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clean up
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  • Mathlib/LinearAlgebra/AffineSpace/AffineSubspace

Mathlib/LinearAlgebra/AffineSpace/AffineSubspace/Shift.lean

Lines changed: 6 additions & 6 deletions
Original file line numberDiff line numberDiff line change
@@ -109,7 +109,7 @@ theorem affineCombination_mem_shift {ι : Type*} [Fintype ι] [Nontrivial ι]
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simp
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classical
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obtain ⟨j, hj⟩ : Set.Nonempty {i}ᶜ := by
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by_contra!
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by_contra
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simp at this
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rw [shift_eq ⟨p j, mem_affineSpan k <| Set.mem_image_of_mem _ hj⟩]
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suffices ∃ q ∈ affineSpan k (p '' {i}ᶜ), w i • (p i -ᵥ p j) +ᵥ q = affineCombination k univ p w by
@@ -132,7 +132,7 @@ theorem _root_.AffineIndependent.affineCombination_mem_shift_iff
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refine ⟨?_, fun h ↦ by simpa [h] using affineCombination_mem_shift p i hw⟩
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classical
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obtain ⟨j, hj⟩ : Set.Nonempty {i}ᶜ := by
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by_contra!
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by_contra
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simp at this
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rw [shift_eq ⟨p j, mem_affineSpan k <| Set.mem_image_of_mem _ hj⟩]
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suffices ∀ q ∈ affineSpan k (p '' {i}ᶜ),
@@ -217,9 +217,9 @@ theorem closedInterior_inter_shift_zero [ZeroLEOneClass k] :
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· simp [h i (mem_univ i)]
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· apply iff_of_false
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· apply not_and_of_not_left
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contrapose! hp
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contrapose hp
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exact Set.mem_of_mem_of_subset hp s.closedInterior_subset_affineSpan
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· contrapose! hp
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· contrapose hp
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rw [Set.mem_singleton_iff] at hp
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rw [hp]
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exact mem_affineSpan _ (by simp)
@@ -293,9 +293,9 @@ theorem closedInterior_inter_shift (hx : x ∈ Set.Icc 0 1) :
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simp [lineMap_apply, hj]
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· apply iff_of_false
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· apply not_and_of_not_left
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contrapose! hp
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contrapose hp
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exact Set.mem_of_mem_of_subset hp s.closedInterior_subset_affineSpan
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· contrapose! hp
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· contrapose hp
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rw [Set.mem_image] at hp
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obtain ⟨q, hq, rfl⟩ := hp
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apply homothety_mem (mem_affineSpan _ (by simp))

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