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Proof step 13 from proof square-neq-any-pos-01 (previous step)

j / gcd(j, j0) * j = j0 / gcd(j0, j) * j0 * i, 0 < i, 0 < j, 0 < j0 ⊦ gcd(j, j0) = 1, j = 0, j0 = 0, ∃ i0. i = i0 * i0

User applied rule cut formula

And obtained the following new goals

Proof step 14:
(j / gcd(j, j0) * j) / gcd(j, j0) = (j0 / gcd(j0, j) * j0 * i) / gcd(j, j0), j / gcd(j, j0) * j = j0 / gcd(j0, j) * j0 * i, 0 < i, 0 < j, 0 < j0 ⊦ gcd(j, j0) = 1, j = 0, j0 = 0, ∃ i0. i = i0 * i0

Rule argument

fma: (j / gcd(j, j0) * j) / gcd(j, j0) = (j0 / gcd(j0, j) * j0 * i) / gcd(j, j0)

Additional information

Used simplifier rules: associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%neqf: ⊦ i / j ≠ i / i0 → j ≠ i0; (forward) from specification int-div Used formulas: (j / gcd(j, j0) * j) / gcd(j, j0) = (j0 / gcd(j0, j) * j0 * i) / gcd(j, j0)