Admitted. (* OUT-OF-SCOPE *)
(* Temp1,2,3,4 identical *)
Inductive multi {X:Type} (R: relation X) : relation X :=
| multi_refl  : forall (x : X), multi R x x
| multi_step : forall (x y z : X),
R x y ->
multi R y z ->
multi R x z.
Notation " t '===>*' t' " := (multi step t t') (at level 40).

(* Specifications: *)
Theorem multi_R : forall (X:Type) (R:relation X) (x y : X),
R x y -> (multi R) x y.