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Proof step 13 from proof mod-div-ls (previous step)

0 < i1, 0 ≤ i0, i1 ≤ (i0 + i1 * j0) / (j0 + 1), i0 < i1, 0 ≤ j0, 0 ≤ i2, i1 * (j0 + 1) ≤ i0 + i1 * j0, i0 < (i0 + i1 * j0) / (j0 + 1), 0 < (i0 + i1 * j0) / (j0 + 1) ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [1, j0, i1] flags: rewrite

Additional information

Used simplifier rules: one: ⊦ 1 * i = i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%lep-02: ⊦ i + j ≤ i + j0 ↔ j ≤ j0; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); 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 Used terms: 1, j0, i1