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Theorem butmin-ins

⊦ s.min < a ∧ s ≠ ∅ → (s ++ a).butmin = s.butmin ++ a

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: 4
Proof steps: 8
Used lemmas: min-insert, min-ins-01, minmax-04, Min-min, Max-max, Min-in, Max-in, Butmin,
Used spec theorems:
- set-union/del-addeq-03
- set-union/delsw
Used simplifier rules: