Definition or_elim_redl (A B C:Prop) (f:A -> C) (g:B -> C)
    (a:A) : f a = or_ind f g (or_introl B a) := eq_refl (f a).Definition or_elim_redr (A B C:Prop) (f:A -> C) (g:B -> C)
    (b:B) : g b = or_ind f g (or_intror A b) := eq_refl (g b).Scheme or_indd := Induction for or Sort Prop.

Theorem proof_irrelevance_cci : forall (B:Prop) (b1 b2:B), b1 = b2.