Package list-dest-thm: Theorems about the list destructors

Information

Files

• Package tarball list-dest-thm-1.1.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

Input Type Operators

• →
• bool
• Data
  • List
    • Data.List.list

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ∨
    • ¬
    • F
    • T
  • List
    • Data.List.::
    • Data.List.[]
    • Data.List.case
    • Data.List.null

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.[])

⊦ (¬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)