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Proof step 7 from proof mult-ls (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i0, i1, j0