Definition alloc_left_sm (mu: SM_Injection) b1 b2 delta: SM_Injection :=
  Build_SM_Injection (fun b => eq_block b b1 || locBlocksSrc mu b)
                     (locBlocksTgt mu) (*b2 is already in locBlocksTgt!*)
                     (pubBlocksSrc mu) (pubBlocksTgt mu)
                     (fun b => if eq_block b b1 then Some(b2, delta)
                               else local_of mu b)
                     (extBlocksSrc mu) (extBlocksTgt mu)
                     (frgnBlocksSrc mu) (frgnBlocksTgt mu) (extern_of mu).

Lemma valid_init_is_global : forall {F V} (prog:AST.program F V) (R: list_norepet (map fst (prog_defs prog))) m (G: Genv.init_mem prog = Some m) b (VB: Mem.valid_block m b), exists id, Genv.find_symbol (Genv.globalenv prog) id = Some b.