:: NECKLACE semantic presentation
theorem Th1: :: NECKLACE:1
canceled;
theorem Th2: :: NECKLACE:2
theorem Th3: :: NECKLACE:3
for b
1, b
2, b
3, b
4, b
5, b
6 being
set holds
[:{b1,b2,b3},{b4,b5,b6}:] = {[b1,b4],[b1,b5],[b1,b6],[b2,b4],[b2,b5],[b2,b6],[b3,b4],[b3,b5],[b3,b6]}
theorem Th4: :: NECKLACE:4
theorem Th5: :: NECKLACE:5
theorem Th6: :: NECKLACE:6
theorem Th7: :: NECKLACE:7
theorem Th8: :: NECKLACE:8
theorem Th9: :: NECKLACE:9
theorem Th10: :: NECKLACE:10
theorem Th11: :: NECKLACE:11
for b
1, b
2, b
3, b
4 being
set holds
not ( ( b
1 = b
2 implies b
3 = b
4 ) & ( b
3 = b
4 implies b
1 = b
2 ) & not
(b1,b2 --> b3,b4) " = b
3,b
4 --> b
1,b
2 )
theorem Th12: :: NECKLACE:12
:: deftheorem Def1 NECKLACE:def 1 :
canceled;
:: deftheorem Def2 defines embeds NECKLACE:def 2 :
theorem Th13: :: NECKLACE:13
:: deftheorem Def3 defines is_equimorphic_to NECKLACE:def 3 :
theorem Th14: :: NECKLACE:14
:: deftheorem Def4 defines symmetric NECKLACE:def 4 :
:: deftheorem Def5 defines asymmetric NECKLACE:def 5 :
theorem Th15: :: NECKLACE:15
:: deftheorem Def6 defines irreflexive NECKLACE:def 6 :
:: deftheorem Def7 defines -SuccRelStr NECKLACE:def 7 :
theorem Th16: :: NECKLACE:16
theorem Th17: :: NECKLACE:17
:: deftheorem Def8 defines SymRelStr NECKLACE:def 8 :
Lemma18:
for b1, b2 being non empty RelStr holds
( b1,b2 are_isomorphic implies Card the InternalRel of b1 = Card the InternalRel of b2 )
:: deftheorem Def9 defines ComplRelStr NECKLACE:def 9 :
theorem Th18: :: NECKLACE:18
:: deftheorem Def10 defines Necklace NECKLACE:def 10 :
theorem Th19: :: NECKLACE:19
theorem Th20: :: NECKLACE:20
theorem Th21: :: NECKLACE:21
theorem Th22: :: NECKLACE:22
theorem Th23: :: NECKLACE:23
theorem Th24: :: NECKLACE:24
theorem Th25: :: NECKLACE:25
theorem Th26: :: NECKLACE:26
theorem Th27: :: NECKLACE:27
theorem Th28: :: NECKLACE:28
theorem Th29: :: NECKLACE:29
theorem Th30: :: NECKLACE:30
theorem Th31: :: NECKLACE:31