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

i + j < 0, 0 < j, i < 0, i < j ⊦ i |%| j = (i + j) |%| 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 + j < 0, 0 < j, i < 0, i < j ⊦ i |%| j = (i + j) |%| j
Proof step 9:
i % j < 0, i + j < 0, 0 < j, i < 0, i < j ⊦ i % j + j = (i + j) |%| 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 terms: j, i