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Proof step 58 from proof make (previous step)

0 ≤ gcd(i, i0), 0 < i0, i0 / gcd(i, i0) ≤ 0, i0 / gcd(i, i0) < i0 ⊦ i0 = 0, i = 0, rational(i / gcd(i, i0), i0 / gcd(i, i0)).num = i / gcd(i, i0) ∧ rational(i / gcd(i, i0), i0 / gcd(i, i0)).denom = i0 / gcd(i, i0)

User applied rule cut formula

And closed the goal!

Rule argument

fma: gcd(i, i0) ≠ 0

Additional information

Used simplifier rules: ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0;% ⊦ i ≠ j → (i ≤ j ↔ i < j);% ⊦ 0 < j → (i / j ≤ 0 ↔ i < j);% ⊦ 0 < i → ¬ i < gcd(i, j);% ⊦ gcd(i, j) = gcd(j, i); Used formulas: gcd(i, i0) ≠ 0