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Proof step 18 from proof mod-div-ls (previous step)

j0 < j, 0 < j, 0 < i1, 0 ≤ i0, i1 ≤ (i0 + i1 * j0) / j, i0 < i1, 0 ≤ j0, 0 ≤ i2, i0 < (i0 + i1 * j0) / j, 0 < (i0 + i1 * j0) / j ⊦ i1 ≤ (i1 + i1 * j0) / j

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: div-le-pos seq: ⊦ j0 ≤ i / j ∧ i ≤ i0 ∧ 0 < j → j0 ≤ i0 / j subst: [j0, i, j, i0] → [i1, i0 + i1 * j0, j, i1 + i1 * j0] flags: rewrite, current

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lep-02: ⊦ i + j ≤ i + j0 ↔ j ≤ j0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: i1, i0 + i1 * j0, j, i1 + i1 * j0