:: SPRECT_5 semantic presentation
theorem Th1: :: SPRECT_5:1
theorem Th2: :: SPRECT_5:2
theorem Th3: :: SPRECT_5:3
theorem Th4: :: SPRECT_5:4
theorem Th5: :: SPRECT_5:5
theorem Th6: :: SPRECT_5:6
theorem Th7: :: SPRECT_5:7
theorem Th8: :: SPRECT_5:8
theorem Th9: :: SPRECT_5:9
theorem Th10: :: SPRECT_5:10
theorem Th11: :: SPRECT_5:11
theorem Th12: :: SPRECT_5:12
theorem Th13: :: SPRECT_5:13
theorem Th14: :: SPRECT_5:14
theorem Th15: :: SPRECT_5:15
theorem Th16: :: SPRECT_5:16
theorem Th17: :: SPRECT_5:17
theorem Th18: :: SPRECT_5:18
theorem Th19: :: SPRECT_5:19
theorem Th20: :: SPRECT_5:20
theorem Th21: :: SPRECT_5:21
Lemma64:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(E-max (L~ z)) .. z < (S-max (L~ z)) .. z
Lemma65:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(E-max (L~ z)) .. z < (S-min (L~ z)) .. z
Lemma66:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(E-max (L~ z)) .. z < (W-min (L~ z)) .. z
Lemma67:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(E-min (L~ z)) .. z < (S-min (L~ z)) .. z
Lemma68:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(E-min (L~ z)) .. z < (W-min (L~ z)) .. z
Lemma69:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(S-max (L~ z)) .. z < (W-min (L~ z)) .. z
Lemma70:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(N-max (L~ z)) .. z < (W-min (L~ z)) .. z
Lemma71:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(N-min (L~ z)) .. z < (W-min (L~ z)) .. z
Lemma72:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(N-max (L~ z)) .. z < (S-max (L~ z)) .. z
Lemma73:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = N-min (L~ z) holds
(N-max (L~ z)) .. z < (S-min (L~ z)) .. z
theorem Th22: :: SPRECT_5:22
theorem Th23: :: SPRECT_5:23
theorem Th24: :: SPRECT_5:24
theorem Th25: :: SPRECT_5:25
theorem Th26: :: SPRECT_5:26
theorem Th27: :: SPRECT_5:27
theorem Th28: :: SPRECT_5:28
theorem Th29: :: SPRECT_5:29
theorem Th30: :: SPRECT_5:30
theorem Th31: :: SPRECT_5:31
Lemma81:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(E-max (L~ z)) .. z < (S-max (L~ z)) .. z
Lemma82:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(N-min (L~ z)) .. z < (E-max (L~ z)) .. z
Lemma83:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(N-min (L~ z)) .. z < (S-max (L~ z)) .. z
Lemma84:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(N-max (L~ z)) .. z < (S-max (L~ z)) .. z
Lemma85:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(W-max (L~ z)) .. z < (S-max (L~ z)) .. z
Lemma86:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(N-max (L~ z)) .. z < (E-min (L~ z)) .. z
Lemma87:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(N-min (L~ z)) .. z < (E-max (L~ z)) .. z
Lemma88:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(W-max (L~ z)) .. z < (E-max (L~ z)) .. z
Lemma89:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = W-min (L~ z) holds
(W-max (L~ z)) .. z < (E-min (L~ z)) .. z
theorem Th32: :: SPRECT_5:32
theorem Th33: :: SPRECT_5:33
theorem Th34: :: SPRECT_5:34
theorem Th35: :: SPRECT_5:35
theorem Th36: :: SPRECT_5:36
theorem Th37: :: SPRECT_5:37
theorem Th38: :: SPRECT_5:38
theorem Th39: :: SPRECT_5:39
theorem Th40: :: SPRECT_5:40
theorem Th41: :: SPRECT_5:41
Lemma98:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = S-max (L~ z) holds
(N-min (L~ z)) .. z < (E-max (L~ z)) .. z
Lemma99:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = S-max (L~ z) holds
(W-max (L~ z)) .. z < (E-max (L~ z)) .. z
Lemma100:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = S-max (L~ z) holds
(W-min (L~ z)) .. z < (E-max (L~ z)) .. z
Lemma101:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = S-max (L~ z) holds
(W-max (L~ z)) .. z < (N-max (L~ z)) .. z
Lemma102:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = S-max (L~ z) holds
(W-min (L~ z)) .. z < (N-min (L~ z)) .. z
Lemma103:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = S-max (L~ z) holds
(S-min (L~ z)) .. z < (N-min (L~ z)) .. z
Lemma104:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = S-max (L~ z) holds
(S-min (L~ z)) .. z < (N-max (L~ z)) .. z
theorem Th42: :: SPRECT_5:42
theorem Th43: :: SPRECT_5:43
theorem Th44: :: SPRECT_5:44
theorem Th45: :: SPRECT_5:45
theorem Th46: :: SPRECT_5:46
theorem Th47: :: SPRECT_5:47
theorem Th48: :: SPRECT_5:48
theorem Th49: :: SPRECT_5:49
theorem Th50: :: SPRECT_5:50
theorem Th51: :: SPRECT_5:51
theorem Th52: :: SPRECT_5:52
theorem Th53: :: SPRECT_5:53
theorem Th54: :: SPRECT_5:54
theorem Th55: :: SPRECT_5:55
Lemma108:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = E-max (L~ z) holds
(S-max (L~ z)) .. z < (W-min (L~ z)) .. z
Lemma109:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = E-max (L~ z) holds
(E-min (L~ z)) .. z < (W-min (L~ z)) .. z
Lemma110:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = E-max (L~ z) holds
(E-min (L~ z)) .. z < (W-max (L~ z)) .. z
Lemma111:
for z being non constant standard clockwise_oriented special_circular_sequence st z /. 1 = E-max (L~ z) holds
(S-min (L~ z)) .. z < (W-max (L~ z)) .. z
theorem Th56: :: SPRECT_5:56
theorem Th57: :: SPRECT_5:57
theorem Th58: :: SPRECT_5:58
theorem Th59: :: SPRECT_5:59
theorem Th60: :: SPRECT_5:60
theorem Th61: :: SPRECT_5:61
theorem Th62: :: SPRECT_5:62
theorem Th63: :: SPRECT_5:63
theorem Th64: :: SPRECT_5:64
theorem Th65: :: SPRECT_5:65
theorem Th66: :: SPRECT_5:66
theorem Th67: :: SPRECT_5:67
theorem Th68: :: SPRECT_5:68
theorem Th69: :: SPRECT_5:69
theorem Th70: :: SPRECT_5:70
theorem Th71: :: SPRECT_5:71
theorem Th72: :: SPRECT_5:72
theorem Th73: :: SPRECT_5:73