Element of REAL
f3 . x is V28() V29() ext-real Element of REAL
arcsin . (f3 . x) is V28() V29() ext-real Element of REAL
dom arccos is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (arccos,A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) (#) arccos is Relation-like Z -defined V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(#R (1 / 2)) * f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) (#) arccos) - ((#R (1 / 2)) * f2) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- ((#R (1 / 2)) * f2) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((#R (1 / 2)) * f2) is Relation-like V6() V34() V35() V36() set
((id Z) (#) arccos) + (- ((#R (1 / 2)) * f2)) is Relation-like Z -defined V6() V34() V35() V36() set
dom (((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) is set
(((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) . (upper_bound A)) - ((((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) . (lower_bound A)) is V28() V29() ext-real Element of REAL
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
x is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 - x is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- x is Relation-like V6() V34() V35() V36() set
K98(1) (#) x is Relation-like V6() V34() V35() V36() set
f1 + (- x) is Relation-like V6() V34() V35() V36() set
arccos | A is Relation-like V6() V34() V35() V36() continuous Element of K19(K20(REAL,REAL))
(((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) `| Z) is set
f2 is V28() V29() ext-real Element of REAL
((((id Z) (#) arccos) - ((#R (1 / 2)) * f2)) `| Z) . f2 is V28() V29() ext-real Element of REAL
arccos . f2 is V28() V29() ext-real Element of REAL
A is V28() V29() ext-real Element of REAL
A ^2 is V28() V29() ext-real Element of REAL
K97(A,A) is set
Z is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
upper_bound Z is V28() V29() ext-real Element of REAL
lower_bound Z is V28() V29() ext-real Element of REAL
f2 is V51() V52() V53() open Element of K19(REAL)
id f2 is Relation-like f2 -defined f2 -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(#R (1 / 2)) * f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
x is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
x - f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- f2 is Relation-like V6() V34() V35() V36() set
K98(1) (#) f2 is Relation-like V6() V34() V35() V36() set
x + (- f2) is Relation-like V6() V34() V35() V36() set
f3 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
arccos * f3 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (arccos * f3) is set
(id f2) (#) (arccos * f3) is Relation-like f2 -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- ((#R (1 / 2)) * f1) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((#R (1 / 2)) * f1) is Relation-like V6() V34() V35() V36() set
((id f2) (#) (arccos * f3)) + (- ((#R (1 / 2)) * f1)) is Relation-like f2 -defined V6() V34() V35() V36() set
dom (((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) is set
(arccos * f3) | Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
integral ((arccos * f3),Z) is V28() V29() ext-real Element of REAL
(((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) . (upper_bound Z) is V28() V29() ext-real Element of REAL
(((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) . (lower_bound Z) is V28() V29() ext-real Element of REAL
((((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) . (upper_bound Z)) - ((((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) . (lower_bound Z)) is V28() V29() ext-real Element of REAL
(((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) `| f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) `| f2) is set
x is V28() V29() ext-real Element of REAL
((((id f2) (#) (arccos * f3)) - ((#R (1 / 2)) * f1)) `| f2) . x is V28() V29() ext-real Element of REAL
(arccos * f3) . x is V28() V29() ext-real Element of REAL
x / A is V28() V29() ext-real Element of REAL
arccos . (x / A) is V28() V29() ext-real Element of REAL
f3 . x is V28() V29() ext-real Element of REAL
arccos . (f3 . x) is V28() V29() ext-real Element of REAL
dom arctan is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (arctan,A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) (#) arctan is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 + f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
ln * (f1 + f2) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(1 / 2) (#) (ln * (f1 + f2)) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2))) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
- ((1 / 2) (#) (ln * (f1 + f2))) is Relation-like V6() V34() V35() V36() set
K98(1) (#) ((1 / 2) (#) (ln * (f1 + f2))) is Relation-like V6() V34() V35() V36() set
((id Z) (#) arctan) + (- ((1 / 2) (#) (ln * (f1 + f2)))) is Relation-like Z -defined V6() V34() V35() V36() set
dom (((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) is set
(((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) . (upper_bound A)) - ((((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) . (lower_bound A)) is V28() V29() ext-real Element of REAL
arctan | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) `| Z) is set
x is V28() V29() ext-real Element of REAL
((((id Z) (#) arctan) - ((1 / 2) (#) (ln * (f1 + f2)))) `| Z) . x is V28() V29() ext-real Element of REAL
arctan . x is V28() V29() ext-real Element of REAL
dom arccot is set
A is non empty V51() V52() V53() closed_interval V76() Element of K19(REAL)
integral (arccot,A) is V28() V29() ext-real Element of REAL
upper_bound A is V28() V29() ext-real Element of REAL
lower_bound A is V28() V29() ext-real Element of REAL
Z is V51() V52() V53() open Element of K19(REAL)
id Z is Relation-like Z -defined Z -valued V6() total V34() V35() V36() continuous V49() Element of K19(K20(REAL,REAL))
(id Z) (#) arccot is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
f1 + f2 is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
ln * (f1 + f2) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(1 / 2) (#) (ln * (f1 + f2)) is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2))) is Relation-like Z -defined V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom (((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) is set
(((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) . (upper_bound A) is V28() V29() ext-real Element of REAL
(((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) . (lower_bound A) is V28() V29() ext-real Element of REAL
((((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) . (upper_bound A)) - ((((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) . (lower_bound A)) is V28() V29() ext-real Element of REAL
arccot | A is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
(((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) `| Z is Relation-like V6() V34() V35() V36() Element of K19(K20(REAL,REAL))
dom ((((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) `| Z) is set
x is V28() V29() ext-real Element of REAL
((((id Z) (#) arccot) + ((1 / 2) (#) (ln * (f1 + f2)))) `| Z) . x is V28() V29() ext-real Element of REAL
arccot . x is V28() V29() ext-real Element of REAL