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

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ i ≤ j → (j ≤ i ↔ i = j); (s)%commutativity: ⊦ i * j = j * i; from specification int-mult% ⊦ i < i + j ↔ 0 < j; (s)% ⊦ i ≤ j → ¬ j < i; (s)%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: i, i0, i1, j0