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style(Topology/Homotopy): tweak subpath homotopy layout
1 parent e7ceb19 commit e07a6a3

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Lines changed: 15 additions & 15 deletions

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Mathlib/Topology/Homotopy/Path.lean

Lines changed: 15 additions & 15 deletions
Original file line numberDiff line numberDiff line change
@@ -510,21 +510,21 @@ private theorem subpathOn_trans_aux₂ (γ : Path x y) (a b : unitInterval) (hab
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((γ.subpathOn a (convexCombo a b t) (le_convexCombo hab _)).trans
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(γ.subpathOn (convexCombo a b t) b (convexCombo_le hab _))) := by
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refine ⟨{
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toFun := fun ⟨u, v⟩ =>
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((γ.subpathOn a (convexCombo a b (convexCombo s t u)) (le_convexCombo hab _)).trans
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(γ.subpathOn (convexCombo a b (convexCombo s t u)) b (convexCombo_le hab _))) v
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continuous_toFun := by
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simp only [trans_apply, one_div, subpathOn_apply, convexCombo]
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simp only [← extend_apply, dite_eq_ite]
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apply continuous_if_le (hfg := by grind) <;> fun_prop
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map_zero_left v := by simp [Path.trans_apply]
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map_one_left v := by simp [Path.trans_apply]
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prop' u x hx := by
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rcases hx with rfl | rfl
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· simp [Path.trans]
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· simp [Path.trans]
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norm_num
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}⟩
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toFun := fun ⟨u, v⟩ =>
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((γ.subpathOn a (convexCombo a b (convexCombo s t u)) (le_convexCombo hab _)).trans
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(γ.subpathOn (convexCombo a b (convexCombo s t u)) b (convexCombo_le hab _))) v
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continuous_toFun := by
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simp only [trans_apply, one_div, subpathOn_apply, convexCombo]
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simp only [← extend_apply, dite_eq_ite]
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apply continuous_if_le (hfg := by grind) <;> fun_prop
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map_zero_left v := by simp [Path.trans_apply]
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map_one_left v := by simp [Path.trans_apply]
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prop' u x hx := by
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rcases hx with rfl | rfl
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· simp [Path.trans]
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· simp [Path.trans]
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norm_num
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}⟩
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/--
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A subpath from a to b composed with a subpath from b to c is homotopic to

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