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

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

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

Additional information

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