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Proof step 48 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 49:
⊦ rational(~ i, j) = ~ rational(i, j)
Proof step 50:
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: negate-01 rotate: F subst: [j, i] → [i0 * j, i * j0]

Additional information

Used terms: i0 * j, i * j0