Definition alloc_right_sm (mu: SM_Injection) sp: SM_Injection :=
  Build_SM_Injection (locBlocksSrc mu)
                     (fun b => eq_block b sp || locBlocksTgt mu b)
                     (pubBlocksSrc mu) (pubBlocksTgt mu)
                     (local_of mu)
                     (extBlocksSrc mu) (extBlocksTgt mu)
                     (frgnBlocksSrc mu) (frgnBlocksTgt mu) (extern_of mu).

Lemma alloc_right_sm_locBlocksTgt: forall mu sp, locBlocksTgt (alloc_right_sm mu sp) = fun b => eq_block b sp || locBlocksTgt mu b.