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Theorem gomaex4 900
 Description: Proof of Mayet Example 4 from 4-variable Godowski equation. R. Mayet, "Equational bases for some varieties of orthomodular lattices related to states," Algebra Universalis 23 (1986), 167-195.
Hypotheses
Ref Expression
go2n4.1
go2n4.2
go2n4.3
go2n4.4
go2n4.5
go2n4.6
go2n4.7
go2n4.8
gomaex4.9
gomaex4.10
Assertion
Ref Expression
gomaex4

Proof of Theorem gomaex4
StepHypRef Expression
1 go2n4.7 . . . . . . 7
2 go2n4.8 . . . . . . 7
3 go2n4.1 . . . . . . 7
4 go2n4.2 . . . . . . 7
5 go2n4.3 . . . . . . 7
6 go2n4.4 . . . . . . 7
7 go2n4.5 . . . . . . 7
8 go2n4.6 . . . . . . 7
9 gomaex4.9 . . . . . . 7
101, 2, 3, 4, 5, 6, 7, 8, 9go2n4 899 . . . . . 6
11 an4 86 . . . . . . 7
12 ancom 74 . . . . . . . 8
13 ancom 74 . . . . . . . . 9
1413ran 78 . . . . . . . 8
1512, 14ax-r2 36 . . . . . . 7
16 an4 86 . . . . . . 7
1711, 15, 163tr 65 . . . . . 6
18 ax-a2 31 . . . . . 6
1910, 17, 18le3tr1 140 . . . . 5
20 ancom 74 . . . . . . . . 9
2120lan 77 . . . . . . . 8
22 an4 86 . . . . . . . 8
23 ancom 74 . . . . . . . . 9
2423lan 77 . . . . . . . 8
2521, 22, 243tr 65 . . . . . . 7
26 ancom 74 . . . . . . . 8
27 ancom 74 . . . . . . . 8
2826, 272an 79 . . . . . . 7
29 ancom 74 . . . . . . 7
3025, 28, 293tr 65 . . . . . 6
31 gomaex4.10 . . . . . . 7
325, 6, 7, 8, 1, 2, 3, 4, 31go2n4 899 . . . . . 6
3330, 32bltr 138 . . . . 5
3419, 33ler2an 173 . . . 4
3534leran 153 . . 3
36 go1 343 . . 3
3735, 36lbtr 139 . 2
38 le0 147 . 2
3937, 38lebi 145 1
 Colors of variables: term Syntax hints:   wb 1   wle 2  wn 4   wo 6   wa 7  wf 9   wi1 12   wi2 13 This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439 This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i1 44  df-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133
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