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Theorem int-notempty-01

⊦ s ∩ s0 = ∅ → (s ∩ ((s0 -- a) ++ b) ≠ ∅ ↔ b ∈ s)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by:
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 2
Used lemmas: int-inserte, del-rax, int-ins, int-c, int-a, int-rax, ext,
Used spec theorems:
- Used simplifier rules:
  - infset-basic/ne-01
  - infset-basic/In-empty