:: JGRAPH_7 semantic presentation
theorem Th1: :: JGRAPH_7:1
theorem Th2: :: JGRAPH_7:2
theorem Th3: :: JGRAPH_7:3
theorem Th4: :: JGRAPH_7:4
theorem Th5: :: JGRAPH_7:5
theorem Th6: :: JGRAPH_7:6
theorem Th7: :: JGRAPH_7:7
theorem Th8: :: JGRAPH_7:8
theorem Th9: :: JGRAPH_7:9
theorem Th10: :: JGRAPH_7:10
theorem Th11: :: JGRAPH_7:11
theorem Th12: :: JGRAPH_7:12
theorem Th13: :: JGRAPH_7:13
theorem Th14: :: JGRAPH_7:14
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `1 = b
5 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 < b
4 `2 & b
4 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th15: :: JGRAPH_7:15
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
5 <= b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th16: :: JGRAPH_7:16
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th17: :: JGRAPH_7:17
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th18: :: JGRAPH_7:18
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th19: :: JGRAPH_7:19
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th20: :: JGRAPH_7:20
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th21: :: JGRAPH_7:21
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th22: :: JGRAPH_7:22
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th23: :: JGRAPH_7:23
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th24: :: JGRAPH_7:24
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th25: :: JGRAPH_7:25
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th26: :: JGRAPH_7:26
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th27: :: JGRAPH_7:27
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th28: :: JGRAPH_7:28
theorem Th29: :: JGRAPH_7:29
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th30: :: JGRAPH_7:30
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 > b
4 `2 & b
4 `2 >= b
7 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th31: :: JGRAPH_7:31
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 >= b
7 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th32: :: JGRAPH_7:32
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
7 <= b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th33: :: JGRAPH_7:33
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 < b
2 `1 & b
2 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th34: :: JGRAPH_7:34
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th35: :: JGRAPH_7:35
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th36: :: JGRAPH_7:36
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th37: :: JGRAPH_7:37
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th38: :: JGRAPH_7:38
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th39: :: JGRAPH_7:39
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th40: :: JGRAPH_7:40
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 > b
4 `2 & b
4 `2 >= b
7 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th41: :: JGRAPH_7:41
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 >= b
7 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th42: :: JGRAPH_7:42
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
7 <= b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th43: :: JGRAPH_7:43
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 < b
2 `1 & b
2 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th44: :: JGRAPH_7:44
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 > b
4 `2 & b
4 `2 >= b
7 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th45: :: JGRAPH_7:45
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 >= b
7 & b
5 < b
4 `1 & b
4 `1 <= b
6 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th46: :: JGRAPH_7:46
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 >= b
7 & b
6 >= b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th47: :: JGRAPH_7:47
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
6 >= b
2 `1 & b
2 `1 > b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th48: :: JGRAPH_7:48
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number holds
( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
7 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
6 >= b
1 `1 & b
1 `1 > b
2 `1 & b
2 `1 > b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 implies b
1,b
2,b
3,b
4 are_in_this_order_on rectangle b
5,b
6,b
7,b
8 )
theorem Th49: :: JGRAPH_7:49
for b
1, b
2, b
3, b
4 being
real number for b
5, b
6 being
Function of
(TOP-REAL 2),
(TOP-REAL 2) holds
( b
1 > 0 & b
3 > 0 & b
5 = AffineMap b
1,b
2,b
3,b
4 & b
6 = AffineMap (1 / b1),
(- (b2 / b1)),
(1 / b3),
(- (b4 / b3)) implies ( b
6 = b
5 " & b
5 = b
6 " ) )
theorem Th50: :: JGRAPH_7:50
theorem Th51: :: JGRAPH_7:51
theorem Th52: :: JGRAPH_7:52
for b
1, b
2, b
3, b
4 being
real number for b
5 being
Function of
(TOP-REAL 2),
(TOP-REAL 2)for b
6 being
Function of
I[01] ,
(TOP-REAL 2) holds
( b
1 < b
2 & b
3 < b
4 & b
5 = AffineMap (2 / (b2 - b1)),
(- ((b2 + b1) / (b2 - b1))),
(2 / (b4 - b3)),
(- ((b4 + b3) / (b4 - b3))) &
rng b
6 c= closed_inside_of_rectangle b
1,b
2,b
3,b
4 implies
rng (b5 * b6) c= closed_inside_of_rectangle (- 1),1,
(- 1),1 )
theorem Th53: :: JGRAPH_7:53
