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Theorem in-02

⊦ a ≠ b → (a ∈ s ++ b ↔ a ∈ s)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: addtwo, del, in-03, in-04, rax, size-exgr, size-three-01, size-three-02,
Used by units in proved state: set-union, oset, store+set,
Proof exists?: Yes

View the proof

Infos about the proof

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