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 forall_vals_inject_extern_incr mu mu' vals1 vals2
(Inj : Forall2 (val_inject (as_inj mu)) vals1 vals2)
(Incr : extern_incr mu mu')
(WD : SM_wd mu') :
Forall2 (val_inject (as_inj mu')) vals1 vals2.