(** * The [option_ge] relator *)

Inductive option_ge {A1 A2} (RA: rel A1 A2): rel (option A1) (option A2) :=
  | Some_ge_def x y: RA x y -> option_ge RA (Some x) (Some y)
  | None_ge_def x: option_ge RA x None.(** * The [option_ge] relator *)

Inductive option_ge {A1 A2} (RA: rel A1 A2): rel (option A1) (option A2) :=
  | Some_ge_def x y: RA x y -> option_ge RA (Some x) (Some y)
  | None_ge_def x: option_ge RA x None.(** * The [option_ge] relator *)

Inductive option_ge {A1 A2} (RA: rel A1 A2): rel (option A1) (option A2) :=
  | Some_ge_def x y: RA x y -> option_ge RA (Some x) (Some y)
  | None_ge_def x: option_ge RA x None.

Lemma None_ge {A B} R x: RIntro True (@option_ge A B R) x None.