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

i < 0, i < j, 0 < j ⊦ i |%| j = 0, j = i |%| j + ~ i |%| 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, i < j, 0 < j ⊦ i |%| j = 0, j = i |%| j + ~ i |%| j
Proof step 6:
i % j < 0, i < 0, i < j, 0 < j ⊦ i % j + j = 0, j = (i % j + j) + ~ i |%| 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