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Proof step 5 from proof gcdex-not-unique (previous step)

⊦ i * (i2 + i1 * j) + j * j0 = i * i2 + j * (j0 + i1 * i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ 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] → [i1 * j, i2, i] flags: rewrite

Additional information

Used simplifier rules: add-in: ⊦ i + j = i + i0 ↔ j = i0; from specification int-basic2%commutativity: ⊦ i * j = j * i; from specification int-mult%eq-dist: ⊦ (i + j) * i0 = j0 + j * i0 ↔ i * i0 = j0; from specification int-mult%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult Used terms: i1 * j, i2, i