Example of an ordered field: ⟨Q,+,×,<⟩

Q is an archemaedian ordered field.

Definition Qlt_is_strict_order := Build_strictorder
 Qlt_is_transitive_unfolded Qlt_is_antisymmetric_unfolded.

Definition Q_is_COrdField := Build_is_COrdField Q_as_CField
 Qlt_is_CSetoid_relation Qle (default_greater Q_as_CField Qlt_is_CSetoid_relation)
 (default_grEq Q_as_CField Qle) Qlt_is_strict_order Qplus_resp_Qlt
 Qmult_resp_pos_Qlt Qlt_gives_apartness Qle_is_not_lt Qgt_is_lt Qge_is_not_gt.

Definition Q_as_COrdField := Build_COrdField _ _ _ _ _ Q_is_COrdField.

Canonical Structure Q_as_COrdField.

Theorem Q_is_archemaedian : forall x : Q_as_COrdField, {n : N | x [<] nring n}.