fact: Record well_ordering : Type := {wfcrr :> Type; order : wfcrr -> wfcrr -> Prop; equality : wfcrr -> wfcrr -> Prop; is_ord : is_order wfcrr order; is_eq : is_equality wfcrr equality; ord_is_wf : wf_ind wfcrr order; ord_wd_rht : is_well_def_rht wfcrr order equality}.