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Theorem ordered-append-split2

⊦ x ≠ [] → (ordered<(x + a ' + y) ↔ ordered<(x) ∧ ordered<(a ' + y) ∧ x.last < a)

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: ordered-append, ordered-append-split1, ordered-last1, ordered-last2, ordered-nodup, ordered-ordered-subset-ordered, ordered-sublist,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 5
Proof steps: 12
Used lemmas: ols-rec, ls-r, ordered-append-first, orderedCombined-Two-Lists,
Used spec theorems:
- Used simplifier rules:
  - list-last/last-elim
  - list/a
  - list/e
  - list/app-02
  - list-last/last-def
  - list/c-08
  - weakord/nll
  - list/Nil
  - list/c
  - list/c-07
  - list/first-02
  - list-data/elim-list-c
  - list/in-17
  - list/in-append
  - list/in-rec
  - list/in-14
  - list/in-15