proposition: Theorem ltP_order_comp : forall (a b c : Term A n) (p q : list (Term A n)), ltP (pX b p) (pX a q) -> ltT a c -> ltT b c.
proof: Proof. Proof using os. intros a b c p q H1; inversion_clear H1. intros; apply ltT_trans with (y := a); auto. apply eqT_compat_ltTl. apply eqT_sym; trivial. Qed.
imports: Coq(Lexicographic_Exponentiation Relation_Definitions) Coq(Inverse_Image Inclusion List Relation_Operators) Buchberger(Relation_Operators_compat Monomials) Buchberger(Term CoefStructure OrderStructure)