proposition: Theorem minusP_inv1 : forall (a b : Term A n) (p q s : list (Term A n)), minusP (pX a p) (pX b q) s -> ltT ltM b a -> s = pX a (minuspf p (pX b q)).
proof: Proof. Proof using os. intros a b p q s H'; inversion_clear H'; intros. apply pX_inj; auto. apply uniq_minusp with (l := (p, pX b q)); simpl in |- *; auto. absurd (ltT ltM b a); auto. apply ltT_not_eqT; auto; apply eqT_sym; auto. absurd (ltT ltM b a); auto. apply ltT_not_eqT; auto; apply eqT_sym; auto. absurd (ltT ltM b a); auto. Qed.
imports: Coq(Arith) Buchberger(LetP)