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chore(analysis/complex/upper_half_plane): don't use abbreviation (#12679)
Some day we should add Poincaré metric as a `metric_space` instance on `upper_half_plane`. In the meantime, make sure that Lean doesn't use `subtype` instances for `uniform_space` and/or `metric_space`.
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src/analysis/complex/upper_half_plane.lean

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@@ -35,13 +35,15 @@ local attribute [-instance] matrix.special_linear_group.has_coe_to_fun
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local prefix `↑ₘ`:1024 := @coe _ (matrix (fin 2) (fin 2) _) _
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/-- The open upper half plane -/
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abbreviation upper_half_plane :=
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{point : ℂ // 0 < point.im}
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@[derive [topological_space, λ α, has_coe α ℂ]]
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def upper_half_plane := {point : ℂ // 0 < point.im}
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localized "notation `ℍ` := upper_half_plane" in upper_half_plane
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namespace upper_half_plane
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instance : inhabited ℍ := ⟨⟨complex.I, by simp⟩⟩
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/-- Imaginary part -/
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def im (z : ℍ) := (z : ℂ).im
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