:: JGRAPH_7 semantic presentation

REAL is V160() V161() V162() V166() set
NAT is V160() V161() V162() V163() V164() V165() V166() Element of K6(REAL)
K6(REAL) is set
omega is V160() V161() V162() V163() V164() V165() V166() set
K6(omega) is set
K217() is non empty strict TopSpace-like TopStruct
the carrier of K217() is non empty set
1 is non empty natural V11() real ext-real positive V112() V113() V160() V161() V162() V163() V164() V165() Element of NAT
K7(1,1) is set
K6(K7(1,1)) is set
K7(K7(1,1),1) is set
K6(K7(K7(1,1),1)) is set
K7(K7(1,1),REAL) is set
K6(K7(K7(1,1),REAL)) is set
K7(REAL,REAL) is set
K7(K7(REAL,REAL),REAL) is set
K6(K7(K7(REAL,REAL),REAL)) is set
2 is non empty natural V11() real ext-real positive V112() V113() V160() V161() V162() V163() V164() V165() Element of NAT
K7(2,2) is set
K7(K7(2,2),REAL) is set
K6(K7(K7(2,2),REAL)) is set
K245() is V94() L7()
K255() is TopSpace-like TopStruct
K6(NAT) is set
COMPLEX is V160() V166() set
RAT is V160() V161() V162() V163() V166() set
INT is V160() V161() V162() V163() V164() V166() set
K6(K7(REAL,REAL)) is set
TOP-REAL 2 is non empty TopSpace-like V126() V172() V173() V174() V175() V176() V177() V178() strict RLTopStruct
the carrier of (TOP-REAL 2) is non empty set
K6( the carrier of (TOP-REAL 2)) is set
K7( the carrier of (TOP-REAL 2),REAL) is set
K6(K7( the carrier of (TOP-REAL 2),REAL)) is set
NonZero (TOP-REAL 2) is Element of K6( the carrier of (TOP-REAL 2))
[#] (TOP-REAL 2) is non empty non proper Element of K6( the carrier of (TOP-REAL 2))
K136((TOP-REAL 2)) is V43(2) V52( TOP-REAL 2) V109() V152() Element of the carrier of (TOP-REAL 2)
the ZeroF of (TOP-REAL 2) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
{K136((TOP-REAL 2))} is non empty set
([#] (TOP-REAL 2)) \ {K136((TOP-REAL 2))} is Element of K6( the carrier of (TOP-REAL 2))
K7((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2))) is set
K6(K7((NonZero (TOP-REAL 2)),(NonZero (TOP-REAL 2)))) is set
K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)) is set
K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2))) is set
K7(COMPLEX,COMPLEX) is set
K6(K7(COMPLEX,COMPLEX)) is set
K7(K7(COMPLEX,COMPLEX),COMPLEX) is set
K6(K7(K7(COMPLEX,COMPLEX),COMPLEX)) is set
K7(RAT,RAT) is set
K6(K7(RAT,RAT)) is set
K7(K7(RAT,RAT),RAT) is set
K6(K7(K7(RAT,RAT),RAT)) is set
K7(INT,INT) is set
K6(K7(INT,INT)) is set
K7(K7(INT,INT),INT) is set
K6(K7(K7(INT,INT),INT)) is set
K7(NAT,NAT) is set
K7(K7(NAT,NAT),NAT) is set
K6(K7(K7(NAT,NAT),NAT)) is set
{} is empty V160() V161() V162() V163() V164() V165() V166() set
0 is empty natural V11() real ext-real V112() V113() V160() V161() V162() V163() V164() V165() V166() Element of NAT
K62(0,1) is V160() V161() V162() Element of K6(REAL)
I[01] is non empty strict TopSpace-like SubSpace of K255()
the carrier of I[01] is non empty set
- 1 is V11() real ext-real set
- 1 is V11() real ext-real Element of REAL
rectangle ((- 1),1,(- 1),1) is Element of K6( the carrier of (TOP-REAL 2))
K7( the carrier of I[01], the carrier of (TOP-REAL 2)) is set
K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2))) is set
closed_inside_of_rectangle ((- 1),1,(- 1),1) is Element of K6( the carrier of (TOP-REAL 2))
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p3 is V11() real ext-real set
|[p1,p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p2,p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p1,p3]|,|[p2,p3]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[p1,p3]|) + (b₁ * |[p2,p3]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
(p4 `1) - p1 is V11() real ext-real Element of REAL
p2 - p1 is V11() real ext-real set
((p4 `1) - p1) / (p2 - p1) is V11() real ext-real Element of REAL
a is V11() real ext-real Element of REAL
(p2 - p1) / (p2 - p1) is V11() real ext-real set
1 - a is V11() real ext-real Element of REAL
(1 - a) * |[p1,p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a * |[p2,p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((1 - a) * |[p1,p3]|) + (a * |[p2,p3]|) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(1 - a) * p1 is V11() real ext-real Element of REAL
(1 - a) * p3 is V11() real ext-real Element of REAL
|[((1 - a) * p1),((1 - a) * p3)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[((1 - a) * p1),((1 - a) * p3)]| + (a * |[p2,p3]|) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a * p2 is V11() real ext-real Element of REAL
a * p3 is V11() real ext-real Element of REAL
|[(a * p2),(a * p3)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[((1 - a) * p1),((1 - a) * p3)]| + |[(a * p2),(a * p3)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((1 - a) * p1) + (a * p2) is V11() real ext-real Element of REAL
((1 - a) * p3) + (a * p3) is V11() real ext-real Element of REAL
|[(((1 - a) * p1) + (a * p2)),(((1 - a) * p3) + (a * p3))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a * (p2 - p1) is V11() real ext-real Element of REAL
p1 + (a * (p2 - p1)) is V11() real ext-real Element of REAL
|[(p1 + (a * (p2 - p1))),p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 + ((p4 `1) - p1) is V11() real ext-real Element of REAL
|[(p1 + ((p4 `1) - p1)),p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 is natural V11() real ext-real V112() V113() V160() V161() V162() V163() V164() V165() Element of NAT
TOP-REAL p1 is non empty TopSpace-like V126() V172() V173() V174() V175() V176() V177() V178() strict RLTopStruct
the carrier of (TOP-REAL p1) is non empty set
K6( the carrier of (TOP-REAL p1)) is set
K7( the carrier of I[01], the carrier of (TOP-REAL p1)) is set
K6(K7( the carrier of I[01], the carrier of (TOP-REAL p1))) is set
p2 is Element of K6( the carrier of (TOP-REAL p1))
p3 is V43(p1) V109() V152() Element of the carrier of (TOP-REAL p1)
p4 is V43(p1) V109() V152() Element of the carrier of (TOP-REAL p1)
(TOP-REAL p1) | p2 is strict SubSpace of TOP-REAL p1
the carrier of ((TOP-REAL p1) | p2) is set
K7( the carrier of I[01], the carrier of ((TOP-REAL p1) | p2)) is set
K6(K7( the carrier of I[01], the carrier of ((TOP-REAL p1) | p2))) is set
a is V19() V22( the carrier of I[01]) V23( the carrier of ((TOP-REAL p1) | p2)) Function-like quasi_total Element of K6(K7( the carrier of I[01], the carrier of ((TOP-REAL p1) | p2)))
a . 0 is set
a . 1 is set
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL p1)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL p1)))
rng b is Element of K6( the carrier of (TOP-REAL p1))
[#] ((TOP-REAL p1) | p2) is non proper Element of K6( the carrier of ((TOP-REAL p1) | p2))
K6( the carrier of ((TOP-REAL p1) | p2)) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 is V11() real ext-real set
p4 is V11() real ext-real set
a is V11() real ext-real set
rectangle ((p1 `1),p3,p4,a) is Element of K6( the carrier of (TOP-REAL 2))
|[(p1 `1),p4]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[(p1 `1),a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[(p1 `1),p4]|,|[(p1 `1),a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[(p1 `1),p4]|) + (b₁ * |[(p1 `1),a]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 is V11() real ext-real set
p4 is V11() real ext-real set
rectangle ((p1 `1),p3,p4,(p2 `2)) is Element of K6( the carrier of (TOP-REAL 2))
|[(p1 `1),p4]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[(p1 `1),(p2 `2)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[(p1 `1),p4]|,|[(p1 `1),(p2 `2)]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[(p1 `1),p4]|) + (b₁ * |[(p1 `1),(p2 `2)]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
|[p3,(p2 `2)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[(p1 `1),(p2 `2)]|,|[p3,(p2 `2)]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[(p1 `1),(p2 `2)]|) + (b₁ * |[p3,(p2 `2)]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
rectangle ((p1 `1),(p2 `1),p3,p4) is Element of K6( the carrier of (TOP-REAL 2))
