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8 changes: 8 additions & 0 deletions reals/constructive_ereal.v
Original file line number Diff line number Diff line change
Expand Up @@ -414,6 +414,14 @@ Lemma le0y : (0 : \bar R) <= +oo. Proof. exact: real0. Qed.

Lemma leNy0 : -oo <= (0 : \bar R). Proof. exact: real0. Qed.

Lemma leyr r : +oo <= r%:E = false. Proof. by []. Qed.

Lemma ltyr r : +oo < r%:E = false. Proof. by []. Qed.

Lemma ltrNy r : r%:E < -oo = false. Proof. by []. Qed.

Lemma lerNy r : r%:E <= -oo = false. Proof. by []. Qed.

Lemma cmp0y : ((0 : \bar R) >=< +oo%E)%O.
Proof. by rewrite /Order.comparable le0y. Qed.

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