proposition: Theorem redInInclQ : forall (P Q R : list (poly A0 eqA ltM)) (a b : poly A0 eqA ltM), redIn a b P Q R -> forall Q1 : list (poly A0 eqA ltM), incl Q Q1 -> redIn a b P Q1 R.
proof: Proof. intros P Q R a b H'; elim H'; auto. intros P0 Q0 R0 a0 b0 H'0 H'1 Q1 H'2; try assumption. apply redIn0b; auto. intros P0 Q0 R0 a0 b0 c H'0 H'1 H'2 H'3 H'4 H'5 Q1 H'6; try assumption. apply redIn2 with (c := c); auto. Qed.
imports: Coq(Arith Inclusion Inverse_Image Wf_nat Relation_Definitions) Coq(Relation_Operators Lexicographic_Product) Buchberger(Relation_Operators_compat LetP)