Package list-take-drop-def: list-take-drop-def

Information

Files

• Package tarball list-take-drop-def-1.14.tgz
• Theory file list-take-drop-def.thy (included in the package tarball)

Defined Constants

• Data
  • List
    • Data.List.drop
    • Data.List.take

Theorems

⊦ (∀l. Data.List.drop 0 l = l) ∧
  ∀n h t.
    Number.Natural.≤ n (Data.List.length t) ⇒
    Data.List.drop (Number.Natural.suc n) (Data.List.:: h t) =
    Data.List.drop n t

⊦ (∀l. Data.List.take 0 l = Data.List.[]) ∧
  ∀n h t.
    Number.Natural.≤ n (Data.List.length t) ⇒
    Data.List.take (Number.Natural.suc n) (Data.List.:: h t) =
    Data.List.:: h (Data.List.take n t)

Input Type Operators

• →
• bool
• Data
  • List
    • Data.List.list
• Number
  • Natural
    • Number.Natural.natural

Input Constants

• =
• select
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ~
    • F
    • T
  • List
    • Data.List.::
    • Data.List.[]
    • Data.List.head
    • Data.List.length
    • Data.List.tail
• Number
  • Natural
    • Number.Natural.≤
    • Number.Natural.suc
    • Number.Natural.zero

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λp. p = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

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

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

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀e f. ∃fn. fn 0 = e ∧ ∀n. fn (Number.Natural.suc n) = f (fn n) n

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

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