Package list-interval: The list interval function
Information
| name | list-interval |
| version | 1.32 |
| description | The list interval function |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| requires | bool natural list-length list-nth |
| show | Data.Bool Data.List Number.Natural |
Files
- Package tarball list-interval-1.32.tgz
- Theory file list-interval.thy (included in the package tarball)
Defined Constant
- Data
- List
- interval
- List
Theorems
⊦ ∀m. interval m 0 = []
⊦ ∀m n. length (interval m n) = n
⊦ ∀m n. interval m (suc n) = m :: interval (suc m) n
⊦ ∀m n i. i < n ⇒ nth i (interval m n) = m + i
Input Type Operators
- →
- bool
- Data
- List
- list
- List
- Number
- Natural
- natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ∨
- F
- T
- List
- ::
- []
- length
- nth
- Bool
- Number
- Natural
- +
- <
- suc
- zero
- Natural
Assumptions
⊦ T
⊦ length [] = 0
⊦ (∃) = λp. p ((select) p)
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. T
⊦ ∀t. T ∧ t ⇔ t
⊦ ∀t. F ⇒ t ⇔ T
⊦ ∀t. T ⇒ t ⇔ t
⊦ ∀t. t ⇒ T ⇔ T
⊦ ∀m. m < 0 ⇔ F
⊦ ∀m. m + 0 = m
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. nth 0 (h :: t) = h
⊦ ∀h t. length (h :: t) = suc (length t)
⊦ ∀m. m = 0 ∨ ∃n. m = suc n
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀m n. m + suc n = suc (m + n)
⊦ ∀m n. suc m + n = suc (m + n)
⊦ ∀m n. suc m = suc n ⇔ m = n
⊦ ∀m n. suc m < suc n ⇔ m < n
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀p. (∀x y. p x y) ⇔ ∀y x. p x y
⊦ ∀p. (∀x. ∃y. p x y) ⇔ ∃y. ∀x. p x (y x)
⊦ ∀P. P 0 ∧ (∀n. P n ⇒ P (suc n)) ⇒ ∀n. P n
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n
⊦ ∀h t n. n < length t ⇒ nth (suc n) (h :: t) = nth n t