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Proof step 14 from proof abs-shift (previous step)

0 ≤ i % j ⊦ i % j = abs(i) % abs(j), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ¬ j < 0 → abs(j) = j
Proof step 16:
¬ ¬ i < 0, 0 ≤ i % j ⊦ i % j = abs(i) % abs(j), j = 0
Proof step 19:
¬ i < 0, 0 ≤ i % j ⊦ i % j = i % abs(j), j = 0

Rule argument

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

Additional information

Used terms: i