Package function-comb: function-comb

Information

Files

• Package tarball function-comb-1.0.tgz
• Theory file function-comb.thy (included in the package tarball)

Theorems

⊦ ∀x. Function.id x = x

⊦ ∀f. Function.o Function.id f = f ∧ Function.o f Function.id = f

⊦ ∀f g x. Function.o f g x = f (g x)

⊦ ∀f g h. Function.o f (Function.o g h) = Function.o (Function.o f g) h

Input Type Operators

• →
• bool

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • T
• Function
  • Function.id
  • Function.o

Assumptions

⊦ T

⊦ Function.id = λx. x

⊦ ∀t. (∀x. t) ⇔ t

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀f y. (λx. f x) y = f y

⊦ ∀f g. Function.o f g = λx. f (g x)

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ ∀f g. f = g ⇔ ∀x. f x = g x