Section PRESERVATION.
Variable prog: program.
Variable tprog : program.
Hypothesis TRANSF: match_prog prog tprog.
Let ge := Genv.globalenv prog.
Let tge := Genv.globalenv tprog.
Proof (Genv.find_symbol_match TRANSF).
Proof (Genv.senv_match TRANSF).
Proof (Genv.find_funct_match TRANSF).
Proof (Genv.find_funct_ptr_match TRANSF).
Definition transf_function' (f: function) (approxs: PMap.t numbering) : function :=
mkfunction
f.(fn_sig)
f.(fn_params)
f.(fn_stacksize)
(transf_code approxs f.(fn_code))
f.(fn_entrypoint).
Definition regs_lessdef (rs1 rs2: regset) : Prop :=
forall r, Val.lessdef (rs1#r) (rs2#r).

Lemma set_reg_lessdef:
forall r v1 v2 rs1 rs2,
Val.lessdef v1 v2 -> regs_lessdef rs1 rs2 -> regs_lessdef (rs1#r <- v1) (rs2#r <- v2).