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Proof step 50 from proof div-def-01 (previous step)

rational(i, j) / ~ rational(i0, j0) = ~ rational(i * j0, i0 * j), 0 < j, 0 < j0, i < 0, i0 < 0 ⊦ i = 0, rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0), i0 = 0, ~ rational(i0, j0) = 0r, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 51:
⊦ rj ≠ 0r → ri / ~ rj = ~(ri / rj)
Proof step 52:
¬ rational(i0, j0) ≠ 0r, rational(i, j) / ~ rational(i0, j0) = ~ rational(i * j0, i0 * j), 0 < j, 0 < j0, i < 0, i0 < 0 ⊦ i = 0, rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0), i0 = 0, ~ rational(i0, j0) = 0r, j = 0

Rule argument

name: div-neg-01 rotate: F subst: [rj, ri] → [rational(i0, j0), rational(i, j)]

Additional information

Used simplifier rules: negate-eq: ⊦ ~ ri = ~ rj ↔ ri = rj;% ⊦ i * j = j * i; Used terms: rational(i0, j0), rational(i, j)