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Proof step 23 from proof gcd-div-gcd-pos (previous step)

j = (i0 * i1) * gcd(j, i), i = (i0 * i3) * gcd(i, j), 0 ≤ j, 0 < i, 0 < j, 0 < i0, 1 < i0, 0 ≤ i, 0 < gcd(i, j), 0 ≤ i3, 0 < i3, 0 ≤ i1, 0 < i1, 0 < gcd(j, i) ⊦ i0 * gcd(i, j) | i ∧ i0 * gcd(i, j) | j ∧ (i ≠ 0 ∨ j ≠ 0)

User applied rule cut formula

And obtained the following new goals

Proof step 24:
i ≠ 0 ∨ j ≠ 0, j = (i0 * i1) * gcd(j, i), i = (i0 * i3) * gcd(i, j), 0 ≤ j, 0 < i, 0 < j, 0 < i0, 1 < i0, 0 ≤ i, 0 < gcd(i, j), 0 ≤ i3, 0 < i3, 0 ≤ i1, 0 < i1, 0 < gcd(j, i) ⊦ i0 * gcd(i, j) | i ∧ i0 * gcd(i, j) | j ∧ (i ≠ 0 ∨ j ≠ 0)

Rule argument

fma: i ≠ 0 ∨ j ≠ 0

Additional information

Used simplifier rules: gcd-zero: ⊦ gcd(0, 0) = 0;%zero-left: ⊦ 0 * i = 0; from specification int-mult%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult Used formulas: i ≠ 0 ∨ j ≠ 0