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Proof step 11 from proof nummult-le-03 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlsp-01 seq: j * i < j * i0 + j0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [i, i0, i1, j0] flags:

Additional information

Used simplifier rules: anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); 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%lst-03: ⊦ i + j < i0 ∧ ¬ j < j0 → i + j0 < i0; from specification int-basic2%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%ler: ⊦ i ≤ i; from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%ls-02: ⊦ i < i + j ↔ 0 < j; from specification int-basic2%lenls: ⊦ i ≤ j → ¬ j < i; from specification int-abs Used terms: i, i0, i1, j0