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Proof step 5 from proof div-neg-01 (previous step)

⊦ rj = 0r, rational(rj.denom * ri.num, ~(rj.num * ri.denom)) = ~(ri / rj)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ j ≠ 0 → rational(i, ~ j) = rational(~ i, j)
Proof step 7:
¬ rj.num * ri.denom ≠ 0 ⊦ rj = 0r, rational(rj.denom * ri.num, ~(rj.num * ri.denom)) = ~(ri / rj)
Proof step 15:
rj.num * ri.denom ≠ 0 ⊦ rj = 0r, rational(~(rj.denom * ri.num), rj.num * ri.denom) = ~(ri / rj)

Rule argument

name: neg-intro rotate: F subst: [j, i] → [rj.num * ri.denom, rj.denom * ri.num]

Additional information

Used terms: rj.num * ri.denom, rj.denom * ri.num