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Proof step 8 from proof nummult-le-03 (previous step)

i1 * i + j0 ≤ i * i0, i1 * i + j0 < i, i1 * i + j0 < 0, j0 < i, j0 ≤ 0, (i1 * i + j0) + 1 < i, 0 < i, abs(j0) < i, i0 < i1 ⊦

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlep-02 seq: j * i + j0 ≤ j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [i, i1, j0, i0] flags:

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i, i1, j0, i0