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Theorem rec

⊦ dups(a ' + x) ↔ ¬ ¬(a ∈ x ∨ dups(x))

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: app-01-02, app-05, c-01, c-02, c-03, d, dups-01, dups-appex, dups-cons, dups-eqsize-01, dups-eqsize-02, dups-firstoc-rew, dups-lesize, dups-rmdup-size-equiv, dups-sw, eq, eq-01, f, f-01, in-06, k-dups, l, rm-eq, rm-nodups, two-01, two-02, two-03,
Used by units in proved state: list-last, list-del, path-reachable, list-set, list-perm,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 6
Proof steps: 19
Used lemmas: dups,
Used spec theorems:
- list/In
Used simplifier rules:
- list/app-08
- list/inapp-02
- list/in-14
- list/c
- list/c-06
- list/Nil
- list/neq
- list-data/elim-list-c
- list/in-01
- list/in-rec
- list/in-append
- list/a