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Proof step 22 from proof gcd-conq-one (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
1 = i * i0 + j0 * j, gcd(i, j) = 1, 0 ≤ j * j0 + i0, 0 ≤ j, i0 + 1 < i, 0 < i, i0 < 0 ⊦ i = 0, j | i * (j * j0 + i0) - 1

Rule argument

Additional information

Used simplifier rules: zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%zero-gels-04: ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j; from specification int-abs%lels: ⊦ ¬ i < j ↔ j ≤ i; from specification int-abs