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Proof step 10 from proof gcdhex (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 11:
i = j, gcd(i, j) = gcd(j, i % j), 0 ≤ i, j ≤ i, 0 < i, 0 < j, ∀ i0, j. i→n(i0) < i→n(i) → 0 ≤ i0 ∧ 0 ≤ j ∧ j ≤ i0 → (∃ i1, j0. gcd(i0, j) = i0 * i1 + j * j0) ⊦ j = 0, ∃ i0, j0. gcd(i, j) = i * i0 + j * j0
Proof step 13:
gcd(i, j) = gcd(j, i % j), 0 ≤ i, j ≤ i, 0 < i, 0 < j, ∀ 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

Rule argument

fma: i = j

Additional information

Used formulas: i = j