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Proof step 3 from proof modlsp (previous step)

j * i < j * (i0 + 1), j * i < j * i0 + j0, 0 ≤ j0, j0 < j, i0 < i, 0 < j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < i → (i * j < i * j0 ↔ j < j0)

Rule argument

spec: int-mult inst: name: ls-pos seq: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0) subst: [j0, j, i] → [i0 + 1, i, j] flags: rewrite, current

Additional information

Used simplifier rules: succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i0 + 1, i, j