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Proof step 9 from proof ls-pos (previous step)

0 < i, ∀ i, j0. 0 < i → (i * j1 < i * j0 ↔ j1 < j0) ⊦ i * j1 -1 < i * j0 ↔ j1 -1 < j0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 10:
j1 = i0 +1, 0 < i, ∀ i, j0. 0 < i → (i * j1 < i * j0 ↔ j1 < j0) ⊦ i * i0 < i * j0 ↔ i0 < j0

Rule argument

spec: int-basic1 inst: name: elim-pred seq: ⊦ i = j -1 ↔ j = i +1 subst: [j, i] → [j1, i0] flags:

Additional information

Used simplifier rules: ⊦ i = j -1 ↔ j = i +1; (elim) Used terms: j1, i0