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Proof step 15 from proof gcdex-pos (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
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

Rule argument

Additional information

Used simplifier rules: forward-le-05: ⊦ i < j ∧ 0 ≤ i → 0 < j; (forward) from specification int-abs%ls-01: ⊦ i < j → ¬ j < i; from specification int-basic1%lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1