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Proof step 13 from proof div-def-01 (previous step)

rational(abs(i), j) / rational(abs(i0), j0) = rational(abs(i) * j0, j * abs(i0)), 0 < j, 0 < j0 ⊦ 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 14:
⊦ i < 0 → abs(i) = ~ i
Proof step 15:
¬ i < 0, rational(abs(i), j) / rational(abs(i0), j0) = rational(abs(i) * j0, j * abs(i0)), 0 < j, 0 < j0 ⊦ i = 0, rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0), i0 = 0
Proof step 31:
i < 0, rational(~ i, j) / rational(abs(i0), j0) = rational(~ i * j0, j * abs(i0)), 0 < j, 0 < j0 ⊦ i = 0, rational(i, j) / rational(i0, j0) = rational(i * j0, j * i0), i0 = 0

Rule argument

seq: ⊦ i < 0 → abs(i) = ~ i subst: [i] → [i] rotate: F spec: int-abs inst: name: abs-08

Additional information

Used terms: i