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Proof step 8 from proof div-div (previous step)

(i / abs(j)) / abs(j0) = i / (abs(j) * abs(j0)), 0 ≤ i ⊦ (i / j) / j0 = i / (j * j0), j0 = 0, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ i < 0 → abs(i) = ~ i
Proof step 10:
¬ j < 0, (i / abs(j)) / abs(j0) = i / (abs(j) * abs(j0)), 0 ≤ i ⊦ (i / j) / j0 = i / (j * j0), j0 = 0, j = 0
Proof step 13:
j < 0, (i / ~ j) / abs(j0) = i / (~ j * abs(j0)), 0 ≤ i ⊦ (i / j) / j0 = i / (j * j0), j0 = 0, j = 0

Rule argument

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

Additional information

Used terms: j