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

Information

Files

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

Defined Constant

• Data
  • List
    • concat

Theorems

⊦ ∀l. null (concat l) ⇔ all null l

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

Input Type Operators

• →
• bool
• Data
  • List
    • list

Input Constants

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

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

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

⊦ (null [] ⇔ T) ∧ ∀h t. null (h :: t) ⇔ F

⊦ ∀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)

⊦ (∀P. all P [] ⇔ T) ∧ ∀h P t. all P (h :: t) ⇔ P h ∧ all P t

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