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Theorem intersect-empty-def

⊦ x intersect y = [] ↔ (∀ a. a ∈ x → ¬ a ∈ y)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: intersect-empty-01, intersect-empty-app, intersect-empty-app-01, intersect-empty-app-02, intersect-empty-app-03, intersect-empty-app-04, intersect-empty-commutative, intersect-empty-cons, intersect-empty-in, intersect-empty-one, intersect-empty-subset, intersect-empty-subset-01, intersect-rev-empty,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 10
Used lemmas: intersect-notempty, inters-n, inters-y, inters-e,
Used spec theorems:
- Used simplifier rules:
  - list/c
  - list/a
  - list/e-01
  - list/in-append
  - list/in-17
  - list/in-rec