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Theorem in-01-01

⊦ a ∈ y → (a ∈ filter(x, y) ↔ a ∈ x)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: filt-dups, filt-in, in-05, in-06,
Used by units in proved state: list-set,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 1
Proof steps: 16
Used lemmas: filt-n, filt-y, filt-e,
Used spec theorems:
- Used simplifier rules:
  - list/in-empty
  - list/c
  - list/in-rec
  - list/a