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Theorem dp15 1160
Description: Part of theorem from Alan Day and Doug Pickering, "A note on the Arguesian lattice identity," Studia Sci. Math. Hungar. 19:303-305 (1982). (1)=>(5)
Hypotheses
Ref Expression
dp15.1 c0 = ((a1 v a2) ^ (b1 v b2))
dp15.2 c1 = ((a0 v a2) ^ (b0 v b2))
dp15.3 p0 = ((a1 v b1) ^ (a2 v b2))
Assertion
Ref Expression
dp15 ((a0 v a1) ^ ((b0 ^ (a0 v p0)) v b1)) =< ((c0 v c1) v (b1 ^ (a0 v a1)))
Proof of Theorem dp15
StepHypRef Expression
1 id 59 . 2 (a2 v (a0 ^ (a1 v b1))) = (a2 v (a0 ^ (a1 v b1)))
2 dp15.3 . 2 p0 = ((a1 v b1) ^ (a2 v b2))
3 id 59 . 2 (b0 ^ (a0 v p0)) = (b0 ^ (a0 v p0))
4 dp15.1 . 2 c0 = ((a1 v a2) ^ (b1 v b2))
5 dp15.2 . 2 c1 = ((a0 v a2) ^ (b0 v b2))
61, 2, 3, 4, 5dp15lemh 1159 1 ((a0 v a1) ^ ((b0 ^ (a0 v p0)) v b1)) =< ((c0 v c1) v (b1 ^ (a0 v a1)))
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2   v wo 6   ^ wa 7
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-ml 1120  ax-arg 1151
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by:  dp53lema  1161  xdp53  1198  xxdp53  1201
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