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Proof step 20 from proof nummult-ls-03 (previous step)

i0 ≤ i3, i2 * (i3 + 1) + j0 ≤ i2 * i0, i2 * (i3 + 1) + j0 ≤ 0, abs(j0) < i2, i3 * i2 + j0 < 0, 0 < i2, j0 < i2, j0 ≤ 0 ⊦

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] → [i2, i3 + 1, j0, i0] flags: []

Additional information

Used simplifier rules: succ-01: ⊦ i + 1 ≤ j ↔ i < j; from specification int-abs%lenls: ⊦ i ≤ j → ¬ j < i; 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 Used terms: i2, i3 + 1, j0, i0