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Proof step 33 from proof gcd-rec (previous step)

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

User applied rule exists right

And obtained the following new goals

Proof step 34:
gcd(abs(j), j0) * i2 = abs(j), abs(i) = i0 * abs(j) + j0, gcd(abs(j), j0) * i1 = j0, gcd(i0 * abs(j) + j0, abs(j)) < gcd(abs(j), j0), 0 ≤ i0, 0 ≤ j0, j0 < abs(j) ⊦ i = 0, j = 0, gcd(i0 * abs(j) + j0, abs(j)) = gcd(abs(j), j0), gcd(abs(j), j0) * (i2 * i0 + i1) = i0 * abs(j) + j0, ∃ i1. gcd(abs(j), j0) * i1 = i0 * abs(j) + j0

Rule argument

pos: right 4 terms: i2 * i0 + i1 abort: F discard: F computed: F

Additional information

Used terms: i2 * i0 + i1