|[(p2 `1),p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[(p2 `1),p4]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[(p2 `1),p3]|,|[(p2 `1),p4]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[(p2 `1),p3]|) + (b₁ * |[(p2 `1),p4]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
|[(p1 `1),p3]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[(p1 `1),p4]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[(p1 `1),p3]|,|[(p1 `1),p4]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[(p1 `1),p3]|) + (b₁ * |[(p1 `1),p4]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
rectangle ((p1 `1),p3,(p2 `2),p4) is Element of K6( the carrier of (TOP-REAL 2))
|[(p1 `1),(p2 `2)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[(p1 `1),p4]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[(p1 `1),(p2 `2)]|,|[(p1 `1),p4]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[(p1 `1),(p2 `2)]|) + (b<sub>1</sub> * |[(p1 `1),p4]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
W-min (rectangle ((p1 `1),p3,(p2 `2),p4)) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(W-min (rectangle ((p1 `1),p3,(p2 `2),p4))) `1 is V11() real ext-real Element of REAL
|[p3,(p2 `2)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p3,(p2 `2)]|,|[(p1 `1),(p2 `2)]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[p3,(p2 `2)]|) + (b₁ * |[(p1 `1),(p2 `2)]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
rectangle (p3,p4,a,b) is Element of K6( the carrier of (TOP-REAL 2))
|[p3,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p4,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p3,b]|,|[p4,b]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[p3,b]|) + (b₁ * |[p4,b]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
rectangle (p3,p4,a,b) is Element of K6( the carrier of (TOP-REAL 2))
|[p4,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p4,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p4,b]|,|[p4,a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[p4,b]|) + (b₁ * |[p4,a]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
|[p3,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p3,b]|,|[p4,b]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[p3,b]|) + (b₁ * |[p4,b]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
rectangle (p3,p4,a,b) is Element of K6( the carrier of (TOP-REAL 2))
|[p4,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p3,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p4,a]|,|[p3,a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[p4,a]|) + (b₁ * |[p3,a]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
W-min (rectangle (p3,p4,a,b)) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(W-min (rectangle (p3,p4,a,b))) `1 is V11() real ext-real Element of REAL
|[p3,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p4,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p3,b]|,|[p4,b]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[p3,b]|) + (b<sub>1</sub> * |[p4,b]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
rectangle (p3,p4,a,b) is Element of K6( the carrier of (TOP-REAL 2))
|[p4,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p4,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p4,b]|,|[p4,a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[p4,b]|) + (b<sub>1</sub> * |[p4,a]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
rectangle (p3,p4,a,b) is Element of K6( the carrier of (TOP-REAL 2))
|[p4,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p4,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p4,b]|,|[p4,a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[p4,b]|) + (b<sub>1</sub> * |[p4,a]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
W-min (rectangle (p3,p4,a,b)) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p3,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(W-min (rectangle (p3,p4,a,b))) `1 is V11() real ext-real Element of REAL
LSeg (|[p4,a]|,|[p3,a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[p4,a]|) + (b₁ * |[p3,a]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
rectangle (p3,p4,a,b) is Element of K6( the carrier of (TOP-REAL 2))
|[p4,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p3,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p4,a]|,|[p3,a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b₁) * |[p4,a]|) + (b₁ * |[p3,a]|)) where b₁ is V11() real ext-real Element of REAL : ( 0 <= b₁ & b₁ <= 1 ) } is set
W-min (rectangle (p3,p4,a,b)) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(W-min (rectangle (p3,p4,a,b))) `1 is V11() real ext-real Element of REAL
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
b is V11() real ext-real set
a is V11() real ext-real set
rectangle (p3,p4,a,b) is Element of K6( the carrier of (TOP-REAL 2))
|[p4,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[p4,a]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p4,b]|,|[p4,a]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[p4,b]|) + (b<sub>1</sub> * |[p4,a]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
|[p3,b]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
LSeg (|[p3,b]|,|[p4,b]|) is Element of K6( the carrier of (TOP-REAL 2))
{ (((1 - b<sub>1</sub>) * |[p3,b]|) + (b<sub>1</sub> * |[p4,b]|)) where b<sub>1</sub> is V11() real ext-real Element of REAL : ( 0 <= b<sub>1</sub> & b<sub>1</sub> <= 1 ) } is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
c is V11() real ext-real set
d is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
rectangle ((p1 `1),(p3 `1),(p4 `2),(p2 `2)) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
p1 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p4 is V11() real ext-real set
AffineMap (p1,p2,p3,p4) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
1 / p1 is V11() real ext-real Element of REAL
p2 / p1 is V11() real ext-real set
- (p2 / p1) is V11() real ext-real set
1 / p3 is V11() real ext-real Element of REAL
p4 / p3 is V11() real ext-real set
- (p4 / p3) is V11() real ext-real set
AffineMap ((1 / p1),(- (p2 / p1)),(1 / p3),(- (p4 / p3))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a " is V19() Function-like set
b " is V19() Function-like set
dom a is Element of K6( the carrier of (TOP-REAL 2))
dom b is Element of K6( the carrier of (TOP-REAL 2))
c is set
d is set
a . c is set
b . d is set
Q is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a . Q is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
Q `1 is V11() real ext-real Element of REAL
p1 * (Q `1) is V11() real ext-real Element of REAL
(p1 * (Q `1)) + p2 is V11() real ext-real Element of REAL
Q `2 is V11() real ext-real Element of REAL
p3 * (Q `2) is V11() real ext-real Element of REAL
(p3 * (Q `2)) + p4 is V11() real ext-real Element of REAL
|[((p1 * (Q `1)) + p2),((p3 * (Q `2)) + p4)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
P is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
(1 / p1) * (P `1) is V11() real ext-real Element of REAL
((1 / p1) * (P `1)) + (- (p2 / p1)) is V11() real ext-real Element of REAL
(1 / p1) * p1 is V11() real ext-real Element of REAL
((1 / p1) * p1) * (Q `1) is V11() real ext-real Element of REAL
(1 / p1) * p2 is V11() real ext-real Element of REAL
(((1 / p1) * p1) * (Q `1)) + ((1 / p1) * p2) is V11() real ext-real Element of REAL
((((1 / p1) * p1) * (Q `1)) + ((1 / p1) * p2)) + (- (p2 / p1)) is V11() real ext-real Element of REAL
1 * (Q `1) is V11() real ext-real Element of REAL
(1 * (Q `1)) + ((1 / p1) * p2) is V11() real ext-real Element of REAL
((1 * (Q `1)) + ((1 / p1) * p2)) + (- (p2 / p1)) is V11() real ext-real Element of REAL
(Q `1) + (p2 / p1) is V11() real ext-real Element of REAL
((Q `1) + (p2 / p1)) + (- (p2 / p1)) is V11() real ext-real Element of REAL
P `2 is V11() real ext-real Element of REAL
(1 / p3) * (P `2) is V11() real ext-real Element of REAL
((1 / p3) * (P `2)) + (- (p4 / p3)) is V11() real ext-real Element of REAL
(1 / p3) * p3 is V11() real ext-real Element of REAL
((1 / p3) * p3) * (Q `2) is V11() real ext-real Element of REAL
(1 / p3) * p4 is V11() real ext-real Element of REAL
(((1 / p3) * p3) * (Q `2)) + ((1 / p3) * p4) is V11() real ext-real Element of REAL
((((1 / p3) * p3) * (Q `2)) + ((1 / p3) * p4)) + (- (p4 / p3)) is V11() real ext-real Element of REAL
1 * (Q `2) is V11() real ext-real Element of REAL
(1 * (Q `2)) + ((1 / p3) * p4) is V11() real ext-real Element of REAL
((1 * (Q `2)) + ((1 / p3) * p4)) + (- (p4 / p3)) is V11() real ext-real Element of REAL
(Q `2) + (p4 / p3) is V11() real ext-real Element of REAL
((Q `2) + (p4 / p3)) + (- (p4 / p3)) is V11() real ext-real Element of REAL
b . P is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[(((1 / p1) * (P `1)) + (- (p2 / p1))),(((1 / p3) * (P `2)) + (- (p4 / p3)))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
P is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b . P is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
P `1 is V11() real ext-real Element of REAL
(1 / p1) * (P `1) is V11() real ext-real Element of REAL
((1 / p1) * (P `1)) + (- (p2 / p1)) is V11() real ext-real Element of REAL
P `2 is V11() real ext-real Element of REAL
(1 / p3) * (P `2) is V11() real ext-real Element of REAL
((1 / p3) * (P `2)) + (- (p4 / p3)) is V11() real ext-real Element of REAL
|[(((1 / p1) * (P `1)) + (- (p2 / p1))),(((1 / p3) * (P `2)) + (- (p4 / p3)))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
Q is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
Q `1 is V11() real ext-real Element of REAL
p1 * (Q `1) is V11() real ext-real Element of REAL
(p1 * (Q `1)) + p2 is V11() real ext-real Element of REAL
p1 * (1 / p1) is V11() real ext-real Element of REAL
(p1 * (1 / p1)) * (P `1) is V11() real ext-real Element of REAL
p1 * (- (p2 / p1)) is V11() real ext-real set
((p1 * (1 / p1)) * (P `1)) + (p1 * (- (p2 / p1))) is V11() real ext-real Element of REAL
(((p1 * (1 / p1)) * (P `1)) + (p1 * (- (p2 / p1)))) + p2 is V11() real ext-real Element of REAL
1 * (P `1) is V11() real ext-real Element of REAL
(1 * (P `1)) + (p1 * (- (p2 / p1))) is V11() real ext-real Element of REAL
((1 * (P `1)) + (p1 * (- (p2 / p1)))) + p2 is V11() real ext-real Element of REAL
- p2 is V11() real ext-real set
(- p2) / p1 is V11() real ext-real set
p1 * ((- p2) / p1) is V11() real ext-real set
(P `1) + (p1 * ((- p2) / p1)) is V11() real ext-real Element of REAL
((P `1) + (p1 * ((- p2) / p1))) + p2 is V11() real ext-real Element of REAL
(P `1) + (- p2) is V11() real ext-real Element of REAL
((P `1) + (- p2)) + p2 is V11() real ext-real Element of REAL
Q `2 is V11() real ext-real Element of REAL
p3 * (Q `2) is V11() real ext-real Element of REAL
(p3 * (Q `2)) + p4 is V11() real ext-real Element of REAL
p3 * (1 / p3) is V11() real ext-real Element of REAL
(p3 * (1 / p3)) * (P `2) is V11() real ext-real Element of REAL
p3 * (- (p4 / p3)) is V11() real ext-real set
((p3 * (1 / p3)) * (P `2)) + (p3 * (- (p4 / p3))) is V11() real ext-real Element of REAL
(((p3 * (1 / p3)) * (P `2)) + (p3 * (- (p4 / p3)))) + p4 is V11() real ext-real Element of REAL
1 * (P `2) is V11() real ext-real Element of REAL
(1 * (P `2)) + (p3 * (- (p4 / p3))) is V11() real ext-real Element of REAL
((1 * (P `2)) + (p3 * (- (p4 / p3)))) + p4 is V11() real ext-real Element of REAL
- p4 is V11() real ext-real set
(- p4) / p3 is V11() real ext-real set
p3 * ((- p4) / p3) is V11() real ext-real set
(P `2) + (p3 * ((- p4) / p3)) is V11() real ext-real Element of REAL
((P `2) + (p3 * ((- p4) / p3))) + p4 is V11() real ext-real Element of REAL
(P `2) + (- p4) is V11() real ext-real Element of REAL
((P `2) + (- p4)) + p4 is V11() real ext-real Element of REAL
a . Q is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
|[((p1 * (Q `1)) + p2),((p3 * (Q `2)) + p4)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
Q is V11() real ext-real Element of REAL
1 / Q is V11() real ext-real Element of REAL
P is V11() real ext-real Element of REAL
P / Q is V11() real ext-real Element of REAL
- (P / Q) is V11() real ext-real Element of REAL
d is V11() real ext-real Element of REAL
1 / d is V11() real ext-real Element of REAL
c is V11() real ext-real Element of REAL
c / d is V11() real ext-real Element of REAL
- (c / d) is V11() real ext-real Element of REAL
AffineMap ((1 / Q),(- (P / Q)),(1 / d),(- (c / d))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
AffineMap (Q,P,d,c) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
rng a is Element of K6( the carrier of (TOP-REAL 2))
rng b is Element of K6( the carrier of (TOP-REAL 2))
p1 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p4 is V11() real ext-real set
AffineMap (p1,p2,p3,p4) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
1 / p1 is V11() real ext-real Element of REAL
p2 / p1 is V11() real ext-real set
- (p2 / p1) is V11() real ext-real set
1 / p3 is V11() real ext-real Element of REAL
p4 / p3 is V11() real ext-real set
- (p4 / p3) is V11() real ext-real set
AffineMap ((1 / p1),(- (p2 / p1)),(1 / p3),(- (p4 / p3))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a " is V19() Function-like set
d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
d `1 is V11() real ext-real Element of REAL
c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
c `1 is V11() real ext-real Element of REAL
a . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . d) `1 is V11() real ext-real Element of REAL
a . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . c) `1 is V11() real ext-real Element of REAL
p1 * (c `1) is V11() real ext-real Element of REAL
(p1 * (c `1)) + p2 is V11() real ext-real Element of REAL
c `2 is V11() real ext-real Element of REAL
p3 * (c `2) is V11() real ext-real Element of REAL
(p3 * (c `2)) + p4 is V11() real ext-real Element of REAL
|[((p1 * (c `1)) + p2),((p3 * (c `2)) + p4)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 * (d `1) is V11() real ext-real Element of REAL
(p1 * (d `1)) + p2 is V11() real ext-real Element of REAL
d `2 is V11() real ext-real Element of REAL
p3 * (d `2) is V11() real ext-real Element of REAL
(p3 * (d `2)) + p4 is V11() real ext-real Element of REAL
|[((p1 * (d `1)) + p2),((p3 * (d `2)) + p4)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom a is Element of K6( the carrier of (TOP-REAL 2))
dom (AffineMap ((1 / p1),(- (p2 / p1)),(1 / p3),(- (p4 / p3)))) is Element of K6( the carrier of (TOP-REAL 2))
rng a is Element of K6( the carrier of (TOP-REAL 2))
a /" is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
d `1 is V11() real ext-real Element of REAL
c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
c `1 is V11() real ext-real Element of REAL
a . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . d) `1 is V11() real ext-real Element of REAL
a . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . c) `1 is V11() real ext-real Element of REAL
p1 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p4 is V11() real ext-real set
AffineMap (p1,p2,p3,p4) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
1 / p1 is V11() real ext-real Element of REAL
p2 / p1 is V11() real ext-real set
- (p2 / p1) is V11() real ext-real set
1 / p3 is V11() real ext-real Element of REAL
p4 / p3 is V11() real ext-real set
- (p4 / p3) is V11() real ext-real set
AffineMap ((1 / p1),(- (p2 / p1)),(1 / p3),(- (p4 / p3))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a " is V19() Function-like set
d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
d `2 is V11() real ext-real Element of REAL
c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
c `2 is V11() real ext-real Element of REAL
a . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . d) `2 is V11() real ext-real Element of REAL
a . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . c) `2 is V11() real ext-real Element of REAL
c `1 is V11() real ext-real Element of REAL
p1 * (c `1) is V11() real ext-real Element of REAL
(p1 * (c `1)) + p2 is V11() real ext-real Element of REAL
p3 * (c `2) is V11() real ext-real Element of REAL
(p3 * (c `2)) + p4 is V11() real ext-real Element of REAL
|[((p1 * (c `1)) + p2),((p3 * (c `2)) + p4)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
d `1 is V11() real ext-real Element of REAL
p1 * (d `1) is V11() real ext-real Element of REAL
(p1 * (d `1)) + p2 is V11() real ext-real Element of REAL
p3 * (d `2) is V11() real ext-real Element of REAL
(p3 * (d `2)) + p4 is V11() real ext-real Element of REAL
|[((p1 * (d `1)) + p2),((p3 * (d `2)) + p4)]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom a is Element of K6( the carrier of (TOP-REAL 2))
dom (AffineMap ((1 / p1),(- (p2 / p1)),(1 / p3),(- (p4 / p3)))) is Element of K6( the carrier of (TOP-REAL 2))
rng a is Element of K6( the carrier of (TOP-REAL 2))
a /" is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
d `2 is V11() real ext-real Element of REAL
c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
c `2 is V11() real ext-real Element of REAL
a . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . d) `2 is V11() real ext-real Element of REAL
a . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(a . c) `2 is V11() real ext-real Element of REAL
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
closed_inside_of_rectangle (p1,p2,p3,p4) is Element of K6( the carrier of (TOP-REAL 2))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng b is Element of K6( the carrier of (TOP-REAL 2))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng (a * b) is Element of K6( the carrier of (TOP-REAL 2))
f is set
dom (a * b) is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
g is set
(a * b) . g is set
A is Element of the carrier of I[01]
(a * b) . A is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b . A is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a . (b . A) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom b is Element of K6( the carrier of I[01])
{ b₁ where b₁ is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2) : ( p1 <= b₁ `1 & b<sub>1</sub> `1 <= p2 & p3 <= b₁ `2 & b<sub>1</sub> `2 <= p4 ) } is set
(b . A) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . A) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . A) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . A) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . A) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . A) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . A) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . A) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(- 1) - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
((- 1) + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) * (p2 - p1) is V11() real ext-real Element of REAL
((- 1) * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
(((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
((((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p1 + p1 is V11() real ext-real set
(p1 + p1) / (p2 - p1) is V11() real ext-real set
((p1 + p1) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(((p1 + p1) / (p2 - p1)) / 2) * (p2 - p1) is V11() real ext-real Element of REAL
(p2 - p1) * ((p1 + p1) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p1 + p1) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p1 + p1) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * (((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
C is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
B is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
B `1 is V11() real ext-real Element of REAL
1 - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
(1 + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 * (p2 - p1) is V11() real ext-real Element of REAL
(1 * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
(((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) / (p2 - p1) is V11() real ext-real set
((p2 + p2) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(((p2 + p2) / (p2 - p1)) / 2) * (p2 - p1) is V11() real ext-real Element of REAL
(p2 - p1) * ((p2 + p2) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p2 + p2) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p2 + p2) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
C is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
1 - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
(1 + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 * (p4 - p3) is V11() real ext-real Element of REAL
(1 * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
(((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p4 + p4 is V11() real ext-real set
(p4 + p4) / (p4 - p3) is V11() real ext-real set
((p4 + p4) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(((p4 + p4) / (p4 - p3)) / 2) * (p4 - p3) is V11() real ext-real Element of REAL
(p4 - p3) * ((p4 + p4) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p4 + p4) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p4 + p4) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
C is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
B `2 is V11() real ext-real Element of REAL
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(((p3 + p3) / (p4 - p3)) / 2) * (p4 - p3) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
C is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
C `1 is V11() real ext-real Element of REAL
C `2 is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
{ b₁ where b₁ is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2) : ( - 1 <= b₁ `1 & b<sub>1</sub> `1 <= 1 & - 1 <= b₁ `2 & b<sub>1</sub> `2 <= 1 ) } is set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `1 is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . c) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
2 * p1 is V11() real ext-real Element of REAL
(2 * p1) / (p2 - p1) is V11() real ext-real Element of REAL
((2 * p1) / (p2 - p1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
- (p2 + p1) is V11() real ext-real set
(- (p2 + p1)) / (p2 - p1) is V11() real ext-real set
((2 * p1) / (p2 - p1)) + ((- (p2 + p1)) / (p2 - p1)) is V11() real ext-real Element of REAL
(2 * p1) + (- (p2 + p1)) is V11() real ext-real Element of REAL
((2 * p1) + (- (p2 + p1))) / (p2 - p1) is V11() real ext-real Element of REAL
- (p2 - p1) is V11() real ext-real set
(- (p2 - p1)) / (p2 - p1) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
2 * p4 is V11() real ext-real Element of REAL
(2 * p4) / (p4 - p3) is V11() real ext-real Element of REAL
((2 * p4) / (p4 - p3)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
- (p4 + p3) is V11() real ext-real set
(- (p4 + p3)) / (p4 - p3) is V11() real ext-real set
((2 * p4) / (p4 - p3)) + ((- (p4 + p3)) / (p4 - p3)) is V11() real ext-real Element of REAL
(2 * p4) + (- (p4 + p3)) is V11() real ext-real Element of REAL
((2 * p4) + (- (p4 + p3))) / (p4 - p3) is V11() real ext-real Element of REAL
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `1 is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . c) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
2 * p2 is V11() real ext-real Element of REAL
(2 * p2) / (p2 - p1) is V11() real ext-real Element of REAL
((2 * p2) / (p2 - p1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
- (p2 + p1) is V11() real ext-real set
(- (p2 + p1)) / (p2 - p1) is V11() real ext-real set
((2 * p2) / (p2 - p1)) + ((- (p2 + p1)) / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) + (- (p2 + p1)) is V11() real ext-real set
((p2 + p2) + (- (p2 + p1))) / (p2 - p1) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
2 * p3 is V11() real ext-real Element of REAL
(2 * p3) / (p4 - p3) is V11() real ext-real Element of REAL
((2 * p3) / (p4 - p3)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
- (p4 + p3) is V11() real ext-real set
(- (p4 + p3)) / (p4 - p3) is V11() real ext-real set
((2 * p3) / (p4 - p3)) + ((- (p4 + p3)) / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) + (- (p4 + p3)) is V11() real ext-real set
((p3 + p3) + (- (p4 + p3))) / (p4 - p3) is V11() real ext-real set
- (p4 - p3) is V11() real ext-real set
(- (p4 - p3)) / (p4 - p3) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `2 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `2 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(((p3 + p3) / (p4 - p3)) / 2) * (p4 - p3) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
(1 + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 * (p4 - p3) is V11() real ext-real Element of REAL
(1 * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
(((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p4 + p4 is V11() real ext-real set
(p4 + p4) / (p4 - p3) is V11() real ext-real set
((p4 + p4) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(((p4 + p4) / (p4 - p3)) / 2) * (p4 - p3) is V11() real ext-real Element of REAL
(p4 - p3) * ((p4 + p4) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p4 + p4) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p4 + p4) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(b . d) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `1 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p4 - p3)) * p4 is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * p4) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(((p3 + p3) / (p4 - p3)) / 2) * (p4 - p3) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
2 * p4 is V11() real ext-real Element of REAL
(2 * p4) / (p4 - p3) is V11() real ext-real Element of REAL
((2 * p4) / (p4 - p3)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
- (p4 + p3) is V11() real ext-real set
(- (p4 + p3)) / (p4 - p3) is V11() real ext-real set
((2 * p4) / (p4 - p3)) + ((- (p4 + p3)) / (p4 - p3)) is V11() real ext-real Element of REAL
(2 * p4) + (- (p4 + p3)) is V11() real ext-real Element of REAL
((2 * p4) + (- (p4 + p3))) / (p4 - p3) is V11() real ext-real Element of REAL
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . d) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(2 / (p2 - p1)) * p2 is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * p2) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * p1 is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * p1) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
2 * p2 is V11() real ext-real Element of REAL
(2 * p2) / (p2 - p1) is V11() real ext-real Element of REAL
((2 * p2) / (p2 - p1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
- (p2 + p1) is V11() real ext-real set
(- (p2 + p1)) / (p2 - p1) is V11() real ext-real set
((2 * p2) / (p2 - p1)) + ((- (p2 + p1)) / (p2 - p1)) is V11() real ext-real Element of REAL
(2 * p2) + (- (p2 + p1)) is V11() real ext-real Element of REAL
((2 * p2) + (- (p2 + p1))) / (p2 - p1) is V11() real ext-real Element of REAL
2 * p1 is V11() real ext-real Element of REAL
(2 * p1) / (p2 - p1) is V11() real ext-real Element of REAL
((2 * p1) / (p2 - p1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((2 * p1) / (p2 - p1)) + ((- (p2 + p1)) / (p2 - p1)) is V11() real ext-real Element of REAL
(2 * p1) + (- (p2 + p1)) is V11() real ext-real Element of REAL
((2 * p1) + (- (p2 + p1))) / (p2 - p1) is V11() real ext-real Element of REAL
- (p2 - p1) is V11() real ext-real set
(- (p2 - p1)) / (p2 - p1) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `2 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `2 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p4 - p3)) * p4 is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * p4) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p3 + p3) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * p3 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * p3) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
2 * p4 is V11() real ext-real Element of REAL
(2 * p4) / (p4 - p3) is V11() real ext-real Element of REAL
((2 * p4) / (p4 - p3)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
- (p4 + p3) is V11() real ext-real set
(- (p4 + p3)) / (p4 - p3) is V11() real ext-real set
((2 * p4) / (p4 - p3)) + ((- (p4 + p3)) / (p4 - p3)) is V11() real ext-real Element of REAL
p4 + p4 is V11() real ext-real set
(p4 + p4) + (- (p4 + p3)) is V11() real ext-real set
((p4 + p4) + (- (p4 + p3))) / (p4 - p3) is V11() real ext-real set
2 * p3 is V11() real ext-real Element of REAL
(2 * p3) / (p4 - p3) is V11() real ext-real Element of REAL
((2 * p3) / (p4 - p3)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((2 * p3) / (p4 - p3)) + ((- (p4 + p3)) / (p4 - p3)) is V11() real ext-real Element of REAL
(p3 + p3) + (- (p4 + p3)) is V11() real ext-real set
((p3 + p3) + (- (p4 + p3))) / (p4 - p3) is V11() real ext-real set
- (p4 - p3) is V11() real ext-real set
(- (p4 - p3)) / (p4 - p3) is V11() real ext-real set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `1 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p4 - p3)) * p4 is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * p4) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p3 + p3) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
2 * p4 is V11() real ext-real Element of REAL
(2 * p4) / (p4 - p3) is V11() real ext-real Element of REAL
((2 * p4) / (p4 - p3)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
- (p4 + p3) is V11() real ext-real set
(- (p4 + p3)) / (p4 - p3) is V11() real ext-real set
((2 * p4) / (p4 - p3)) + ((- (p4 + p3)) / (p4 - p3)) is V11() real ext-real Element of REAL
p4 + p4 is V11() real ext-real set
(p4 + p4) + (- (p4 + p3)) is V11() real ext-real set
((p4 + p4) + (- (p4 + p3))) / (p4 - p3) is V11() real ext-real set
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . d) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(2 / (p2 - p1)) * p2 is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * p2) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * p1 is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * p1) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
2 * p2 is V11() real ext-real Element of REAL
(2 * p2) / (p2 - p1) is V11() real ext-real Element of REAL
((2 * p2) / (p2 - p1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
- (p2 + p1) is V11() real ext-real set
(- (p2 + p1)) / (p2 - p1) is V11() real ext-real set
((2 * p2) / (p2 - p1)) + ((- (p2 + p1)) / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) + (- (p2 + p1)) is V11() real ext-real set
((p2 + p2) + (- (p2 + p1))) / (p2 - p1) is V11() real ext-real set
2 * p1 is V11() real ext-real Element of REAL
(2 * p1) / (p2 - p1) is V11() real ext-real Element of REAL
((2 * p1) / (p2 - p1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((2 * p1) / (p2 - p1)) + ((- (p2 + p1)) / (p2 - p1)) is V11() real ext-real Element of REAL
p1 + p1 is V11() real ext-real set
(p1 + p1) + (- (p2 + p1)) is V11() real ext-real set
((p1 + p1) + (- (p2 + p1))) / (p2 - p1) is V11() real ext-real set
- (p2 - p1) is V11() real ext-real set
(- (p2 - p1)) / (p2 - p1) is V11() real ext-real set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `1 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `1 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . c) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
(1 + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 * (p2 - p1) is V11() real ext-real Element of REAL
(1 * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
(((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) / (p2 - p1) is V11() real ext-real set
