Package list-append-thm: Properties of the list append function
Information
| name | list-append-thm |
| version | 1.13 |
| description | Properties of the list append function |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-11-15 |
| requires | bool natural set list-def list-thm list-dest list-length list-set list-append-def |
| show | Data.Bool Data.List Number.Natural Set |
Files
- Package tarball list-append-thm-1.13.tgz
- Theory file list-append-thm.thy (included in the package tarball)
Theorems
⊦ ∀l. l @ [] = l
⊦ ∀l m. null (l @ m) ⇔ null l ∧ null m
⊦ ∀l m. length (l @ m) = length l + length m
⊦ ∀l1 l2. toSet (l1 @ l2) = toSet l1 ∪ toSet l2
⊦ ∀l m n. l @ m @ n = (l @ m) @ n
⊦ ∀l m. head (l @ m) = if l = [] then head m else head l
⊦ ∀l m. l @ m = [] ⇔ l = [] ∧ m = []
Input Type Operators
- →
- bool
- Data
- List
- list
- List
- Number
- Natural
- natural
- Natural
- Set
- set
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ¬
- cond
- F
- T
- List
- ::
- @
- []
- head
- length
- null
- toSet
- Bool
- Number
- Natural
- +
- suc
- zero
- Natural
- Set
- ∅
- insert
- ∪
Assumptions
⊦ T
⊦ ¬F ⇔ T
⊦ length [] = 0
⊦ toSet [] = ∅
⊦ F ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ F
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. T
⊦ ∀t. (T ⇔ t) ⇔ t
⊦ ∀t. F ∧ t ⇔ F
⊦ ∀t. T ∧ t ⇔ t
⊦ ∀t. t ∧ t ⇔ t
⊦ ∀n. 0 + n = n
⊦ ∀l. [] @ l = l
⊦ ∀t. (F ⇔ t) ⇔ ¬t
⊦ ∀l. null l ⇔ l = []
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀t1 t2. (if F then t1 else t2) = t2
⊦ ∀t1 t2. (if T then t1 else t2) = t1
⊦ ∀h t. ¬(h :: t = [])
⊦ ∀h t. head (h :: t) = h
⊦ ∀h t. length (h :: t) = suc (length t)
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ ∀h t. toSet (h :: t) = insert h (toSet t)
⊦ ∀x s. insert x ∅ ∪ s = insert x s
⊦ ∀m n. suc m + n = suc (m + n)
⊦ (∀s. ∅ ∪ s = s) ∧ ∀s. s ∪ ∅ = s
⊦ ∀P. (∀x y. P x y) ⇔ ∀y x. P x y
⊦ ∀l h t. (h :: t) @ l = h :: t @ l
⊦ ∀s t u. s ∪ t ∪ u = s ∪ (t ∪ u)
⊦ ∀P. P [] ∧ (∀a0 a1. P a1 ⇒ P (a0 :: a1)) ⇒ ∀x. P x