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Proof step 12 from proof gcdex-pos (previous step)

gcd(i, j) = i * i0 + j * j0, gcd(i, j) = i * i0 * (j + 1) + j * (j0 - i0 * i), j < 0, i0 < 0 ⊦ j = 0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
j0 = i1 + i0 * i, gcd(i, j) = i * i0 + j * j0, gcd(i, j) = i * i0 * (j + 1) + j * i1, j < 0, i0 < 0 ⊦ j = 0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0

Rule argument

spec: int-abs inst: name: elim-sub seq: ⊦ i0 = i - j ↔ i = i0 + j subst: [i, j, i0] → [j0, i0 * i, i2] flags:

Additional information

Used simplifier rules: ⊦ i0 = i - j ↔ i = i0 + j; (elim) Used terms: j0, i0 * i, i2