Library Coq.Logic.PropFacts


Basic facts about Prop as a type

An intuitionistic theorem from topos theory [LambekScott]
References:
[LambekScott] Jim Lambek, Phil J. Scott, Introduction to higher order categorical logic, Cambridge Studies in Advanced Mathematics (Book 7), 1988.

Theorem injection_is_involution_in_Prop
  (f : Prop -> Prop)
  (inj : forall A B, (f A <-> f B) -> (A <-> B))
  (ext : forall A B, A <-> B -> f A <-> f B)
  : forall A, f (f A) <-> A.