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Proof step 35 from proof div-pos-def (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ i ∧ 0 < j ∧ 0 < j0 → (i / j) / j0 = i / (j * j0) subst: [j0, j, i] → [gcd(i, j), gcd(j0, i0), j0 * i] rotate: F spec: int-div inst: name: div-div-pos

Additional information

Used simplifier rules: ⊦ 0 < i → (0 ≤ i * j ↔ 0 ≤ j);% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ gcd(i, j) ≤ 0 ↔ gcd(i, j) = 0;% ⊦ gcd(i, j) = 0 ↔ i = 0 ∧ j = 0; Used terms: gcd(i, j), gcd(j0, i0), j0 * i