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(** * 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.