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Proof step 17 from proof gcd-div-gcd-pos (previous step)

i = i1 * gcd(i, j), j = i2 * gcd(j, i), 0 < gcd(j, i), 0 < gcd(i, j), 1 < i0, 0 < i0, 0 < i, 0 < j, i0 | i2, 0 ≤ i2, 0 ≤ j, 0 ≤ i1, 0 ≤ i, ∃ i2. i0 * i2 = i1 ⊦

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
i = (i0 * i3) * gcd(i, j), j = i2 * gcd(j, i), 0 < j, 0 < i, 0 < i0, 1 < i0, 0 < gcd(i, j), 0 < gcd(j, i), i0 | i2, 0 ≤ j, 0 ≤ i2, 0 ≤ i, 0 ≤ i3 ⊦

Rule argument

Additional information

Used simplifier rules: forward-le-01: ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward) from specification int-abs%commutativity: ⊦ i * j = j * i; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult% ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j); (s)