Fact pos_divr_closed : divr_closed (@pos R).Canonical pos_mulrPred := MulrPred pos_divr_closed.Canonical pos_divrPred := DivrPred pos_divr_closed.Fact nneg_divr_closed : divr_closed (@nneg R).Canonical nneg_mulrPred := MulrPred nneg_divr_closed.Canonical nneg_divrPred := DivrPred nneg_divr_closed.Fact nneg_addr_closed : addr_closed (@nneg R).Canonical nneg_addrPred := AddrPred nneg_addr_closed.Canonical nneg_semiringPred := SemiringPred nneg_divr_closed.Fact real_oppr_closed : oppr_closed (@real R).Canonical real_opprPred := OpprPred real_oppr_closed.Fact real_addr_closed : addr_closed (@real R).Canonical real_addrPred := AddrPred real_addr_closed.Canonical real_zmodPred := ZmodPred real_oppr_closed.Fact real_divr_closed : divr_closed (@real R).Canonical real_mulrPred := MulrPred real_divr_closed.Canonical real_smulrPred := SmulrPred real_divr_closed.Canonical real_divrPred := DivrPred real_divr_closed.Canonical real_sdivrPred := SdivrPred real_divr_closed.Canonical real_semiringPred := SemiringPred real_divr_closed.Canonical real_subringPred := SubringPred real_divr_closed.Canonical real_divringPred := DivringPred real_divr_closed.Fact archi_bound_subproof (R : archiFieldType) : archimedean_axiom R.

Lemma poly_ivt : real_closed_axiom R.