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

Information

Files

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

Defined Constant

• Data
  • List
    • @

Theorems

⊦ ∀l. l @ [] = l

⊦ ∀l m. null (l @ m) ⇔ null l ∧ null m

⊦ ∀l m n. l @ m @ n = (l @ m) @ n

⊦ ∀l m. l @ m = [] ⇔ l = [] ∧ m = []

⊦ ∀l m. head (l @ m) = (if l = [] then head m else head l)

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

Input Type Operators

• →
• bool
• Data
  • List
    • list

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ¬
    • cond
    • select
    • F
    • T
  • List
    • ::
    • []
    • head
    • null

Assumptions

⊦ T

⊦ F ⇔ ∀p. p

⊦ (¬) = λp. p ⇒ F

⊦ (∃) = λP. P ((select) P)

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ ∀l. null l ⇔ l = []

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀h t. ¬(h :: t = [])

⊦ ∀t h. head (h :: t) = h

⊦ (¬T ⇔ F) ∧ (¬F ⇔ T)

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀t1 t2. (if T then t1 else t2) = t1 ∧ (if F then t1 else t2) = t2

⊦ ∀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)

⊦ ∀t. ((T ⇔ t) ⇔ t) ∧ ((t ⇔ T) ⇔ t) ∧ ((F ⇔ t) ⇔ ¬t) ∧ ((t ⇔ F) ⇔ ¬t)

⊦ ∀t. (T ∧ t ⇔ t) ∧ (t ∧ T ⇔ t) ∧ (F ∧ t ⇔ F) ∧ (t ∧ F ⇔ F) ∧ (t ∧ t ⇔ t)