:: JORDAN1B semantic presentation
theorem Th1: :: JORDAN1B:1
theorem Th2: :: JORDAN1B:2
theorem Th3: :: JORDAN1B:3
theorem Th4: :: JORDAN1B:4
theorem Th5: :: JORDAN1B:5
theorem Th6: :: JORDAN1B:6
theorem Th7: :: JORDAN1B:7
theorem Th8: :: JORDAN1B:8
theorem Th9: :: JORDAN1B:9
theorem Th10: :: JORDAN1B:10
theorem Th11: :: JORDAN1B:11
theorem Th12: :: JORDAN1B:12
theorem Th13: :: JORDAN1B:13
theorem Th14: :: JORDAN1B:14
theorem Th15: :: JORDAN1B:15
theorem Th16: :: JORDAN1B:16
theorem Th17: :: JORDAN1B:17
theorem Th18: :: JORDAN1B:18
theorem Th19: :: JORDAN1B:19
theorem Th20: :: JORDAN1B:20
theorem Th21: :: JORDAN1B:21
Lemma77:
for i, m being Element of NAT st i <= m & m <= i + 1 & not i = m holds
i = m -' 1
theorem Th22: :: JORDAN1B:22
theorem Th23: :: JORDAN1B:23
theorem Th24: :: JORDAN1B:24
theorem Th25: :: JORDAN1B:25
theorem Th26: :: JORDAN1B:26
theorem Th27: :: JORDAN1B:27
theorem Th28: :: JORDAN1B:28
theorem Th29: :: JORDAN1B:29
theorem Th30: :: JORDAN1B:30
theorem Th31: :: JORDAN1B:31
theorem Th32: :: JORDAN1B:32
theorem Th33: :: JORDAN1B:33
theorem Th34: :: JORDAN1B:34
theorem Th35: :: JORDAN1B:35
theorem Th36: :: JORDAN1B:36
theorem Th37: :: JORDAN1B:37
theorem Th38: :: JORDAN1B:38
theorem Th39: :: JORDAN1B:39
Lemma92:
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for j, n, i being Element of NAT st j <= width (Gauge C,n) & cell (Gauge C,n),i,j c= BDD C holds
i <> 0
Lemma93:
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for i, n, j being Element of NAT st i <= len (Gauge C,n) & cell (Gauge C,n),i,j c= BDD C holds
j <> 0
Lemma94:
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for j, n, i being Element of NAT st j <= width (Gauge C,n) & cell (Gauge C,n),i,j c= BDD C holds
i <> len (Gauge C,n)
Lemma95:
for C being connected compact non horizontal non vertical Subset of (TOP-REAL 2)
for i, n, j being Element of NAT st i <= len (Gauge C,n) & cell (Gauge C,n),i,j c= BDD C holds
j <> width (Gauge C,n)
theorem Th40: :: JORDAN1B:40
theorem Th41: :: JORDAN1B:41
theorem Th42: :: JORDAN1B:42
theorem Th43: :: JORDAN1B:43
theorem Th44: :: JORDAN1B:44