Package list-zipwith-thm: list-zipwith-thm

Information

Files

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

Theorem

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

Input Type Operators

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

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ∨
    • ¬
    • F
    • T
  • List
    • Data.List.::
    • Data.List.[]
    • Data.List.length
    • Data.List.zipWith
• Number
  • Natural
    • Number.Natural.suc
  • Numeral
    • Number.Numeral.zero

Assumptions

⊦ T

⊦ F ⇔ ∀p. p

⊦ (¬) = λp. p ⇒ F

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ ∀n. ¬(Number.Natural.suc n = Number.Numeral.zero)

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀m. m = Number.Numeral.zero ∨ ∃n. m = Number.Natural.suc n

⊦ (∧) = 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

⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r

⊦ Data.List.length Data.List.[] = Number.Numeral.zero ∧
  ∀h t.
    Data.List.length (Data.List.:: h t) =
    Number.Natural.suc (Data.List.length t)

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

⊦ ∀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)

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