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Theorem ols-rec

⊦ x ≠ [] ∧ x.tail ≠ [] → (ordered<(x) ↔ x.head < x.tail.head ∧ ordered<(x.tail))

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: del1, ols-two, ordered-append-first, ordered-append-split2, orderedCombined-Two-Lists, orderedls-all, orderedls-le-attach, orderedls-ls-attach,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 0
Proof steps: 5
Used lemmas: ls-r, cons,
Used spec theorems:
- Used simplifier rules:
  - list-data/elim-list-c
  - list/a
  - list/e
  - list/app-02
  - list/c