Package list-zipwith: Definitions and theorems about the list zipWith function

Information

Files

• Package tarball list-zipwith-1.12.tgz
• Theory file list-zipwith.thy (included in the package tarball)

Defined Constant

• Data
  • List
    • zipWith

Theorems

⊦ ∀f. zipWith f [] [] = []

⊦ ∀f l1 l2 n. length l1 = n ∧ length l2 = n ⇒ length (zipWith f l1 l2) = n

⊦ ∀f h1 h2 t1 t2.
    length t1 = length t2 ⇒
    zipWith f (h1 :: t1) (h2 :: t2) = f h1 h2 :: zipWith f t1 t2

⊦ (∀f. zipWith f [] [] = []) ∧
  ∀f h1 h2 t1 t2.
    length t1 = length t2 ⇒
    zipWith f (h1 :: t1) (h2 :: t2) = f h1 h2 :: zipWith f t1 t2

Input Type Operators

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

Input Constants

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

Assumptions

⊦ T

⊦ F ⇔ ∀p. p

⊦ (~) = λp. p ⇒ F

⊦ (∃) = λP. P ((select) P)

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λp. p = λx. T

⊦ ∀x. x = x ⇔ T

⊦ ∀n. ¬(Number.Natural.suc n = 0)

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀h t. head (h :: t) = h

⊦ ∀h t. tail (h :: t) = t

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀m n. Number.Natural.suc m = Number.Natural.suc n ⇔ m = n

⊦ length [] = 0 ∧ ∀h t. length (h :: t) = Number.Natural.suc (length t)

⊦ ∀P. P 0 ∧ (∀n. P n ⇒ P (Number.Natural.suc n)) ⇒ ∀n. P n

⊦ ∀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 ⇔ F) ∧ (t ∧ F ⇔ F) ∧ (t ∧ t ⇔ t)

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