Standard Library | The Coq Proof Assistant

The Coq Proof Assistant

# 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.