Remark select_loc_l_monotone:
  forall l q1 q2,
  OrderedEquation'.eq q1 q2 \/ OrderedEquation'.lt q1 q2 ->
  select_loc_l l q1 = true -> select_loc_l l q2 = true.Remark select_loc_h_monotone:
  forall l q1 q2,
  OrderedEquation'.eq q1 q2 \/ OrderedEquation'.lt q2 q1 ->
  select_loc_h l q1 = true -> select_loc_h l q2 = true.Remark select_loc_charact:
  forall l q,
  select_loc_l l q = false \/ select_loc_h l q = false <-> Loc.diff l (eloc q).

Lemma reg_loc_unconstrained_sound: forall r l e q, reg_loc_unconstrained r l e = true -> EqSet.In q e -> ereg q <> r /\ Loc.diff l (eloc q).