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Proof step 5 from proof div-est-nle-pos (previous step)

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

User applied rule insert spec-lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: modlsp-02 seq: j * i + j0 < j * i0, abs(j0) < j ⊦ i ≤ i0 subst: [j, i, j0, i0] → [j, i1, j0, i0] flags:

Additional information

Used simplifier rules: anti: ⊦ i ≤ j → (j ≤ i ↔ i = j); from specification int-abs%ler: ⊦ i ≤ i; from specification int-abs%mods-ls-04: ⊦ j0 < j ∧ 0 ≤ i ∧ 0 ≤ i0 ∧ 0 ≤ j0 → (i * j + j0 < i0 * j ↔ i < i0); from specification int-mult%irref: ⊦ ¬ i < i; from specification int-basic1%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%absle: ⊦ 0 ≤ i → abs(i) = i; from specification int-abs Used terms: j, i1, j0, i0