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Theorem sort-max-max-list

⊦ x ≠ [] → max(sort(x)) = max(x)

Type: A user defined theorem
Validity: The proof is valid.
Features: simp, localsimp,
Comment:
Used by: max-ins-max-last-sort, max-sort-sublist, sort-max,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 7
Proof steps: 14
Used lemmas: max-ins, ordered-max, ins-max, max-rec, max-base,
Used spec theorems:
- olist/ordered-append
Used simplifier rules:
- list/app
- olist/ins-e
- olist-sort/empty
- list/e-01
- olist-sort/rec
- list/c
- oelem/ls-le
- oelem/nen
- list-last/last-def
- list/a
- list/e-02
- oelem/transitivity
- list/first
- list/e
- olist/le-o
- olist-sort/Ordered
- oelem/irreflexivity
- olist-sort/emptyp
- oelem/lel
- oelem/nll