@@ -245,7 +245,7 @@ lemma finite_inter {n : ℕ} : FiniteInter (α := T.CompleteType (Fin n)) basis
245245
246246lemma basic_open_compl {n : ℕ} (T : L.Theory) (φ : L[[Fin n]].Sentence) :
247247 BasicOpen (T := T) φ.not = (BasicOpen φ)ᶜ := by
248- ext p ; exact p.not_mem_iff φ
248+ ext p; exact p.not_mem_iff φ
249249
250250instance (n : ℕ) : TopologicalSpace (T.CompleteType (Fin n)) := generateFrom basis
251251
@@ -257,15 +257,15 @@ instance {n : ℕ} : T0Space (T.CompleteType (Fin n)) := by
257257 replace h := inseparable_iff_forall_isOpen.1 a
258258 have b : IsOpen (X := (T.CompleteType (Fin n))) (BasicOpen φ) := by
259259 apply TopologicalSpace.GenerateOpen.basic
260- use φ ; trivial
260+ use φ; trivial
261261 exact h (BasicOpen φ) b
262262
263263instance {n : ℕ} : TotallySeparatedSpace (T.CompleteType (Fin n)) := by
264264 apply totallySeparatedSpace_of_t0_of_basis_clopen
265265 have a := isTopologicalBasis_of_subbasis_of_finiteInter
266266 (α := T.CompleteType (Fin n)) (s := basis) (by trivial) finite_inter
267267 apply IsTopologicalBasis.of_isOpen_of_subset
268- · intro _ h ; exact h.2
268+ · intro _ h; exact h.2
269269 · exact a
270270 · intro s ⟨φ, b⟩
271271 constructor
@@ -276,7 +276,7 @@ instance {n : ℕ} : TotallySeparatedSpace (T.CompleteType (Fin n)) := by
276276 exact ⟨φ.not, by trivial⟩
277277 rw[←compl_compl s]
278278 exact isClosed_compl_iff.2 h
279- · apply TopologicalSpace.GenerateOpen.basic ; use φ
279+ · apply TopologicalSpace.GenerateOpen.basic; use φ
280280
281281instance {n : ℕ} : T2Space (T.CompleteType (Fin n)) := TotallySeparatedSpace.t2Space
282282
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