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Proof step 1 from proof mult-def-01 (conclusion)

gcd(i1, j1) = 1, gcd(i2, j2) = 1, 0 < j1, 0 < j2 ⊦ rational(i1, j1) * rational(i2, j2) = rational(i1 * i2, j1 * j2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ri * rj = rational(ri.num * rj.num, ri.denom * rj.denom)

Rule argument

name: mult-def rotate: F subst: [rj, ri] → [rational(i2, j2), rational(i1, j1)]

Additional information

Used simplifier rules: num-id: ⊦ gcd(i, j) = 1 ∧ 0 < j → rational(i, j).num = i;%denom-id: ⊦ gcd(i, j) = 1 ∧ 0 < j → rational(i, j).denom = j;% ⊦ i * j = j * i; Used terms: rational(i2, j2), rational(i1, j1)