(* This code is copyrighted by its authors; it is distributed under  *)
(* the terms of the LGPL license (see LICENSE and description files) *)
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(*          Buchberger : ordering: lexi and total                            *)
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(*          Laurent Thery 	                                             *)
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Section lexi_order.
Inductive orderc : forall n : nat, mon n -> mon n -> Prop :=
| lo1 :
forall (n a b : nat) (p : mon n),
b < a -> orderc (S n) (c_n n a p) (c_n n b p)
| lo2 :
forall (n a b : nat) (p q : mon n),
orderc n p q -> orderc (S n) (c_n n a p) (c_n n b q).
Hint Resolve lo1 lo2.

Theorem orderc_dec :
forall (n : nat) (a b : mon n), {orderc n a b} + {orderc n b a} + {a = b}.