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Proof step 10 from proof gcd-div-gcd-pos (previous step)

j = i2 * gcd(i, j) + j0 ∧ 0 ≤ j0 ∧ j0 < gcd(i, j) ∧ 0 ≤ i2 ∧ 0 ≤ j, i = i1 * gcd(i, j), i0 | i1, i0 | i2, 0 < i, 0 < j, 0 < i0, 1 < i0, 0 ≤ i1, 0 < gcd(i, j), 0 ≤ i, 0 < i1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
i = i1 * gcd(i, j), j = i2 * gcd(i, j) + j0, 0 ≤ j, 0 ≤ i2, 0 ≤ j0, 0 < i1, 0 ≤ i, 0 < gcd(i, j), 0 ≤ i1, 1 < i0, 0 < i0, 0 < j, 0 < i, i0 | i2, i0 | i1, j0 < gcd(i, j) ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%lf-02: ⊦ i < j ∧ j = i0 → i < i0; (forward) from specification int-basic1