:: TOLER_1 semantic presentation
theorem Th1: :: TOLER_1:1
canceled;
theorem Th2: :: TOLER_1:2
theorem Th3: :: TOLER_1:3
theorem Th4: :: TOLER_1:4
theorem Th5: :: TOLER_1:5
theorem Th6: :: TOLER_1:6
theorem Th7: :: TOLER_1:7
theorem Th8: :: TOLER_1:8
theorem Th9: :: TOLER_1:9
theorem Th10: :: TOLER_1:10
canceled;
theorem Th11: :: TOLER_1:11
canceled;
theorem Th12: :: TOLER_1:12
canceled;
theorem Th13: :: TOLER_1:13
theorem Th14: :: TOLER_1:14
canceled;
theorem Th15: :: TOLER_1:15
theorem Th16: :: TOLER_1:16
theorem Th17: :: TOLER_1:17
canceled;
theorem Th18: :: TOLER_1:18
canceled;
theorem Th19: :: TOLER_1:19
theorem Th20: :: TOLER_1:20
canceled;
theorem Th21: :: TOLER_1:21
theorem Th22: :: TOLER_1:22
canceled;
theorem Th23: :: TOLER_1:23
canceled;
theorem Th24: :: TOLER_1:24
canceled;
theorem Th25: :: TOLER_1:25
theorem Th26: :: TOLER_1:26
canceled;
theorem Th27: :: TOLER_1:27
theorem Th28: :: TOLER_1:28
theorem Th29: :: TOLER_1:29
theorem Th30: :: TOLER_1:30
canceled;
theorem Th31: :: TOLER_1:31
canceled;
theorem Th32: :: TOLER_1:32
theorem Th33: :: TOLER_1:33
:: deftheorem Def1 TOLER_1:def 1 :
canceled;
:: deftheorem Def2 TOLER_1:def 2 :
canceled;
:: deftheorem Def3 defines TolSet TOLER_1:def 3 :
theorem Th34: :: TOLER_1:34
:: deftheorem Def4 defines TolClass-like TOLER_1:def 4 :
theorem Th35: :: TOLER_1:35
canceled;
theorem Th36: :: TOLER_1:36
canceled;
theorem Th37: :: TOLER_1:37
canceled;
theorem Th38: :: TOLER_1:38
theorem Th39: :: TOLER_1:39
theorem Th40: :: TOLER_1:40
theorem Th41: :: TOLER_1:41
theorem Th42: :: TOLER_1:42
theorem Th43: :: TOLER_1:43
theorem Th44: :: TOLER_1:44
canceled;
theorem Th45: :: TOLER_1:45
theorem Th46: :: TOLER_1:46
theorem Th47: :: TOLER_1:47
theorem Th48: :: TOLER_1:48
canceled;
theorem Th49: :: TOLER_1:49
theorem Th50: :: TOLER_1:50
theorem Th51: :: TOLER_1:51
theorem Th52: :: TOLER_1:52
for
Y being
set for
T,
R being
Tolerance of
union Y st ( for
x,
y being
set holds
(
[x,y] in T iff ex
Z being
set st
(
Z in Y &
x in Z &
y in Z ) ) ) & ( for
x,
y being
set holds
(
[x,y] in R iff ex
Z being
set st
(
Z in Y &
x in Z &
y in Z ) ) ) holds
T = R
theorem Th53: :: TOLER_1:53
theorem Th54: :: TOLER_1:54
theorem Th55: :: TOLER_1:55
canceled;
theorem Th56: :: TOLER_1:56
canceled;
theorem Th57: :: TOLER_1:57
canceled;
theorem Th58: :: TOLER_1:58
theorem Th59: :: TOLER_1:59
:: deftheorem Def5 TOLER_1:def 5 :
canceled;
:: deftheorem Def6 defines TolSets TOLER_1:def 6 :
:: deftheorem Def7 defines TolClasses TOLER_1:def 7 :
theorem Th60: :: TOLER_1:60
canceled;
theorem Th61: :: TOLER_1:61
canceled;
theorem Th62: :: TOLER_1:62
canceled;
theorem Th63: :: TOLER_1:63
canceled;
theorem Th64: :: TOLER_1:64
theorem Th65: :: TOLER_1:65
theorem Th66: :: TOLER_1:66
theorem Th67: :: TOLER_1:67
theorem Th68: :: TOLER_1:68
theorem Th69: :: TOLER_1:69
theorem Th70: :: TOLER_1:70
theorem Th71: :: TOLER_1:71
theorem Th72: :: TOLER_1:72
theorem Th73: :: TOLER_1:73
theorem Th74: :: TOLER_1:74