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Theorem inapp

⊦ a ∈ ax + ay ↔ ¬ ¬(a ∈ ax ∨ a ∈ ay)

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by: app, ex, firstoc, in-02, in-03, in-put, incons, inrec, insfirst, insnotin, lenequal, lenle, nuni, nuni-01, unique, unique-01, uniquelen,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 14
Used lemmas: inassoc,
Used spec theorems:
- Used simplifier rules:
  - list/assoclista/a
  - list/assoclista/in-append