Context stringlengths 57 6.04k | file_name stringlengths 21 79 | start int64 14 1.49k | end int64 18 1.5k | theorem stringlengths 25 1.55k | proof stringlengths 5 7.36k | eval_complexity float64 0 1 |
|---|---|---|---|---|---|---|
import Mathlib.Topology.Algebra.Module.WeakDual
import Mathlib.Algebra.Algebra.Spectrum
import Mathlib.Topology.ContinuousFunction.Algebra
import Mathlib.Data.Set.Lattice
#align_import topology.algebra.module.character_space from "leanprover-community/mathlib"@"a148d797a1094ab554ad4183a4ad6f130358ef64"
namespace ... | Mathlib/Topology/Algebra/Module/CharacterSpace.lean | 128 | 134 | theorem union_zero_isClosed [T2Space π] [ContinuousMul π] :
IsClosed (characterSpace π A βͺ {0}) := by |
simp only [union_zero, Set.setOf_forall]
exact
isClosed_iInter fun x =>
isClosed_iInter fun y =>
isClosed_eq (eval_continuous _) <| (eval_continuous _).mul (eval_continuous _)
| 0 |
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