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Proof step 5 from proof ls-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
i * j1 < i * (j0 - 1) ↔ j1 + 1 < j0, 0 < i, ∀ i, j0. 0 < i → (i * j1 < i * j0 ↔ j1 < j0) ⊦ i * j1 + i < i * j0 ↔ j1 + 1 < j0

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%sub-ls-01: ⊦ i < j - i0 ↔ i + i0 < j; from specification int-abs%sub-pred: ⊦ i -1 = i - 1; from specification int-abs