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Proof step 34 from proof div-def-01 (previous step)

~ 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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ rj ≠ 0r → ~ ri / rj = ~(ri / rj)
Proof step 36:
¬ 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
Proof step 41:
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

Rule argument

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

Additional information

Used terms: rational(abs(i0), j0), rational(i, j)