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Theorem sub-insert

⊦ ¬ a ∈ s → (s ⊆ s0 ++ a ↔ s ⊆ s0)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: sizesubl, subset, subset-insert, subset-insert-01, subset-insert-02,
Used by units in proved state: set-union,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 10
Used lemmas: ne-02, ne-01, rax, Subset, sub-idem, eq, sub-ntrans, sub-insert-01,
Used spec theorems:
- Used simplifier rules: