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Theorem orderedCombined-Two-Lists

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

Type: A user defined theorem
Validity: The proof is valid.
Features:
Comment:
Used by: ordered-append-split2,
Used by units in proved state:
Proof exists?: Yes

View the proof

Infos about the proof

Proved?: Yes
Interactions: 4
Proof steps: 12
Used lemmas: ols-rec, ls-r, ls-o, cons,
Used spec theorems:
- list-last/lapp
Used simplifier rules:
- list-data/elim-add
- list/a
- list/c
- list/e
- list/app-02
- list/app
- list-last/last-one
- list/Nil
- list/c-07
- list/first-01
- list/c-08