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Proof step 9 from proof estimate-01 (previous step)

j * i0 < i1 * j + j1, 0 ≤ j1, i1 < i0, j1 < j, 1 < i, 0 < i, 0 < j, 0 < i0, i1 ≤ j0, j0 < i0, j < i, i * i0 ≤ i1 * j + j1 ⊦

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, j1] 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, j1