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_left_sm_as_inj_same: forall mu b1 b2 delta (WD: SM_wd mu)
(NEW1: DomSrc mu b1 = false),
as_inj (alloc_left_sm mu b1 b2 delta) b1 = Some(b2,delta).