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Proof step 11 from proof div-le-modnotzero (previous step)

i0 * j < i1 * j + j0, j0 < j, 1 < j, 0 < j, 0 ≤ i1, 0 ≤ i1 * j + j0, 0 < j0, i1 < i0, 0 < i0 ⊦ j0 = 0

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlsp seq: j * i < j * i0 + j0, 0 ≤ j0, 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%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs Used terms: j, i0, i1, j0