Goal:
    A : Type  R : ReflectEq A
  ============================
   (forall x y : A, false = (x == y) -> x <> y)


DEBUG:Going to execute:
match goal with
           | |- context [ eq_rect_r _ _ eq_refl ] => progress simpl eq_rect_r
           | |- context [ eq_rect _ _ _ _ eq_refl ] => progress simpl eq_rect
           | |- context [ Logic.transport _ eq_refl _ ] =>
                 progress simpl Logic.transport
           | |- context [ Logic.eq_elim _ _ _ _ _ eq_refl ] =>
                 progress simpl eq_rect
           | |- context [ Logic.eq_elim_r _ _ _ _ eq_refl ] =>
                 progress simpl Logic.eq_elim_r
           | |- context [ noConfusion_inv _ ] =>
                 progress simpl noConfusion_inv
           | |- DepElim.opaque_ind_pack_eq_inv ?G eq_refl =>
                 apply (DepElim.simplify_ind_pack_inv B x p G)
           | |- let _ := CoreTactics.block in _ => fail 1
           | |- _ => simplify * || simplify ?; cbv beta
           | |- _ -> ?B =>
                 let ty := type of B in
                 intro || (let H := fresh in
                           intro
                           H)
           | |- forall x, _ => let H := fresh x in
                               intro
                               H
           | |- _ => intro
           end