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feat(HermitianMat/Proj): add projector positivity, kernel, and posPart=0 lemmas#1074

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jstoobysmith merged 1 commit intoleanprover-community:masterfrom
dennj:proj
May 5, 2026
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feat(HermitianMat/Proj): add projector positivity, kernel, and posPart=0 lemmas#1074
jstoobysmith merged 1 commit intoleanprover-community:masterfrom
dennj:proj

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@dennj dennj commented May 2, 2026

proof wanted to theorem

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Couple of small comments - otherwise this looks good

@@ -8,6 +8,7 @@ module
public import QuantumInfo.ForMathlib.HermitianMat.CFC

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I think this file should be named “Projector”. If easy could we change it? No worries if not.

erw [ Subtype.mk_eq_mk ];
ext i j; simp [ LinearMap.toMatrix_apply, Matrix.one_apply ] ;

theorem projector_nonneg : 0 ≤ projector S := by
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Most of the QuantumInfo “theorem” will eventually be changed to “lemma” could we use “lemma” here and throughout the changes

@jstoobysmith jstoobysmith added the t-quantum-info Quantum information label May 5, 2026
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Let me actually approve this one, as my comments can be left to a future PR. I think this is undeniably an improvement, and therefore should be merged. I will do so shortly.

@jstoobysmith jstoobysmith added the ready-to-merge This PR is approved and will be merged shortly label May 5, 2026
@jstoobysmith jstoobysmith merged commit 3ba9339 into leanprover-community:master May 5, 2026
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@dennj dennj deleted the proj branch May 5, 2026 09:59
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