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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 = ((a1a2) ∩ (b1b2))
dp15.2 c1 = ((a0a2) ∩ (b0b2))
dp15.3 p0 = ((a1b1) ∩ (a2b2))
Assertion
Ref Expression
dp15 ((a0a1) ∩ ((b0 ∩ (a0p0)) ∪ b1)) ≤ ((c0c1) ∪ (b1 ∩ (a0a1)))

Proof of Theorem dp15
StepHypRef Expression
1 id 59 . 2 (a2 ∪ (a0 ∩ (a1b1))) = (a2 ∪ (a0 ∩ (a1b1)))
2 dp15.3 . 2 p0 = ((a1b1) ∩ (a2b2))
3 id 59 . 2 (b0 ∩ (a0p0)) = (b0 ∩ (a0p0))
4 dp15.1 . 2 c0 = ((a1a2) ∩ (b1b2))
5 dp15.2 . 2 c1 = ((a0a2) ∩ (b0b2))
61, 2, 3, 4, 5dp15lemh 1159 1 ((a0a1) ∩ ((b0 ∩ (a0p0)) ∪ b1)) ≤ ((c0c1) ∪ (b1 ∩ (a0a1)))
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2   ∪ 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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