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Proof step 18 from proof nummult-le-01 (previous step)

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

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 + 1, j0, i0]

Additional information

Used simplifier rules: ⊦ i + 1 ≤ j ↔ i < j; (s)% ⊦ i ≤ j → (j < i ↔ false); (as)%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, i1 + 1, j0, i0