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Proof step 41 from proof div-def-01 (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 42:
rational(i, j) / rational(abs(i0), j0) = rational(i * j0, j * abs(i0)), 0 < j, 0 < j0, i < 0 ⊦ i = 0, rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0), i0 = 0, rational(abs(i0), j0) = 0r

Rule argument

Additional information

Used simplifier rules: negate-eq: ⊦ ~ ri = ~ rj ↔ ri = rj;