Corollary paco2_3_0_mult: forall r_0 r_1 r_2,
  paco2_3_0 gf_0 gf_1 gf_2 (paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.Corollary paco2_3_1_mult: forall r_0 r_1 r_2,
  paco2_3_1 gf_0 gf_1 gf_2 (paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.Corollary paco2_3_2_mult: forall r_0 r_1 r_2,
  paco2_3_2 gf_0 gf_1 gf_2 (paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.

(* Specifications: *)
Theorem paco2_3_0_fold: forall r_0 r_1 r_2, gf_0 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_1_fold: forall r_0 r_1 r_2, gf_1 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_2_fold: forall r_0 r_1 r_2, gf_2 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2) <2= paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2.
Theorem paco2_3_0_unfold: forall (MON: monotone2_3 gf_0) (MON: monotone2_3 gf_1) (MON: monotone2_3 gf_2) r_0 r_1 r_2, paco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2 <2= gf_0 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2).
Theorem paco2_3_1_unfold: forall (MON: monotone2_3 gf_0) (MON: monotone2_3 gf_1) (MON: monotone2_3 gf_2) r_0 r_1 r_2, paco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2 <2= gf_1 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2).
Theorem paco2_3_2_unfold: forall (MON: monotone2_3 gf_0) (MON: monotone2_3 gf_1) (MON: monotone2_3 gf_2) r_0 r_1 r_2, paco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2 <2= gf_2 (upaco2_3_0 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_1 gf_0 gf_1 gf_2 r_0 r_1 r_2) (upaco2_3_2 gf_0 gf_1 gf_2 r_0 r_1 r_2).