Package list-interval: Definitions and theorems about the list interval function
Information
| name | list-interval |
| version | 1.13 |
| description | Definitions and theorems about the list interval function |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| show | Data.Bool Data.List Number.Natural |
Files
- Package tarball list-interval-1.13.tgz
- Theory file list-interval.thy (included in the package tarball)
Defined Constant
- Data
- List
- interval
- List
Theorems
⊦ ∀m n. length (interval m n) = n
⊦ ∀m n i. i < n ⇒ nth i (interval m n) = m + i
⊦ (∀m. interval m 0 = []) ∧
∀m n. interval m (suc n) = m :: interval (suc m) n
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
⊦ (∃) = λP. P ((select) P)
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ ∀m. m + 0 = m
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. nth 0 (h :: t) = h
⊦ ∀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 = 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
⊦ length [] = 0 ∧ ∀h t. length (h :: t) = suc (length t)
⊦ ∀P. P 0 ∧ (∀n. P n ⇒ P (suc n)) ⇒ ∀n. P n
⊦ ∀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
⊦ (∀n. 0 + n = n) ∧ ∀m n. suc m + n = suc (m + n)
⊦ (∀m. m < 0 ⇔ F) ∧ ∀m n. m < suc n ⇔ m = n ∨ m < n
⊦ ∀t. (T ∧ t ⇔ t) ∧ (t ∧ T ⇔ t) ∧ (F ∧ t ⇔ F) ∧ (t ∧ F ⇔ F) ∧ (t ∧ t ⇔ t)
⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)