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Proof step 5 from proof zero-ge-add (previous step)

0 ≤ (i0 + 1) * j, 0 ≤ i0 * j + j1, 0 ≤ j1, j1 < j, 0 < j ⊦ 0 ≤ i0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: zero-ge-03 seq: ⊦ i ≤ 0 → (0 ≤ i * j ↔ ¬ ¬(i = 0 ∨ j ≤ 0)) subst: [j, i] → [j, i0 + 1] flags: rewrite, current

Additional information

Used simplifier rules: dist-rsplit: ⊦ i * (j + j0) = i * j + i * j0;%one: ⊦ 1 * i = i;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%minus-one: ⊦ i + 1 = 0 → i * j = ~ j;%associativity: ⊦ i * j * j0 = (i * j) * j0;%commutativity: ⊦ i * j = j * i;%succ-01: ⊦ i + 1 ≤ j ↔ i < j; 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%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%neg-15: ⊦ i + ~ j = i - j; from specification int-abs%sub-le-01: ⊦ i ≤ j - i0 ↔ i + i0 ≤ j; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs Used terms: j, i0 + 1