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Proof step 10 from proof gcd-div-rest (previous step)

gcd(i, j) * i0 = i1 * gcd(i, j) + j0, gcd(i, j) * i0 = i, i = i1 * gcd(i, j) + j0, abs(j0) < gcd(i, j) ⊦ j0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult inst: name: mod-neq seq: ⊦ abs(j1) < abs(i) ∧ j1 ≠ 0 → i * j ≠ i * j0 + j1 subst: [j1, j0, j, i] → [j0, i1, i0, gcd(i, j)] flags: rewrite

Additional information

Used simplifier rules: gcd-abs: ⊦ abs(gcd(i, j)) = gcd(i, j);%commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: j0, i1, i0, gcd(i, j)