Definition smvalid_src (mu : SM_Injection) m1 :=
  forall b1, DOM mu b1 -> Memory.Mem.valid_block m1 b1.Definition smvalid_tgt (mu : SM_Injection) m2 :=
  forall b2, RNG mu b2 -> Memory.Mem.valid_block m2 b2.

Lemma inject_separated_intern_incr_fwd: forall mu mu' m1 m2 mu'' m2' (SEP: sm_inject_separated mu mu' m1 m2) (SEP': sm_inject_separated mu' mu'' m1 m2') (INC: intern_incr mu mu') (INC': intern_incr mu' mu'') (FWD: mem_forward m2 m2') (WD': SM_wd mu') (WD'': SM_wd mu''), sm_inject_separated mu mu'' m1 m2.