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CoolRmalEtienneC30
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Update Mathlib/Analysis/LocallyConvex/Separation.lean
Co-authored-by: Etienne Marion <66847262+EtienneC30@users.noreply.github.com>
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Mathlib/Analysis/LocallyConvex/Separation.lean

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@@ -387,7 +387,7 @@ theorem iInter_nat_halfSpaces_eq_of_prod {F : Type*} {s : Set (E × F)}
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∃ (L : ℕ → E →L[𝕜] 𝕜) (T : ℕ → F →L[𝕜] 𝕜) (c : ℕ → ℝ),
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⋂ (i : ℕ), {(x, y) | c i ≤ re (L i x) + re (T i y)} = s
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∧ (s.Nonempty → s ≠ univ → ∀ i, ∃ (x : E) (y : F), re (L i x) + re (T i y) ≠ 0) := by
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have ⟨LT, c, eq1, eq2⟩ := iInter_nat_halfSpaces_eq (𝕜 := 𝕜) hs₁ hs₂ hsep
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obtain ⟨LT, c, eq1, eq2⟩ := iInter_nat_halfSpaces_eq (𝕜 := 𝕜) hs₁ hs₂ hsep
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use fun i ↦ (LT i).comp (.inl 𝕜 E F), fun i ↦ (LT i).comp (.inr 𝕜 E F), c
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constructor
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· rw [← eq1]

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