intros P Q R a b H'; elim H'; auto.
intros P0 Q0 R0 a0 b0 H'0 H'1 P1 H'2.
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.
apply redIn2 with (c := c); auto.
Qed.

(* Specifications: *)
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.