Package list-dest-thm: Theorems about the list destructors
Information
| name | list-dest-thm |
| version | 1.5 |
| description | Theorems about the list destructors |
| author | Joe Hurd <joe@gilith.com> |
| license | HOLLight |
| provenance | HOL Light theory extracted on 2011-09-21 |
| show | Data.Bool |
Files
- Package tarball list-dest-thm-1.5.tgz
- Theory file list-dest-thm.thy (included in the package tarball)
Theorems
⊦ ∀l. Data.List.null l ⇔ l = Data.List.[]
⊦ ∀l. Data.List.case Data.List.[] Data.List.:: l = l
⊦ ∀l.
¬(l = Data.List.[]) ⇒
Data.List.:: (Data.List.head l) (Data.List.tail l) = l
Input Type Operators
- →
- bool
- Data
- List
- Data.List.list
- List
Input Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- F
- T
- List
- Data.List.::
- Data.List.[]
- Data.List.case
- Data.List.head
- Data.List.null
- Data.List.tail
- Bool
Assumptions
⊦ T
⊦ F ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ F
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. ¬(Data.List.:: h t = Data.List.[])
⊦ ∀h t. Data.List.head (Data.List.:: h t) = h
⊦ ∀h t. Data.List.tail (Data.List.:: h t) = t
⊦ (¬T ⇔ F) ∧ (¬F ⇔ T)
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q
⊦ ∀x. x = Data.List.[] ∨ ∃a0 a1. x = Data.List.:: a0 a1
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ (Data.List.null Data.List.[] ⇔ T) ∧
∀h t. Data.List.null (Data.List.:: h t) ⇔ F
⊦ ∀P. P Data.List.[] ∧ (∀a0 a1. P a1 ⇒ P (Data.List.:: a0 a1)) ⇒ ∀x. P x
⊦ (∀b f. Data.List.case b f Data.List.[] = b) ∧
∀b f h t. Data.List.case b f (Data.List.:: h t) = f h t
⊦ ∀t. ((T ⇔ t) ⇔ t) ∧ ((t ⇔ T) ⇔ t) ∧ ((F ⇔ t) ⇔ ¬t) ∧ ((t ⇔ F) ⇔ ¬t)
⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)