Package list-quant-def: list-quant-def

Information

Files

• Package tarball list-quant-def-1.10.tgz
• Theory file list-quant-def.thy (included in the package tarball)

Defined Constants

• Data
  • List
    • Data.List.all
    • Data.List.exists

Theorems

⊦ (∀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

⊦ (∀P. Data.List.exists P Data.List.[] ⇔ F) ∧
  ∀P h t.
    Data.List.exists P (Data.List.:: h t) ⇔ P h ∨ Data.List.exists P t

Input Type Operators

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

Input Constants

• =
• select
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ∨
    • F
    • T
  • List
    • Data.List.::
    • Data.List.[]

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ (∀) = λp. p = λx. T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀NIL' CONS'.
    ∃fn.
      fn Data.List.[] = NIL' ∧
      ∀a0 a1. fn (Data.List.:: a0 a1) = CONS' a0 a1 (fn a1)