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Proof step 3 from proof ls-neg (previous step)

i < 0 ⊦ i * j < i * j0 ↔ j0 < j

User applied rule apply lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < i → (i * j < i * j0 ↔ j < j0)
Proof step 5:
i < 0, 0 < ~ i → (~ i * j0 < ~ i * j ↔ j0 < j) ⊦ i * j < i * j0 ↔ j0 < j

Rule argument

spec: <toplevel> name: ls-pos seq: ⊦ 0 < i → (i * j < i * j0 ↔ j < j0) subst: [i, j, j0] → [~ i, j0, j]

Additional information

Used terms: ~ i, j0, j