Package list-zipwith-thm: list-zipwith-thm
Information
| name | list-zipwith-thm |
| version | 1.10 |
| description | list-zipwith-thm |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| show | Data.Bool |
Files
- Package tarball list-zipwith-thm-1.10.tgz
- Theory file list-zipwith-thm.thy (included in the package tarball)
Theorems
⊦ ∀f. Data.List.zipWith f Data.List.[] Data.List.[] = Data.List.[]
⊦ ∀f l1 l2 n.
Data.List.length l1 = n ∧ Data.List.length l2 = n ⇒
Data.List.length (Data.List.zipWith f l1 l2) = n
⊦ ∀f h1 h2 t1 t2.
Data.List.length t1 = Data.List.length t2 ⇒
Data.List.zipWith f (Data.List.:: h1 t1) (Data.List.:: h2 t2) =
Data.List.:: (f h1 h2) (Data.List.zipWith f t1 t2)
Input Type Operators
- →
- bool
- Data
- List
- Data.List.list
- List
- Number
- Natural
- Number.Natural.natural
- Natural
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ¬
- F
- T
- List
- Data.List.::
- Data.List.[]
- Data.List.length
- Data.List.zipWith
- Bool
- Number
- Natural
- Number.Natural.suc
- Number.Natural.zero
- Natural
Assumptions
⊦ T
⊦ F ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ F
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ ∀n. ¬(Number.Natural.suc n = 0)
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ ∀m n. Number.Natural.suc m = Number.Natural.suc n ⇔ m = n
⊦ Data.List.length Data.List.[] = 0 ∧
∀h t.
Data.List.length (Data.List.:: h t) =
Number.Natural.suc (Data.List.length t)
⊦ ∀P. P 0 ∧ (∀n. P n ⇒ P (Number.Natural.suc n)) ⇒ ∀n. P n
⊦ ∀P. P Data.List.[] ∧ (∀a0 a1. P a1 ⇒ P (Data.List.:: a0 a1)) ⇒ ∀x. P x
⊦ ∀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)
⊦ (∀f. Data.List.zipWith f Data.List.[] Data.List.[] = Data.List.[]) ∧
∀f h1 h2 t1 t2.
Data.List.length t1 = Data.List.length t2 ⇒
Data.List.zipWith f (Data.List.:: h1 t1) (Data.List.:: h2 t2) =
Data.List.:: (f h1 h2) (Data.List.zipWith f t1 t2)