theorem Th54: :: JGRAPH_7:54
theorem Th55: :: JGRAPH_7:55
theorem Th56: :: JGRAPH_7:56
theorem Th57: :: JGRAPH_7:57
theorem Th58: :: JGRAPH_7:58
theorem Th59: :: JGRAPH_7:59
theorem Th60: :: JGRAPH_7:60
theorem Th61: :: JGRAPH_7:61
theorem Th62: :: JGRAPH_7:62
theorem Th63: :: JGRAPH_7:63
theorem Th64: :: JGRAPH_7:64
theorem Th65: :: JGRAPH_7:65
theorem Th66: :: JGRAPH_7:66
theorem Th67: :: JGRAPH_7:67
set c1 = rectangle (- 1),1,(- 1),1;
theorem Th68: :: JGRAPH_7:68
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `1 = b
5 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 < b
4 `2 & b
4 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th69: :: JGRAPH_7:69
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `1 = b
5 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 < b
4 `2 & b
4 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th70: :: JGRAPH_7:70
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
5 <= b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th71: :: JGRAPH_7:71
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
5 <= b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th72: :: JGRAPH_7:72
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th73: :: JGRAPH_7:73
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th74: :: JGRAPH_7:74
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th75: :: JGRAPH_7:75
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
5 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 < b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th76: :: JGRAPH_7:76
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th77: :: JGRAPH_7:77
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th78: :: JGRAPH_7:78
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th79: :: JGRAPH_7:79
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th80: :: JGRAPH_7:80
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th81: :: JGRAPH_7:81
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 <= b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th82: :: JGRAPH_7:82
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th83: :: JGRAPH_7:83
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th84: :: JGRAPH_7:84
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th85: :: JGRAPH_7:85
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th86: :: JGRAPH_7:86
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th87: :: JGRAPH_7:87
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
5 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th88: :: JGRAPH_7:88
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th89: :: JGRAPH_7:89
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th90: :: JGRAPH_7:90
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th91: :: JGRAPH_7:91
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th92: :: JGRAPH_7:92
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th93: :: JGRAPH_7:93
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th94: :: JGRAPH_7:94
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th95: :: JGRAPH_7:95
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th96: :: JGRAPH_7:96
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th97: :: JGRAPH_7:97
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th98: :: JGRAPH_7:98
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th99: :: JGRAPH_7:99
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
8 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 <= b
2 `1 & b
2 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th100: :: JGRAPH_7:100
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 < b
2 `2 & b
2 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th101: :: JGRAPH_7:101
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 < b
2 `2 & b
2 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th102: :: JGRAPH_7:102
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
7 <= b
3 `2 & b
3 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th103: :: JGRAPH_7:103
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
7 <= b
3 `2 & b
3 `2 < b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th104: :: JGRAPH_7:104
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
7 <= b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th105: :: JGRAPH_7:105
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
7 <= b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th106: :: JGRAPH_7:106
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 < b
2 `1 & b
2 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th107: :: JGRAPH_7:107
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
5 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 < b
2 `1 & b
2 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th108: :: JGRAPH_7:108
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th109: :: JGRAPH_7:109
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
8 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th110: :: JGRAPH_7:110
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th111: :: JGRAPH_7:111
