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formal statement (Lean)
268theorem involutionOp_candidateOp (S : Finset Nat.Primes) (lam : Nat.Primes → ℝ) :
269 involutionOp ∘ₗ candidateOp S lam = candidateOp S lam ∘ₗ involutionOp := by
proof body
Term-mode proof.
270 unfold candidateOp
271 rw [LinearMap.comp_add, LinearMap.add_comp]
272 rw [involutionOp_diagOp_comm]
273 rw [involutionOp_sum_primeHop]
274
275/-! ## Master certificate -/
276
277/-- Master certificate: the structural properties of the candidate
278 Hilbert--Pólya operator that this module establishes. -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (12)
Lean names referenced from this declaration's body.
-
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
-
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
-
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
-
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
-
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
-
Primes
in IndisputableMonolith.NumberTheory.EulerInstantiation
decl_use
-
candidateOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
-
involutionOp
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
-
involutionOp_diagOp_comm
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
-
involutionOp_sum_primeHop
in IndisputableMonolith.NumberTheory.HilbertPolyaCandidate
decl_use
-
that
in IndisputableMonolith.NumberTheory.PhiLadderLattice
decl_use
-
S
in IndisputableMonolith.Relativity.ILG.Action
decl_use