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Proof step 21 from proof abs-shift (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ j < 0 → abs(j) = 0 - j

Rule argument

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

Additional information

Used simplifier rules: mod-neg: j ≠ 0 ⊦ i % ~ j = i % j;% ⊦ 0 - i = ~ i; (s)% ⊦ ¬ i < j → (i = j ↔ ¬ j < i); (ss)% ⊦ ¬ j < 0 → abs(j) = j; (s) Used terms: j