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Proof step 26 from proof gcdhex (previous step)

gcd(i, j) = i * j0 + j * (i0 - i / j * j0), gcd(i, j) = gcd(j, i - i / j * j), 0 < j, 0 ≤ i, j < i, 1 < i, 0 < i, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 ≤ j ∧ j ≤ i0 → (∃ i1, j0. gcd(i0, j) = i0 * i1 + j * j0) ⊦ i = j, j = 0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0

User applied rule exists right

And closed the goal!

Rule argument

pos: right 3 terms: j0, i0 - i / j * j0 abort: F discard: T computed: T

Additional information

Used terms: j0, i0 - i / j * j0