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Proof step 17 from proof gcd-conq-one (previous step)

j * j0 + i0 < 0, gcd(i, j) = 1, 1 = i * i0 + j0 * j, i0 < 0, 0 < i, i0 + 1 < i, 0 ≤ j ⊦ 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 18:
1 = i * i0 + j0 * j, gcd(i, j) = 1, j * j0 + i0 < i, j * j0 + i0 < 0, 0 ≤ j, i0 + 1 < i, 0 < i, i0 < 0, (j * j0 + i0) + 1 < i ⊦ i = 0

Rule argument

Additional information

Used simplifier rules: lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%zero-gels-01: ⊦ i < 0 ∧ 0 ≤ j → i < j; from specification int-abs%succ-01: ⊦ i +1 = i + 1; from specification int-basic2%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%trans: ⊦ i < j ∧ j < j0 → i < j0; (forward) from specification int-basic1%lf-01: ⊦ i < j ∧ j < i0 → i +1 < i0; (forward) from specification int-basic1