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Proof step 4 from proof mult-03 (previous step)

i0 < j, 0 < i0, 0 < j, 1 < j, 0 < i, 0 < j0 ⊦ ((i - 1) * j + (j - i0)) / (j0 * j) = (i - 1) / j0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-div inst: name: mult-02 seq: ⊦ 0 ≤ i0 ∧ i0 < j ∧ 0 ≤ i ∧ 0 < j0 → (i * j + i0) / (j0 * j) = i / j0 subst: [j0, i0, j, i] → [j0, j - i0, j, i - 1] flags: rewrite, current

Additional information

Used simplifier rules: sub-add-01: ⊦ i + (j - i0) = i + j - i0; 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%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%add-less: ⊦ 0 < i → i1 < i1 + i; from specification int-basic2%leone: ⊦ 1 ≤ i ↔ 0 < i; from specification int-abs%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1 Used terms: j0, j - i0, j, i - 1