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Theorem dp41 1193
 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). (4)=>(1)
Hypotheses
Ref Expression
dp41.1 c0 = ((a1a2) ∩ (b1b2))
dp41.2 c1 = ((a0a2) ∩ (b0b2))
dp41.3 c2 = ((a0a1) ∩ (b0b1))
dp41.4 p2 = ((a0b0) ∩ (a1b1))
dp41.5 p2 ≤ (a2b2)
Assertion
Ref Expression
dp41 c2 ≤ (c0c1)

Proof of Theorem dp41
StepHypRef Expression
1 dp41.1 . 2 c0 = ((a1a2) ∩ (b1b2))
2 dp41.2 . 2 c1 = ((a0a2) ∩ (b0b2))
3 dp41.3 . 2 c2 = ((a0a1) ∩ (b0b1))
4 id 59 . 2 (((a0b0) ∩ (a1b1)) ∩ (a2b2)) = (((a0b0) ∩ (a1b1)) ∩ (a2b2))
5 dp41.4 . 2 p2 = ((a0b0) ∩ (a1b1))
6 dp41.5 . 2 p2 ≤ (a2b2)
71, 2, 3, 4, 5, 6dp41lemm 1192 1 c2 ≤ (c0c1)
 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: (None)
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