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Proof step 14 from proof div-nearer-zero (previous step)

i / abs(j) * abs(j) < 0, i < 0, i / abs(j) * abs(j) < i, i / abs(j) * abs(j) < ~1 ⊦ j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ j < 0 → abs(j) = 0 - j
Proof step 16:
¬ j < 0, i / abs(j) * abs(j) < 0, i < 0, i / abs(j) * abs(j) < i, i / abs(j) * abs(j) < ~1 ⊦ j = 0
Proof step 22:
j < 0, i / (0 - j) * (0 - j) < 0, i < 0, i / (0 - j) * (0 - j) < i, i / (0 - j) * (0 - j) < ~1 ⊦ j = 0

Rule argument

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

Additional information

Used terms: j