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Linting errors
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Mathlib/ModelTheory/Types.lean

Lines changed: 4 additions & 4 deletions
Original file line numberDiff line numberDiff line change
@@ -245,7 +245,7 @@ lemma finite_inter {n : ℕ} : FiniteInter (α := T.CompleteType (Fin n)) basis
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lemma basic_open_compl {n : ℕ} (T : L.Theory) (φ : L[[Fin n]].Sentence) :
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BasicOpen (T := T) φ.not = (BasicOpen φ)ᶜ := by
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ext p ; exact p.not_mem_iff φ
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ext p; exact p.not_mem_iff φ
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instance (n : ℕ) : TopologicalSpace (T.CompleteType (Fin n)) := generateFrom basis
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@@ -257,15 +257,15 @@ instance {n : ℕ} : T0Space (T.CompleteType (Fin n)) := by
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replace h := inseparable_iff_forall_isOpen.1 a
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have b : IsOpen (X := (T.CompleteType (Fin n))) (BasicOpen φ) := by
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apply TopologicalSpace.GenerateOpen.basic
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use φ ; trivial
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use φ; trivial
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exact h (BasicOpen φ) b
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instance {n : ℕ} : TotallySeparatedSpace (T.CompleteType (Fin n)) := by
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apply totallySeparatedSpace_of_t0_of_basis_clopen
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have a := isTopologicalBasis_of_subbasis_of_finiteInter
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(α := T.CompleteType (Fin n)) (s := basis) (by trivial) finite_inter
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apply IsTopologicalBasis.of_isOpen_of_subset
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· intro _ h ; exact h.2
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· intro _ h; exact h.2
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· exact a
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· intro s ⟨φ, b⟩
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constructor
@@ -276,7 +276,7 @@ instance {n : ℕ} : TotallySeparatedSpace (T.CompleteType (Fin n)) := by
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exact ⟨φ.not, by trivial⟩
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rw[←compl_compl s]
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exact isClosed_compl_iff.2 h
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· apply TopologicalSpace.GenerateOpen.basic ; use φ
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· apply TopologicalSpace.GenerateOpen.basic; use φ
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instance {n : ℕ} : T2Space (T.CompleteType (Fin n)) := TotallySeparatedSpace.t2Space
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