Package function-def: Definition of function constants

Information

Files

• Package tarball function-def-1.1.tgz
• Theory file function-def.thy (included in the package tarball)

Defined Constants

• Function
  • id
  • injective
  • o
  • surjective

Theorems

⊦ id = λx. x

⊦ ∀f g. (f o g) = λx. f (g x)

⊦ ∀f. surjective f ⇔ ∀y. ∃x. y = f x

⊦ ∀f. injective f ⇔ ∀x1 x2. f x1 = f x2 ⇒ x1 = x2

Input Type Operators

• →
• bool

Input Constants

• =
• Data
  • Bool
    • ∀
    • ⇒
    • ∃
    • T

Assumptions

⊦ T

⊦ (∀) = λP. P = λx. T