Canonical Structure S_pulb_constr := Build_Setoid_pred S_pulb_reg.Definition S_pulb_prod := SubSetoid S_pulb_constr.Definition S_pulb_p := RestrictedMap (Proj1_SPROD A C) S_pulb_constr.Definition S_pulb_q := RestrictedMap (Proj2_SPROD A C) S_pulb_constr.

Lemma Check_S_pulb_constr : forall d : D, S_pulb_constr (Build_Sprod (t1 d) (t2 d)).