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Proof step 31 from proof equality-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 32:
⊦ i * j = j * i
Proof step 33:
gcd(j0, i0) ≠ 0, 0 < j ∧ 0 < j0 ∧ 0 ≤ i0, 0 < j0 ∧ 0 < j ∧ 0 ≤ i, 0 < i0 ∧ 0 < i ∧ 0 ≤ j, i * j0 = j * i0, 0 < j, 0 < j0, 0 < i, 0 < i0 ⊦ j0 = 0, j = 0, i = 0, i0 = 0, i = gcd(i * i0, j * i0) / gcd(i0, j0) ∧ j = j

Rule argument

seq: ⊦ i * j = j * i subst: [j, i] → [j, i0] rotate: F spec: int-mult inst: name: commutativity

Additional information

Used simplifier rules: ⊦ i * j = j * i; Used terms: j, i0