Definition Qcabs (x:Qc) : Qc := {| canon := Qcabs_canon x (canon x) |}.Notation "[ q ]" := (Qcabs q) : Qc_scope.Ltac Qc_unfolds :=
  unfold Qcabs, Qcminus, Qcopp, Qcplus, Qcmult, Qcle, Q2Qc, this.

Lemma Qcabs_null x : [x] = 0 -> x = 0.