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(*                                                                    *)
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(* 02110-1301 USA                                                     *)
(* Contribution to the Coq Library   V6.3 (July 1999)                    *)
(* ---                           develop.v                              --- *)
(*                                                                          *)
(* Author: Pierre Casteran.                                                 *)
(*    LABRI, URA CNRS 1304,                                                 *)
(*    Departement d'Informatique, Universite Bordeaux I,                    *)
(*    33405 Talence CEDEX,                                                  *)
(*    e-mail:  casteran@labri.u-bordeaux.fr                                 *)
(*  This file contains some important lemmas used in the "generation" module. It tells how to compose abstract machine code (with append) to build code for Call_M, Call_C and Call_K calls (see the module "spec") *)

(* Specifications: *)
(* A sequence for computing the cube of some m in M *)
Lemma M3 : gencode (Call_M three).
(******************************)
(* A sequence for computing the (2^q)-th power of some m in M; this is a sequence of q SQRs  *)
Lemma M2q : forall q : nat, gencode (Call_M (two_power q)).
(**********************************************)
(* code generation  for (Call_M p) from the code for (Call_C p q) (it's the same!) *)
Lemma C2M : forall p q : nat, gencode (Call_C p q) -> gencode (Call_M p).
(****************************************)
(*  code generation for  (Call_C qp p) from the codes for (Call_M p) and (Call_M q) just append !                                                          *)
Lemma MMC :
forall p q : nat,
gencode (Call_M p) -> gencode (Call_M q) -> gencode (Call_C (q * p) p).