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feat(data/real/sqrt): add continuity attributes (#6388)
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I add continuity attributes to `continuous_sqrt` and `continuous.sqrt`.
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benjamindavidson committed Feb 23, 2021
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Expand Up @@ -123,6 +123,7 @@ nnreal.sqrt (nnreal.of_real x)

variables {x y : ℝ}

@[continuity]
lemma continuous_sqrt : continuous sqrt :=
nnreal.continuous_coe.comp $ nnreal.sqrt.continuous.comp nnreal.continuous_of_real

Expand Down Expand Up @@ -280,4 +281,5 @@ lemma continuous_at.sqrt (h : continuous_at f x) : continuous_at (λ x, sqrt (f
lemma continuous_on.sqrt (h : continuous_on f s) : continuous_on (λ x, sqrt (f x)) s :=
λ x hx, (h x hx).sqrt

@[continuity]
lemma continuous.sqrt (h : continuous f) : continuous (λ x, sqrt (f x)) := continuous_sqrt.comp h

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