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Proof step 15 from proof gcd-conq-one (previous step)

1 = i * i0 + j0 * j, gcd(i, j) = 1, 0 < i, i0 < 0 ⊦ i = 0, j < 0, ∃ i0. 0 ≤ i0 ∧ j | i * i0 - 1

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 16:
1 = i * i0 + j0 * j, gcd(i, j) = 1, i0 < 0, 0 < i, 0 ≤ j ⊦ i = 0, ∃ i0. 0 ≤ i0 ∧ j | i * i0 - 1

Rule argument

Additional information

Used simplifier rules: ⊦ i < j ↔ ¬ j ≤ i; (ss)