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Theorem rax

⊦ a ∈ s ++ b ↔ ¬ ¬(a = b ∨ a ∈ s)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: addthree, addtwo, del, eq-01, eq-04, ext-rec, in-04, in-05, ne, size-exgr, size-one, size-one-02, size-three-02, size-two-03, size-two-05, size-two-06, sub-add, sub-add-01, sub-add-03, sub-add-04, sub-insert, subset, subset-ins, subset-insert, subset-insert-01, subset-insert-02, subset-insert-03, subset-insert-04, subset-insert-05, subset-insert-06, subset-insert-same, subsize-eq, sw-01, two,
Used by units in proved state: set-union, ostore, oset, store+set,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 1
Used lemmas: add, in-02,
Used spec theorems:
- Used simplifier rules: