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(** * Peano induction and recursion on binary positive positive numbers *)
(** The Peano-like recursor function for [positive] (due to Daniel Schepler) *)

(* Specifications: *)
Theorem peano_rect_succ (P:positive->Type) (a:P 1)
(f:forall p, P p -> P (succ p)) (p:positive) :
peano_rect P a f (succ p) = f _ (peano_rect P a f p).
Theorem peano_rect_base (P:positive->Type) (a:P 1)
(f:forall p, P p -> P (succ p)) :
peano_rect P a f 1 = a.