Corollary paco4_2_0_mult: forall r_0 r_1,
  paco4_2_0 gf_0 gf_1 (paco4_2_0 gf_0 gf_1 r_0 r_1) (paco4_2_1 gf_0 gf_1 r_0 r_1) <4= paco4_2_0 gf_0 gf_1 r_0 r_1.Corollary paco4_2_1_mult: forall r_0 r_1,
  paco4_2_1 gf_0 gf_1 (paco4_2_0 gf_0 gf_1 r_0 r_1) (paco4_2_1 gf_0 gf_1 r_0 r_1) <4= paco4_2_1 gf_0 gf_1 r_0 r_1.

(* Specifications: *)
Theorem paco4_2_0_fold: forall r_0 r_1, gf_0 (upaco4_2_0 gf_0 gf_1 r_0 r_1) (upaco4_2_1 gf_0 gf_1 r_0 r_1) <4= paco4_2_0 gf_0 gf_1 r_0 r_1.
Theorem paco4_2_1_fold: forall r_0 r_1, gf_1 (upaco4_2_0 gf_0 gf_1 r_0 r_1) (upaco4_2_1 gf_0 gf_1 r_0 r_1) <4= paco4_2_1 gf_0 gf_1 r_0 r_1.
Theorem paco4_2_0_unfold: forall (MON: monotone4_2 gf_0) (MON: monotone4_2 gf_1) r_0 r_1, paco4_2_0 gf_0 gf_1 r_0 r_1 <4= gf_0 (upaco4_2_0 gf_0 gf_1 r_0 r_1) (upaco4_2_1 gf_0 gf_1 r_0 r_1).
Theorem paco4_2_1_unfold: forall (MON: monotone4_2 gf_0) (MON: monotone4_2 gf_1) r_0 r_1, paco4_2_1 gf_0 gf_1 r_0 r_1 <4= gf_1 (upaco4_2_0 gf_0 gf_1 r_0 r_1) (upaco4_2_1 gf_0 gf_1 r_0 r_1).