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Proof step 10 from proof estimate-01 (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult name: modlsp seq: j * i < j * i0 + j0, 0 ≤ j0, j0 < j ⊦ i ≤ i0 subst: [j, i, i0, j0] → [j, i0, i1, j1]

Additional information

Used simplifier rules: ⊦ i < j → (j ≤ i ↔ false); (as)%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j, i0, i1, j1