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

i % j < 0, 0 < j, j + i % j ≤ 0, i % j + 1 < j ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0
Proof step 4:
0 < j, i < 0 ∧ i % j ≠ 0, 0 < j, j + i % j ≤ 0, i % j + 1 < j ⊦

Rule argument

spec: int-div inst: name: mod-ls-zero seq: 0 < j ⊦ i % (* j) < 0 ↔ i < 0 ∧ i % j ≠ 0 subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i