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Theorem sub-add-03

⊦ s ++ a ⊆ s0 ↔ s ⊆ s0 ∧ a ∈ s0

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp, localcut,
Comment:
Used by: sub-add-02, sub-one-02, sub-two, subset-ins, subset-insert-same,
Used by units in proved state: set-union, oset,
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 4
Used lemmas: ne-02, ne-01, sub-add, rax, Subset,
Used spec theorems:
- Used simplifier rules: