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Expand file tree Collapse file tree Original file line number Diff line number Diff line change @@ -889,11 +889,13 @@ lemma ChartedSpace.sum_chartAt_inr (x' : M') :
889889 chartAt H (Sum.inr x') = (chartAt H x').lift_openEmbedding (X' := M ⊕ M') IsOpenEmbedding.inr :=
890890 rfl
891891
892+ @[simp]
892893lemma sum_chartAt_inl_apply {x : M} :
893894 ((chartAt H (.inl x : M ⊕ M')) (Sum.inl x)) = (chartAt H x) x := by
894895 rw [ChartedSpace.sum_chartAt_inl]
895896 exact PartialHomeomorph.lift_openEmbedding_apply _ _
896897
898+ @[simp]
897899lemma sum_chartAt_inr_apply {x : M'} :
898900 ((chartAt H (.inr x : M ⊕ M')) (Sum.inr x)) = (chartAt H x) x := by
899901 rw [ChartedSpace.sum_chartAt_inr]
Original file line number Diff line number Diff line change @@ -395,10 +395,12 @@ lemma ContMDiff.inr : ContMDiff I I n (@Sum.inr M M') := by
395395 rw [← I.image_eq (chartAt H x).target]
396396 exact (chartAt H x).extend_image_target_mem_nhds (mem_chart_source _ x)
397397
398+ @[simp]
398399lemma extChartAt_inl_apply {x : M} :
399400 ((extChartAt I (.inl x : M ⊕ M')) (Sum.inl x)) = (extChartAt I x) x := by
400401 simp [sum_chartAt_inl_apply]
401402
403+ @[simp]
402404lemma extChartAt_inr_apply {x : M'} :
403405 ((extChartAt I (.inr x : M ⊕ M')) (Sum.inr x)) = (extChartAt I x) x := by
404406 simp [sum_chartAt_inr_apply]
Original file line number Diff line number Diff line change @@ -1371,6 +1371,7 @@ noncomputable def lift_openEmbedding (e : PartialHomeomorph X Z) (hf : IsOpenEmb
13711371lemma lift_openEmbedding_toFun (e : PartialHomeomorph X Z) (hf : IsOpenEmbedding f) :
13721372 (e.lift_openEmbedding hf) = extend f e (fun _ ↦ (Classical.arbitrary Z)) := rfl
13731373
1374+ @[simp]
13741375lemma lift_openEmbedding_apply (e : PartialHomeomorph X Z) (hf : IsOpenEmbedding f) {x : X} :
13751376 (lift_openEmbedding e hf) (f x) = e x := by
13761377 simp_rw [e.lift_openEmbedding_toFun]
@@ -1397,6 +1398,7 @@ lemma lift_openEmbedding_symm_target (e : PartialHomeomorph X Z) (hf : IsOpenEmb
13971398 (e.lift_openEmbedding hf).symm.target = f '' e.source := by
13981399 rw [PartialHomeomorph.symm_target, e.lift_openEmbedding_source]
13991400
1401+ @[simp]
14001402lemma lift_openEmbedding_trans_apply
14011403 (e e' : PartialHomeomorph X Z) (hf : IsOpenEmbedding f) (z : Z) :
14021404 (e.lift_openEmbedding hf).symm.trans (e'.lift_openEmbedding hf) z = (e.symm.trans e') z := by
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