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Proof step 13 from proof even-rec (previous step)

i0 + 2 = 2 * (i1 + 1) ⊦ i0 = 2 * i1, ∃ j0. i0 = 2 * j0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ i * (j + j0) = i * j + i * j0

Rule argument

spec: int-mult inst: name: dist-rsplit seq: ⊦ i * (j + j0) = i * j + i * j0 subst: [j0, j, i] → [1, i1, 2] flags: rewrite

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%numadd: ⊦ i + (* j) = i0 + (* j0) ↔ i = i0 + (j0 - j); from specification int-abs%add-zero-rev: ⊦ 0 + i = i; from specification int-basic2%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, i1, 2