-inductive fqu: tri_relation genv lenv term ≝
-| fqu_lref_O : ∀I,G,L,V. fqu G (L.ⓑ{I}V) (#0) G L V
-| fqu_pair_sn: ∀I,G,L,V,T. fqu G L (②{I}V.T) G L V
-| fqu_bind_dx: ∀p,I,G,L,V,T. fqu G L (ⓑ{p,I}V.T) G (L.ⓑ{I}V) T
-| fqu_flat_dx: ∀I,G,L,V,T. fqu G L (ⓕ{I}V.T) G L T
-| fqu_drop : ∀I,G,L,V,T,U. ⬆*[1] T ≡ U → fqu G (L.ⓑ{I}V) U G L T
+inductive fqu (b:bool): tri_relation genv lenv term ≝
+| fqu_lref_O : ∀I,G,L,V. fqu b G (L.ⓑ{I}V) (#0) G L V
+| fqu_pair_sn: ∀I,G,L,V,T. fqu b G L (②{I}V.T) G L V
+| fqu_bind_dx: ∀p,I,G,L,V,T. fqu b G L (ⓑ{p,I}V.T) G (L.ⓑ{I}V) T
+| fqu_clear : ∀p,I,G,L,V,T. b = Ⓕ → fqu b G L (ⓑ{p,I}V.T) G (L.ⓧ) T
+| fqu_flat_dx: ∀I,G,L,V,T. fqu b G L (ⓕ{I}V.T) G L T
+| fqu_drop : ∀I,G,L,T,U. ⬆*[1] T ≘ U → fqu b G (L.ⓘ{I}) U G L T