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Proof step 57 from proof gcd-rec (previous step)

gcd(abs(i), abs(j)) * i2 = abs(i), gcd(abs(i), abs(j)) * i1 = abs(j), abs(i) = i0 * abs(j) + j0, j0 < abs(j), gcd(abs(j), j0) < gcd(abs(i), abs(j)), 0 ≤ j0, 0 ≤ i0 ⊦ j = 0, gcd(abs(i), abs(j)) | gcd(abs(i), abs(j)) * i2 - i0 * gcd(abs(i), abs(j)) * i1

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-mult name: commutativity seq: ⊦ i * j = j * i subst: [j, i] → [gcd(abs(i), abs(j)) * i1, i0] flags: <all paths>

Additional information

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