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Proof step 2 from proof gcdex-not-unique (previous step)

gcd(i, j) = i * i0 + j * j0 ⊦ gcd(i, j) = i * (i0 - i1 * j) + j * (j0 + i1 * i)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 3:
i0 = i2 + i1 * j, gcd(i, j) = i * i0 + j * j0 ⊦ gcd(i, j) = i * i2 + j * (j0 + i1 * i)

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [i0, i1 * j, i2] flags:

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: i0, i1 * j, i2