Inductive boolP : Prop :=
    | trueP : boolP
    | falseP : boolP.Inductive boolP : Prop :=
    | trueP : boolP
    | falseP : boolP.Inductive boolP : Prop :=
    | trueP : boolP
    | falseP : boolP.Definition boolP_elim_redl (C:Prop) (c1 c2:C) :
    c1 = boolP_ind C c1 c2 trueP := eq_refl c1.Definition boolP_elim_redr (C:Prop) (c1 c2:C) :
    c2 = boolP_ind C c1 c2 falseP := eq_refl c2.Scheme boolP_indd := Induction for boolP Sort Prop.

(* Specifications: *)
Lemma ext_prop_dep_proof_irrel_cic : prop_extensionality -> proof_irrelevance.
Lemma p2p1 : forall A:Prop, A -> b2p (p2b A).
Lemma p2p2 : b1 <> b2 -> forall A:Prop, b2p (p2b A) -> A.
Theorem proof_irrelevance_cc : b1 = b2.