Package list-append-thm: list-append-thm

Information

Files

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

Theorems

⊦ ∀l. Data.List.@ l Data.List.[] = l

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

⊦ ∀l m n. Data.List.@ l (Data.List.@ m n) = Data.List.@ (Data.List.@ l m) n

⊦ ∀l m.
    Data.List.@ l m = Data.List.[] ⇔ l = Data.List.[] ∧ m = Data.List.[]

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

Input Type Operators

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

Input Constants

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

Assumptions

⊦ T

⊦ F ⇔ ∀p. p

⊦ (¬) = λp. p ⇒ F

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ ∀l. Data.List.null l ⇔ l = Data.List.[]

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀h t. ¬(Data.List.:: h t = Data.List.[])

⊦ ∀t h. Data.List.head (Data.List.:: h t) = h

⊦ (¬T ⇔ F) ∧ (¬F ⇔ T)

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

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

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

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

⊦ ∀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)