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memo
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affeldt-aist committed Jan 13, 2025
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Expand Up @@ -1423,6 +1423,9 @@ rewrite (@fun_predC _ -%R)/=; last exact: opprK.
by rewrite image_id; under eq_fun do rewrite ltrNl opprK.
Qed.

(* NB: In not_near_at_rightP (and not_near_at_rightP), R has type numFieldType.
It is possible realDomainType could make the proof simpler and at least as
useful. *)
Lemma not_near_at_rightP (p : R) (P : pred R) :
~ (\forall x \near p^'+, P x) <->
forall e : {posnum R}, exists2 x, p < x < p + e%:num & ~ P x.
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