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Proof step 2 from proof mod-abs-neg-neg (previous step)

i < 0, j < 0 ⊦ i % j = 0, i |%| j = i |%| ~ j + 2 * j

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ i % j < 0 → i |%| j = i % j + j
Proof step 4:
i % j < 0, i < 0, j < 0 ⊦ i % j = 0, i % j + j = i |%| ~ j + 2 * j

Rule argument

spec: int-mod inst: name: mod-neg-def seq: ⊦ i % j < 0 → i |%| j = i % j + j subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used simplifier rules: lst-01: ⊦ ¬ i < j → (i ≠ j ↔ j < i); from specification int-basic1%mod-grz-02: ⊦ i < 0 ∧ j < 0 → ¬ 0 < i % j; from specification int-div Used terms: j, i