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chore: make (x : M) implicit in `extChartAt_image_nhd_mem_nhds_of_bou…
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…ndaryless` (#10081)

Fixes an oversight in #10001: x is already included in the hypothesis `hx`, so should be implicit.
A follow-up PR will address this issue more systematically.
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grunweg committed Jan 31, 2024
1 parent ec49709 commit 58df996
Showing 1 changed file with 3 additions and 2 deletions.
5 changes: 3 additions & 2 deletions Mathlib/Geometry/Manifold/SmoothManifoldWithCorners.lean
Expand Up @@ -1372,10 +1372,11 @@ theorem map_extChartAt_nhds_of_boundaryless [I.Boundaryless] :
rw [extChartAt]
exact map_extend_nhds_of_boundaryless (chartAt H x) I (mem_chart_source H x)

variable {x} in
theorem extChartAt_image_nhd_mem_nhds_of_boundaryless [I.Boundaryless]
(h : s ∈ 𝓝 x) : extChartAt I x '' s ∈ 𝓝 (extChartAt I x x) := by
(hx : s ∈ 𝓝 x) : extChartAt I x '' s ∈ 𝓝 (extChartAt I x x) := by
rw [extChartAt]
exact extend_image_nhd_mem_nhds_of_boundaryless _ I (mem_chart_source H x) h
exact extend_image_nhd_mem_nhds_of_boundaryless _ I (mem_chart_source H x) hx

theorem extChartAt_target_mem_nhdsWithin' {y : M} (hy : y ∈ (extChartAt I x).source) :
(extChartAt I x).target ∈ 𝓝[range I] extChartAt I x y :=
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