(****************************************************************)
(* Les registres: *)
Fixpoint R1 (st : nat) : BV :=
match st return BV with
| O => V1
| S t =>
appbv (highs (R1 t))
(Mux (lowbit (R1 t))
(consbv (lowbit (BV_full_adder_sum (R2 t) V2 false)) nilbv)
(consbv (lowbit (R2 t)) nilbv))
end
with R2 (st : nat) : BV :=
match st return BV with
| O => BV_null size
| S t =>
appbv
(highs
(Mux (lowbit (R1 t)) (BV_full_adder_sum (R2 t) V2 false) (R2 t)))
(Mux (lowbit (R1 t))
(consbv (BV_full_adder_carry (R2 t) V2 false) nilbv)
(consbv false nilbv))
end.

Lemma R1_eq2 :
forall t : nat,
R1 (S t) =
appbv (highs (R1 t))
(Mux (lowbit (R1 t))
(consbv (lowbit (BV_full_adder_sum (R2 t) V2 false)) nilbv)
(consbv (lowbit (R2 t)) nilbv)).