Package list-concat-thm: list-concat-thm

Information

Files

• Package tarball list-concat-thm-1.2.tgz
• Theory file list-concat-thm.thy (included in the package tarball)

Theorem

⊦ ∀l. Data.List.null (Data.List.concat l) ⇔ Data.List.all Data.List.null l

Input Type Operators

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

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ~
    • F
    • T
  • List
    • Data.List.::
    • Data.List.@
    • Data.List.[]
    • Data.List.all
    • Data.List.concat
    • Data.List.null

Assumptions

⊦ T

⊦ (∀) = 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.
    Data.List.null (Data.List.@ l m) ⇔ Data.List.null l ∧ Data.List.null m

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

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

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

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

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