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Proof step 3 from proof zero-gr-01 (previous step)

i < 0 ⊦ 0 < i * j ↔ j < 0

User applied rule apply lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < i → (0 < i * j ↔ 0 < j)
Proof step 5:
i < 0, 0 < ~ i → (0 < ~ i * ~ j ↔ 0 < ~ j) ⊦ 0 < i * j ↔ j < 0

Rule argument

spec: <toplevel> name: zero-gr seq: ⊦ 0 < i → (0 < i * j ↔ 0 < j) subst: [i, j] → [~ i, ~ j]

Additional information

Used terms: ~ i, ~ j