Corollary paco1_2_0_mult: forall r_0 r_1,
  paco1_2_0 gf_0 gf_1 (paco1_2_0 gf_0 gf_1 r_0 r_1) (paco1_2_1 gf_0 gf_1 r_0 r_1) <1= paco1_2_0 gf_0 gf_1 r_0 r_1.Corollary paco1_2_1_mult: forall r_0 r_1,
  paco1_2_1 gf_0 gf_1 (paco1_2_0 gf_0 gf_1 r_0 r_1) (paco1_2_1 gf_0 gf_1 r_0 r_1) <1= paco1_2_1 gf_0 gf_1 r_0 r_1.

(* Specifications: *)
Theorem paco1_2_0_fold: forall r_0 r_1, gf_0 (upaco1_2_0 gf_0 gf_1 r_0 r_1) (upaco1_2_1 gf_0 gf_1 r_0 r_1) <1= paco1_2_0 gf_0 gf_1 r_0 r_1.
Theorem paco1_2_1_fold: forall r_0 r_1, gf_1 (upaco1_2_0 gf_0 gf_1 r_0 r_1) (upaco1_2_1 gf_0 gf_1 r_0 r_1) <1= paco1_2_1 gf_0 gf_1 r_0 r_1.
Theorem paco1_2_0_unfold: forall (MON: monotone1_2 gf_0) (MON: monotone1_2 gf_1) r_0 r_1, paco1_2_0 gf_0 gf_1 r_0 r_1 <1= gf_0 (upaco1_2_0 gf_0 gf_1 r_0 r_1) (upaco1_2_1 gf_0 gf_1 r_0 r_1).
Theorem paco1_2_1_unfold: forall (MON: monotone1_2 gf_0) (MON: monotone1_2 gf_1) r_0 r_1, paco1_2_1 gf_0 gf_1 r_0 r_1 <1= gf_1 (upaco1_2_0 gf_0 gf_1 r_0 r_1) (upaco1_2_1 gf_0 gf_1 r_0 r_1).