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Theorem in-append

⊦ a ∈ x + y ↔ ¬ ¬(a ∈ x ∨ a ∈ y)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: app-06, append-size-less, c-02, eq-01, first-02, first-app, firsteq, firsteq-01, firstoc, in-11, in-12, in-13, in-15, in-append0-not-left, in-last-rest, inapp, inapp-02, inapp-03, inapp-04, inapp-05, inapp-06, inapp-07, inapp-08, inapp-09, inapp-10, inapp-11, inapp-12, inapp-13, inapp-14, inex, inex-01, isin, isin-01, lastoc, lasttwo, len-01, len-03, len-04, len-last-rest, neq, neq-01, neq-02, neq-03, neq-05, neq-06, neq-07, ni, two,
Used by units in proved state: list-last, list-del, path-reachable, olist-sort, olist-min-max, olist, list-set, list-perm, assoclist, list-dup,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 11
Used lemmas: in-rec, c, in-empty, a, Nil,
Used spec theorems:
- Used simplifier rules: