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Proof step 15 from proof le-abs-numerator (previous step)

j0 ≤ 0, j < 0, j < j0, 0 < i0 + i0 * j + j0, i0 * j + j0 < 0, 0 ≤ i0, j0 < i0 + i0 * j, 0 < i0 + i0 * j ⊦ 0 < i0 * (j + 1) + j0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [i0, 1, j] 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%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: i0, 1, j