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Proof step 6 from proof gcdex-smallest-pos (previous step)

gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0, ∀ i1, i, j, j0. i→n(i1) < i→n(i0) → gcd(i, j) = i * i1 + j * j0 ∧ 0 ≤ i1 → j = 0 ∨ (∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0 ∧ (∀ i1. 0 ≤ i1 ∧ i1 < i0 → ¬(∃ j1. gcd(i, j) = i * i1 + j * j1))) ⊦ j = 0 ∨ (∃ i0, j0. gcd(i, j) = i * i0 + j * j0 ∧ 0 ≤ i0 ∧ (∀ i1. 0 ≤ i1 ∧ i1 < i0 → ¬(∃ j1. gcd(i, j) = i * i1 + j * j1)))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

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