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Proof step 52 from proof gcd-rec (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 53:
j0 = abs(i) - i0 * abs(j), abs(i) = i0 * abs(j) + j0, gcd(abs(i), abs(j)) * i1 = abs(j), gcd(abs(i), abs(j)) * i2 = abs(i), j0 < abs(j), 0 ≤ j0, 0 ≤ i0, gcd(abs(j), j0) < gcd(abs(i), abs(j)) ⊦ j = 0, gcd(abs(i), abs(j)) | j0

Rule argument

fma: j0 = abs(i) - i0 * abs(j)

Additional information

Used simplifier rules: sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: j0 = abs(i) - i0 * abs(j)