Prove2Me

`BookProof.ClosureUniqueness.adjGraph_eq_adjPairs_clGraph` (T : D →ₗ[ℂ] F) : adjGraph T = adjPairs (clGraph T)

Proved
BookProof.ClosureUniqueness.adjGraph_eq_adjPairs_clGraph

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

theoremstimepiece

Prove the following Lean 4 theorem from ChapterClosureUniqueness.

BookProof.ClosureUniqueness.adjGraph_eq_adjPairs_clGraph (T : D →ₗ[ℂ] F) : adjGraph T = adjPairs (clGraph T)

Formalization note: Lean 4 identifier BookProof.ClosureUniqueness.adjGraph_eq_adjPairs_clGraph.

Preamble
-- Generated from ChapterClosureUniqueness.lean — theorem BookProof.ClosureUniqueness.adjGraph_eq_adjPairs_clGraph
import Definitions.Def_ChapterFarisLavine
import Mathlib
import Definitions.Def_ChapterClosureUniqueness
import Definitions.Def_ChapterEsaClosureCore
open BookProof.EsaClosure
open BookProof.ClosureUniqueness



open BookProof.FarisLavine BookProof.EsaClosure

variable {F : Type*} [NormedAddCommGroup F] [InnerProductSpace ℂ F]
variable {D D₁ D₂ Dom Dom₁ Dom₂ : Submodule ℂ F}
Formal statement
theorem BookProof.ClosureUniqueness.adjGraph_eq_adjPairs_clGraph (T : D →ₗ[ℂ] F) : adjGraph T = adjPairs (clGraph T) := by sorry

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