:: EQUATION semantic presentation
theorem Th1: :: EQUATION:1
theorem Th2: :: EQUATION:2
theorem Th3: :: EQUATION:3
theorem Th4: :: EQUATION:4
canceled;
theorem Th5: :: EQUATION:5
theorem Th6: :: EQUATION:6
theorem Th7: :: EQUATION:7
:: deftheorem Def1 defines "" EQUATION:def 1 :
theorem Th8: :: EQUATION:8
theorem Th9: :: EQUATION:9
theorem Th10: :: EQUATION:10
theorem Th11: :: EQUATION:11
theorem Th12: :: EQUATION:12
theorem Th13: :: EQUATION:13
theorem Th14: :: EQUATION:14
theorem Th15: :: EQUATION:15
theorem Th16: :: EQUATION:16
theorem Th17: :: EQUATION:17
theorem Th18: :: EQUATION:18
canceled;
theorem Th19: :: EQUATION:19
theorem Th20: :: EQUATION:20
theorem Th21: :: EQUATION:21
theorem Th22: :: EQUATION:22
:: deftheorem Def2 defines SuperAlgebraSet EQUATION:def 2 :
theorem Th23: :: EQUATION:23
theorem Th24: :: EQUATION:24
theorem Th25: :: EQUATION:25
theorem Th26: :: EQUATION:26
theorem Th27: :: EQUATION:27
theorem Th28: :: EQUATION:28
theorem Th29: :: EQUATION:29
theorem Th30: :: EQUATION:30
:: deftheorem Def3 defines TermAlg EQUATION:def 3 :
:: deftheorem Def4 defines Equations EQUATION:def 4 :
theorem Th31: :: EQUATION:31
theorem Th32: :: EQUATION:32
:: deftheorem Def5 defines |= EQUATION:def 5 :
:: deftheorem Def6 defines |= EQUATION:def 6 :
theorem Th33: :: EQUATION:33
theorem Th34: :: EQUATION:34
theorem Th35: :: EQUATION:35
theorem Th36: :: EQUATION:36
theorem Th37: :: EQUATION:37
theorem Th38: :: EQUATION:38
Lemma316:
for S being non empty non void ManySortedSign
for s being SortSymbol of S
for e being Element of (Equations S) . s
for I being non empty set
for A being MSAlgebra-Family of I,S st ( for i being Element of I holds A . i |= e ) holds
product A |= e
theorem Th39: :: EQUATION:39
theorem Th40: :: EQUATION:40