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Theorem empty-01

⊦ st ≠ ∅ → (st.keys = ∅ ↔ false)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by: min-put-ls, mk-in,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 8
Used lemmas: empty, Keys, inf, Min-min, Min-in,
Used spec theorems:
- store/Extension
- set-basic/Extension
Used simplifier rules:
- weakord/tord/irreflexivity
- store/In-empty
- set-basic/In-empty