((p2 + p2) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p2 + p2) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p2 + p2) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p2 + p2) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p2 + p2) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(- 1) - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
((- 1) + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) * (p2 - p1) is V11() real ext-real Element of REAL
((- 1) * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
(((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
((((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p1 + p1 is V11() real ext-real set
(p1 + p1) / (p2 - p1) is V11() real ext-real set
((p1 + p1) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p1 + p1) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p1 + p1) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p1 + p1) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p1 + p1) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * (((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . d) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `2 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `1 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `2 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . c) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(- 1) - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
((- 1) + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) * (p2 - p1) is V11() real ext-real Element of REAL
((- 1) * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
(((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
((((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p1 + p1 is V11() real ext-real set
(p1 + p1) / (p2 - p1) is V11() real ext-real set
((p1 + p1) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p1 + p1) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p1 + p1) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p1 + p1) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p1 + p1) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * (((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p3 + p3) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
(1 + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 * (p2 - p1) is V11() real ext-real Element of REAL
(1 * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
(((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) / (p2 - p1) is V11() real ext-real set
((p2 + p2) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p2 + p2) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p2 + p2) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p2 + p2) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p2 + p2) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . d) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
(1 + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 * (p4 - p3) is V11() real ext-real Element of REAL
(1 * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
(((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p4 + p4 is V11() real ext-real set
(p4 + p4) / (p4 - p3) is V11() real ext-real set
((p4 + p4) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p4 + p4) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p4 + p4) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p4 + p4) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p4 + p4) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `1 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `1 is V11() real ext-real Element of REAL
1 - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
(1 + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 * (p2 - p1) is V11() real ext-real Element of REAL
(1 * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
(((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) / (p2 - p1) is V11() real ext-real set
((p2 + p2) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p2 + p2) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p2 + p2) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p2 + p2) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p2 + p2) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(- 1) - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
((- 1) + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) * (p2 - p1) is V11() real ext-real Element of REAL
((- 1) * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
(((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
((((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p1 + p1 is V11() real ext-real set
(p1 + p1) / (p2 - p1) is V11() real ext-real set
((p1 + p1) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p1 + p1) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p1 + p1) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p1 + p1) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p1 + p1) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * (((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `2 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `2 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p3 + p3) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
(1 + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 * (p4 - p3) is V11() real ext-real Element of REAL
(1 * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
(((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p4 + p4 is V11() real ext-real set
(p4 + p4) / (p4 - p3) is V11() real ext-real set
((p4 + p4) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p4 + p4) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p4 + p4) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p4 + p4) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p4 + p4) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(b . d) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `2 is V11() real ext-real Element of REAL
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `2 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `1 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(- 1) - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
((- 1) + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) * (p2 - p1) is V11() real ext-real Element of REAL
((- 1) * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
(((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
((((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p1 + p1 is V11() real ext-real set
(p1 + p1) / (p2 - p1) is V11() real ext-real set
((p1 + p1) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p1 + p1) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p1 + p1) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p1 + p1) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p1 + p1) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * (((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(- 1) - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
((- 1) + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
(- 1) * (p4 - p3) is V11() real ext-real Element of REAL
((- 1) * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
(((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
((((- 1) * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p3 + p3 is V11() real ext-real set
(p3 + p3) / (p4 - p3) is V11() real ext-real set
((p3 + p3) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p3 + p3) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p3 + p3) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p3 + p3) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p3 + p3) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * (((- 1) - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
((- 1) - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
(1 + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 * (p2 - p1) is V11() real ext-real Element of REAL
(1 * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
(((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) / (p2 - p1) is V11() real ext-real set
