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.

Lemma ext_prop_dep_proof_irrel_cic : prop_extensionality -> proof_irrelevance.