Numina/aqft in lean - #39
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New subsection "The von Neumann Density Theorem" before thrm:quasilocal-strongly-dense: the reducing-subspace, cyclic-subspace and single-vector lemmas, the finite amplification with its block-matrix and diagonal-bicommutant lemmas, the finite-vectors lemma and the strong neighbourhood basis. The theorem's proof now cites them; its statement is unchanged. A new heading "Lorentz Covariance and the Haag--Kastler Net" follows the theorem. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
New Physicslib4/Operators/ReducingSubspace.lean: a closed subspace invariant under an operator and its adjoint has orthogonal projection commuting with it. New Physicslib4/Operators/DensityTheorem.lean: the cyclic subspace of a vector reduces a unital *-representation, so every element of the bicommutant maps the vector into the closure of its orbit. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
ampDiag (diag(T) on l2(i; E) via lpDiag), diagAmplification (a StarAlgHom for a bare *-algebra, each copy bounded by its own norm) and toLp2 (a finite family of vectors as an element of l2), with simp lemmas. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
blockEntry with its commutation and block-expansion lemmas, and ampDiag_mem_bicommutant: diag(T) lies in the bicommutant of the amplified representation whenever T lies in the bicommutant of the original one. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
exists_forall_norm_sub_lt_of_mem_bicommutant approximates finitely many vectors at once through the amplification; hasBasis_nhds_ofFun gives the basic strong neighbourhoods of an operator; together they prove dense_range_in_bicommutant, the project's last sorry. Its Restriction is removed, and its unused [StarModule ℂ 𝔄] assumption is dropped. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Adds the new §10.5 density subsection entries, renumbers items and pages for the 324-page build (607 declarations, 606 formalised), and records that no sorry remains: the density theorem is now proved locally. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
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The von Neumann density theorem