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Theorem ordle-append

⊦ ordered≤(x) ∧ ordered≤(y) → (ordered≤(x + y) ↔ x ≠ [] ∧ y ≠ [] → ¬ y.head < x.last)

Type: A user defined theorem
Validity: The proof is valid.
Features: s, ls,
Comment:
Used by:
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: orderedle-append2-split, app, orderedle-append, app-01, cons-02,
Used spec theorems:
- Used simplifier rules:
  - list/app
  - list/a
  - list-data/elim-list-c
  - list/c
  - list/e
  - list/app-02
  - list/Nil
  - list/c-08
  - list-last/last-elim