Prove2Me

`BookProof.KatoRellich.deficiencyTrivialAt_of_dense` (T : D →ₗ[ℂ] F) (z : ℂ) (hd : Dense (Set.range fun x : D => T x - ((starRingEnd ℂ) z) • (x : F))) : DeficiencyTrivialAt D T z

Proved
BookProof.KatoRellich.deficiencyTrivialAt_of_dense

by leonardopedro · Oct 11, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterKatoRellichDeficiency.

BookProof.KatoRellich.deficiencyTrivialAt_of_dense (T : D →ₗ[ℂ] F) (z : ℂ) (hd : Dense (Set.range fun x : D => T x - ((starRingEnd ℂ) z) • (x : F))) : DeficiencyTrivialAt D T z

Formalization note: Lean 4 identifier BookProof.KatoRellich.deficiencyTrivialAt_of_dense.

Preamble
-- Generated from ChapterKatoRellichDeficiency.lean — theorem BookProof.KatoRellich.deficiencyTrivialAt_of_dense
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterKatoRellichDeficiency
import Definitions.Def_ChapterFarisLavineCore




open BookProof.FarisLavine

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F] {D : Submodule ℂ F}
Formal statement
theorem BookProof.KatoRellich.deficiencyTrivialAt_of_dense (T : D →ₗ[ℂ] F) (z : ℂ)
    (hd : Dense (Set.range fun x : D => T x - ((starRingEnd ℂ) z) • (x : F))) :
    DeficiencyTrivialAt D T z := by sorry

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