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Proof step 27 from proof gcd-rec (previous step)

abs(i) = i0 * abs(j) + j0, gcd(i0 * abs(j) + j0, abs(j)) < gcd(abs(j), j0), j0 < abs(j), gcd(abs(j), j0) | abs(j), 0 ≤ i0, 0 ≤ j0, ∃ i0. gcd(abs(j), j0) * i0 = j0 ⊦ gcd(i0 * abs(j) + j0, abs(j)) = gcd(abs(j), j0), i = 0, j = 0, gcd(abs(j), j0) | i0 * abs(j) + j0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 28:
gcd(abs(j), j0) * i1 = j0, abs(i) = i0 * abs(j) + j0, j0 < abs(j), gcd(abs(i), abs(j)) < gcd(abs(j), j0), gcd(abs(j), j0) | abs(j), 0 ≤ j0, 0 ≤ i0 ⊦ gcd(abs(i), abs(j)) = gcd(abs(j), j0), i = 0, j = 0, gcd(abs(j), j0) | abs(i)

Proof step 27 from proof gcd-rec (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information