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Theorem min-def

⊦ st ≠ ∅ → st.min = st.keys.min

Type: A user defined theorem
Validity: The proof is valid.
Features: localsimp,
Comment:
Used by: butmin-id, butmin-in, butmin-put, butmin-put-01, butmin-put-rew, butmin-rewput, butmin-size, butmin-size-01, min, min-in, min-put, min-put-01, min-put-ls,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 2
Proof steps: 4
Used lemmas: inkeys-01, mk-in, Keys, inf, Min-min, Min-in,
Used spec theorems:
- oset/Min-min
Used simplifier rules:
- oelem/irreflexivity
- oelem/sls