Definition smvalid_src (mu : SM_Injection) m1 :=
  forall b1, DOM mu b1 -> Memory.Mem.valid_block m1 b1.

Lemma sm_locally_allocated_trans: forall mu mu' mu'' m2 m3 m2' m3' m2'' m3'' (LocAlloc23 : sm_locally_allocated mu mu' m2 m3 m2'' m3') (LocAlloc23' : sm_locally_allocated mu' mu'' m2'' m3' m2' m3'') (Fwd2 : mem_forward m2 m2'') (Fwd2' : mem_forward m2'' m2') (Fwd3 : mem_forward m3 m3') (Fwd3' : mem_forward m3' m3''), sm_locally_allocated mu mu'' m2 m3 m2' m3''.