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th112: :: JGRAPH_7:112
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th113: :: JGRAPH_7:113
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
8 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 < b
3 `1 & b
3 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th114: :: JGRAPH_7:114
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th115: :: JGRAPH_7:115
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
4 `2 & b
4 `2 < b
3 `2 & b
3 `2 <= b
8 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th116: :: JGRAPH_7:116
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th117: :: JGRAPH_7:117
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
7 <= b
3 `2 & b
3 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th118: :: JGRAPH_7:118
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th119: :: JGRAPH_7:119
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
8 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 < b
2 `1 & b
2 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th120: :: JGRAPH_7:120
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 > b
4 `2 & b
4 `2 >= b
7 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th121: :: JGRAPH_7:121
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 > b
4 `2 & b
4 `2 >= b
7 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th122: :: JGRAPH_7:122
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 >= b
7 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th123: :: JGRAPH_7:123
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
8 >= b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 >= b
7 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th124: :: JGRAPH_7:124
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
7 <= b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th125: :: JGRAPH_7:125
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
7 <= b
2 `2 & b
2 `2 <= b
8 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th126: :: JGRAPH_7:126
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 < b
2 `1 & b
2 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th127: :: JGRAPH_7:127
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
8 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
5 <= b
1 `1 & b
1 `1 <= b
6 & b
5 < b
4 `1 & b
4 `1 < b
3 `1 & b
3 `1 < b
2 `1 & b
2 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th128: :: JGRAPH_7:128
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 > b
4 `2 & b
4 `2 >= b
7 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th129: :: JGRAPH_7:129
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `1 = b
6 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 > b
4 `2 & b
4 `2 >= b
7 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th130: :: JGRAPH_7:130
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 >= b
7 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th131: :: JGRAPH_7:131
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `1 = b
6 & b
4 `2 = b
7 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 > b
3 `2 & b
3 `2 >= b
7 & b
5 < b
4 `1 & b
4 `1 <= b
6 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th132: :: JGRAPH_7:132
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 >= b
7 & b
6 >= b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th133: :: JGRAPH_7:133
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `1 = b
6 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
8 >= b
1 `2 & b
1 `2 > b
2 `2 & b
2 `2 >= b
7 & b
6 >= b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th134: :: JGRAPH_7:134
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
6 >= b
2 `1 & b
2 `1 > b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th135: :: JGRAPH_7:135
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `1 = b
6 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
7 <= b
1 `2 & b
1 `2 <= b
8 & b
6 >= b
2 `1 & b
2 `1 > b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )
theorem Th136: :: JGRAPH_7:136
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Function of
I[01] ,
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
7 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
6 >= b
1 `1 & b
1 `1 > b
2 `1 & b
2 `1 > b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 & b
9 . 0
= b
1 & b
9 . 1
= b
3 & b
10 . 0
= b
2 & b
10 . 1
= b
4 & b
9 is
continuous & b
9 is
one-to-one & b
10 is
continuous & b
10 is
one-to-one &
rng b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 &
rng b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not
rng b
9 meets rng b
10 )
theorem Th137: :: JGRAPH_7:137
for b
1, b
2, b
3, b
4 being
Point of
(TOP-REAL 2)for b
5, b
6, b
7, b
8 being
real number for b
9, b
10 being
Subset of
(TOP-REAL 2) holds
not ( b
5 < b
6 & b
7 < b
8 & b
1 `2 = b
7 & b
2 `2 = b
7 & b
3 `2 = b
7 & b
4 `2 = b
7 & b
6 >= b
1 `1 & b
1 `1 > b
2 `1 & b
2 `1 > b
3 `1 & b
3 `1 > b
4 `1 & b
4 `1 > b
5 & b
9 is_an_arc_of b
1,b
3 & b
10 is_an_arc_of b
2,b
4 & b
9 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & b
10 c= closed_inside_of_rectangle b
5,b
6,b
7,b
8 & not b
9 meets b
10 )