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Theorem ole-rec

⊦ x ≠ [] ∧ x.rest ≠ [] → (ordered≤(x) ↔ ¬ x.rest.first < x.first ∧ ordered≤(x.rest))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: app, del1-01, del1-01-02, ole-01, ole-last, ordered-postfix, orderedle-all,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 4
Used lemmas: le-r, app-01,
Used spec theorems:
- Used simplifier rules:
  - list/c
  - list/e-01
  - list/a
  - list-data/elim-list-c