Definition mkinitial_SM (mu: SM_Injection) frgnS frgnT :=
match mu with
Build_SM_Injection locBSrc locBTgt pSrc pTgt local extBSrc extBTgt fSrc fTgt extern =>
Build_SM_Injection (fun b => false) (fun b => false) (fun b => false) (fun b => false) (fun b => None)
(DomSrc mu) (DomTgt mu) frgnS frgnT (as_inj mu)
end.

Lemma mkinitial_SM_local: forall mu S T,
local_of (mkinitial_SM mu S T) = fun b => None.