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Proof step 16 from proof gcdex-pos (previous step)

gcd(i, j) = i * i0 + j * j0, 0 < j, ∀ i1. gcd(i, j) = i * (i0 - i1 * j) + j * (j0 + i1 * i) ⊦ 0 ≤ i0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0

User applied rule cut formula

And obtained the following new goals

Rule argument

fma: j = 0

Additional information

Used simplifier rules: gcd-zero-04: ⊦ gcd(i, 0) = abs(i);%Mult-zero: ⊦ i * 0 = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used formulas: j = 0