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Theorem zero-gr-01

⊦ i < 0 → (0 < i * j ↔ j < 0)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp, simp,
Comment:
Used by: eq-one, mult-pos, square-le-06, zero-gr-03, zero-gr-add-01, zero-gr-case,
Used by units in proved state: int-gcd, int-div, intnat,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 2
Used lemmas: commutativity, associativity, minus-left, zero-gr,
Used spec theorems:
- Used simplifier rules: