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Theorem ordered-append

⊦ ordered≤(x) ∧ ordered≤(x0) ∧ (x ≠ [] ∧ x0 ≠ [] → ¬ x0.first < x.last) → ordered≤(x + x0)

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

View the proof

Infos about the proof

Proved?: Yes
Interactions: 3
Proof steps: 12
Used lemmas: k-le-r, le-r, le-o, cons-02, app-01, le-e,
Used spec theorems:
- Used simplifier rules:
  - list/app
  - list-last/l
  - list/Nil
  - list-last/l-02
  - list/c-08
  - list/first-01
  - list/c-07
  - nat/le-num-06
  - nat-basic2/c
  - nat-basic2/a
  - nat-basic2/succ
  - list/len
  - list/len-05
  - list/c
  - list/e-01
  - list/a
  - list-data/elim-list-c