((p2 + p2) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p2 + p2) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p2 + p2) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p2 + p2) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p2 + p2) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . d) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 + ((p4 + p3) / (p4 - p3)) is V11() real ext-real Element of REAL
(1 + ((p4 + p3) / (p4 - p3))) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
1 * (p4 - p3) is V11() real ext-real Element of REAL
(1 * (p4 - p3)) + (p4 + p3) is V11() real ext-real Element of REAL
((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3) is V11() real ext-real Element of REAL
(((1 * (p4 - p3)) + (p4 + p3)) / (p4 - p3)) / (2 / (p4 - p3)) is V11() real ext-real Element of REAL
p4 + p4 is V11() real ext-real set
(p4 + p4) / (p4 - p3) is V11() real ext-real set
((p4 + p4) / (p4 - p3)) / 2 is V11() real ext-real Element of REAL
(p4 - p3) * (((p4 + p4) / (p4 - p3)) / 2) is V11() real ext-real Element of REAL
(p4 - p3) * ((p4 + p4) / (p4 - p3)) is V11() real ext-real set
((p4 - p3) * ((p4 + p4) / (p4 - p3))) / 2 is V11() real ext-real Element of REAL
(p4 + p4) / 2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((1 - (- ((p4 + p3) / (p4 - p3)))) / (2 / (p4 - p3))) is V11() real ext-real Element of REAL
(1 - (- ((p4 + p3) / (p4 - p3)))) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
p2 is V11() real ext-real set
p1 is V11() real ext-real set
p2 - p1 is V11() real ext-real set
2 / (p2 - p1) is V11() real ext-real Element of REAL
p2 + p1 is V11() real ext-real set
(p2 + p1) / (p2 - p1) is V11() real ext-real set
- ((p2 + p1) / (p2 - p1)) is V11() real ext-real set
p4 is V11() real ext-real set
p3 is V11() real ext-real set
p4 - p3 is V11() real ext-real set
2 / (p4 - p3) is V11() real ext-real Element of REAL
p4 + p3 is V11() real ext-real set
(p4 + p3) / (p4 - p3) is V11() real ext-real set
- ((p4 + p3) / (p4 - p3)) is V11() real ext-real set
AffineMap ((2 / (p2 - p1)),(- ((p2 + p1) / (p2 - p1))),(2 / (p4 - p3)),(- ((p4 + p3) / (p4 - p3)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
a is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
a * b is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
d is Element of the carrier of I[01]
b . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . d) `1 is V11() real ext-real Element of REAL
c is Element of the carrier of I[01]
b . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(b . c) `1 is V11() real ext-real Element of REAL
(a * b) . d is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . d) `1 is V11() real ext-real Element of REAL
(a * b) . c is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((a * b) . c) `1 is V11() real ext-real Element of REAL
a . (b . c) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(2 / (p2 - p1)) * ((b . c) `1) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . c) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . c) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . c) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . c) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
1 - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
(1 + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
1 * (p2 - p1) is V11() real ext-real Element of REAL
(1 * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
(((1 * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p2 + p2 is V11() real ext-real set
(p2 + p2) / (p2 - p1) is V11() real ext-real set
((p2 + p2) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p2 + p2) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p2 + p2) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p2 + p2) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p2 + p2) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((1 - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
(1 - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
dom b is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
a . (b . d) is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(- 1) - (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) + ((p2 + p1) / (p2 - p1)) is V11() real ext-real Element of REAL
((- 1) + ((p2 + p1) / (p2 - p1))) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
(- 1) * (p2 - p1) is V11() real ext-real Element of REAL
((- 1) * (p2 - p1)) + (p2 + p1) is V11() real ext-real Element of REAL
(((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1) is V11() real ext-real Element of REAL
((((- 1) * (p2 - p1)) + (p2 + p1)) / (p2 - p1)) / (2 / (p2 - p1)) is V11() real ext-real Element of REAL
p1 + p1 is V11() real ext-real set
(p1 + p1) / (p2 - p1) is V11() real ext-real set
((p1 + p1) / (p2 - p1)) / 2 is V11() real ext-real Element of REAL
(p2 - p1) * (((p1 + p1) / (p2 - p1)) / 2) is V11() real ext-real Element of REAL
(p2 - p1) * ((p1 + p1) / (p2 - p1)) is V11() real ext-real set
((p2 - p1) * ((p1 + p1) / (p2 - p1))) / 2 is V11() real ext-real Element of REAL
(p1 + p1) / 2 is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * ((b . d) `1) is V11() real ext-real Element of REAL
(2 / (p2 - p1)) * (((- 1) - (- ((p2 + p1) / (p2 - p1)))) / (2 / (p2 - p1))) is V11() real ext-real Element of REAL
((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
((- 1) - (- ((p2 + p1) / (p2 - p1)))) + (- ((p2 + p1) / (p2 - p1))) is V11() real ext-real Element of REAL
(b . d) `2 is V11() real ext-real Element of REAL
(2 / (p4 - p3)) * ((b . d) `2) is V11() real ext-real Element of REAL
((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))) is V11() real ext-real Element of REAL
|[(((2 / (p2 - p1)) * ((b . d) `1)) + (- ((p2 + p1) / (p2 - p1)))),(((2 / (p4 - p3)) * ((b . d) `2)) + (- ((p4 + p3) / (p4 - p3))))]| is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `1 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(g2 . p2) `1 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `1 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `1 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
f . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p1) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
(f2 . p2) `1 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `1 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
f . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p1) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `1 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
f . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p1) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(f2 . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p2) `1 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(f2 . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `2 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
(f2 . p2) `1 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `2 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(f2 . p2) `1 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p2) `1 is V11() real ext-real Element of REAL
dom f2 is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
z2 is set
f2 . z2 is set
dom f is Element of K6( the carrier of I[01])
f . z2 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
dom g is Element of K6( the carrier of I[01])
g . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z1) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z2) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `1 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `1 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom g is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(g2 . p2) `2 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
(f2 . p2) `1 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `1 is V11() real ext-real Element of REAL
f . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p1) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `1 is V11() real ext-real Element of REAL
f . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p1) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(f2 . p2) `1 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `2 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(g2 . p2) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `1 is V11() real ext-real Element of REAL
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(f2 . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
dom f is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
(g2 . p1) `2 is V11() real ext-real Element of REAL
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `1 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `2 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `1 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(g2 . p2) `1 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `1 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `2 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `1 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `2 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
(f2 . p2) `2 is V11() real ext-real Element of REAL
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `1 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(rng g2) /\ (rng f2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng g2) /\ (rng f2) is Element of (rng g2) /\ (rng f2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
f . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p1) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom f2 is Element of K6( the carrier of I[01])
z2 is set
f2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom g2 is Element of K6( the carrier of I[01])
z1 is set
g2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `1 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `2 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
(f2 . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `2 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `2 is V11() real ext-real Element of REAL
(g2 . p2) `1 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `1 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `1 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `2 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `2 is V11() real ext-real Element of REAL
(f2 . p1) `1 is V11() real ext-real Element of REAL
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
p2 is Element of the carrier of I[01]
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
(g2 . p2) `2 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
g . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p2) `2 is V11() real ext-real Element of REAL
(g2 . p1) `1 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `1 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `2 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
a `2 is V11() real ext-real Element of REAL
b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
b `2 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
a `1 is V11() real ext-real Element of REAL
b `1 is V11() real ext-real Element of REAL
d is V11() real ext-real set
c is V11() real ext-real set
Q is V11() real ext-real set
P is V11() real ext-real set
closed_inside_of_rectangle (c,d,P,Q) is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g . 0 is set
g . 1 is set
rng f is Element of K6( the carrier of (TOP-REAL 2))
rng g is Element of K6( the carrier of (TOP-REAL 2))
d - c is V11() real ext-real set
2 / (d - c) is V11() real ext-real Element of REAL
d + c is V11() real ext-real set
(d + c) / (d - c) is V11() real ext-real set
- ((d + c) / (d - c)) is V11() real ext-real set
Q - P is V11() real ext-real set
2 / (Q - P) is V11() real ext-real Element of REAL
Q + P is V11() real ext-real set
(Q + P) / (Q - P) is V11() real ext-real set
- ((Q + P) / (Q - P)) is V11() real ext-real set
AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P)))) is non empty V19() V22( the carrier of (TOP-REAL 2)) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of (TOP-REAL 2)) quasi_total continuous Element of K6(K7( the carrier of (TOP-REAL 2), the carrier of (TOP-REAL 2)))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
g2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
p1 is Element of the carrier of I[01]
g . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g . p1) `2 is V11() real ext-real Element of REAL
p2 is Element of the carrier of I[01]
g2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p2) `1 is V11() real ext-real Element of REAL
rng g2 is Element of K6( the carrier of (TOP-REAL 2))
(g2 . p2) `2 is V11() real ext-real Element of REAL
g2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(g2 . p1) `2 is V11() real ext-real Element of REAL
dom g is Element of K6( the carrier of I[01])
K6( the carrier of I[01]) is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) * f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
f2 is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f2 is Element of K6( the carrier of (TOP-REAL 2))
f2 . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p2) `2 is V11() real ext-real Element of REAL
f . p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f . p2) `2 is V11() real ext-real Element of REAL
f2 . p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(f2 . p1) `1 is V11() real ext-real Element of REAL
(f2 . p1) `2 is V11() real ext-real Element of REAL
(rng f2) /\ (rng g2) is Element of K6( the carrier of (TOP-REAL 2))
the Element of (rng f2) /\ (rng g2) is Element of (rng f2) /\ (rng g2)
dom f is Element of K6( the carrier of I[01])
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p3) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . p4) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . a) `1 is V11() real ext-real Element of REAL
((AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . b) `1 is V11() real ext-real Element of REAL
dom g2 is Element of K6( the carrier of I[01])
z2 is set
g2 . z2 is set
g . z2 is set
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (g . z2) is set
dom f2 is Element of K6( the carrier of I[01])
z1 is set
f2 . z1 is set
f . z1 is set
dom (AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) is Element of K6( the carrier of (TOP-REAL 2))
(AffineMap ((2 / (d - c)),(- ((d + c) / (d - c))),(2 / (Q - P)),(- ((Q + P) / (Q - P))))) . (f . z1) is set
p1 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p1 `2 is V11() real ext-real Element of REAL
p2 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p2 `2 is V11() real ext-real Element of REAL
p3 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p3 `2 is V11() real ext-real Element of REAL
p4 is V43(2) V109() V152() Element of the carrier of (TOP-REAL 2)
p4 `2 is V11() real ext-real Element of REAL
p1 `1 is V11() real ext-real Element of REAL
p2 `1 is V11() real ext-real Element of REAL
p3 `1 is V11() real ext-real Element of REAL
p4 `1 is V11() real ext-real Element of REAL
b is V11() real ext-real set
a is V11() real ext-real set
d is V11() real ext-real set
c is V11() real ext-real set
closed_inside_of_rectangle (a,b,c,d) is Element of K6( the carrier of (TOP-REAL 2))
P is Element of K6( the carrier of (TOP-REAL 2))
Q is Element of K6( the carrier of (TOP-REAL 2))
f is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng f is Element of K6( the carrier of (TOP-REAL 2))
f . 0 is set
f . 1 is set
g is non empty V19() V22( the carrier of I[01]) V23( the carrier of (TOP-REAL 2)) Function-like V29( the carrier of I[01]) quasi_total Element of K6(K7( the carrier of I[01], the carrier of (TOP-REAL 2)))
rng g is Element of K6( the carrier of (TOP-REAL 2))
g . 0 is set
g . 1 is set