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Proof step 31 from proof mod-ls-same-01 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: dist-lsplit seq: ⊦ (i + i0) * j = i * j + i0 * j subst: [j, i0, i] → [j, 1, i0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 1 * i = i; (s)%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2% ⊦ i < j ↔ ¬ j ≤ i; (ss)%add-c: ⊦ i + j = j + i; from specification int-basic2% ⊦ i < j → (j ≤ i ↔ false); (as) Used terms: j, 1, i0