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Theorem zero-ls-03

⊦ i ≤ 0 → (i * j < 0 ↔ ¬ ¬(0 < j ∧ i ≠ 0))

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp, simp,
Comment:
Used by: numle-07, numls-07, square-le-01, square-zero-02, zero-ge-03, zero-ls-01, zero-ls-case, zero-ls-sub,
Used by units in proved state: int-pot,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: zero-ls, commutativity, associativity, zero-left, ls-neg,
Used spec theorems:
- Used simplifier rules: