Ltac proper_normalization :=
  match goal with
    | [ _ : normalization_done |- _ ] => fail 1
    | [ _ : apply_subrelation |- @Proper _ ?R _ ] => 
      let H := fresh "H" in
      set(H:=did_normalization) ; class_apply @proper_normalizes_proper
  end.

Lemma PartialOrder_StrictOrder `(PartialOrder A eqA R) : StrictOrder (relation_conjunction R (complement eqA)).