Package list-reverse: Definitions and theorems about the list reverse function

Information

Files

• Package tarball list-reverse-1.0.tgz
• Theory file list-reverse.thy (included in the package tarball)

Defined Constant

• Data
  • List
    • reverse

Theorems

⊦ ∀l. reverse (reverse l) = l

⊦ ∀l m. reverse (l @ m) = reverse m @ reverse l

⊦ reverse [] = [] ∧ ∀l x. reverse (x :: l) = reverse l @ x :: []

Input Type Operators

• →
• bool
• Data
  • List
    • list

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • select
    • T
  • List
    • ::
    • @
    • []

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ ∀l. l @ [] = l

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀l m n. l @ m @ n = (l @ m) @ n

⊦ ∀P. P [] ∧ (∀a0 a1. P a1 ⇒ P (a0 :: a1)) ⇒ ∀x. P x

⊦ ∀NIL' CONS'.
    ∃fn. fn [] = NIL' ∧ ∀a0 a1. fn (a0 :: a1) = CONS' a0 a1 (fn a1)

⊦ (∀l. [] @ l = l) ∧ ∀h t l. (h :: t) @ l = h :: t @ l