Source-pinned research

Research proof index

Search theorem names, mathematical ideas, modules, topics, projects, and role-labelled researchers. Open a result for its complete indexed Lean declaration and source record.

This index contains 2,569 research declarations. Search 10,000 more complete Mathlib declarations.

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2569 results

Project-declaredLean 4.28.0

V rho conj mul self eq

V_rho_conj_mul_self_eq

Plain-language statement

V_rho^H * V_rho simplifies to sandwiching the traceRight by the inverse square root.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.28.0

V rho isometry

V_rho_isometry

Plain-language statement

V_rho is an isometry.

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.32.0

Van der Corput

van_der_Corput

Plain-language statement

Let φ\varphi be KK-Lipschitz and bounded in norm by BB on (a,b)(a,b). For every integer frequency nn,

abeinxφ(x)dx2π(ba)(B+K(ba)2)(1+n(ba))1.\left\lVert\int_a^b e^{inx}\varphi(x)\,dx\right\rVert \le 2\pi(b-a)\left(B+\frac{K(b-a)}2\right)\left(1+|n|(b-a)\right)^{-1}.

harmonic analysisFourier analysismeasure theory

Source project: Carleson formalization

Person-level attribution pending.

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Project-declaredLean 4.31.0

Rank nonsquare eq deg of deg le

Vandermonde.rank_nonsquare_eq_deg_of_deg_le

Plain-language statement

The rank of a non-square Vandermonde matrix with more rows than columns is the number of columns.

cryptographyproof systemscoding theory

Source project: ArkLib

Person-level attribution pending.

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Project-declaredLean 4.32.0

Vector support map M index

Vector.support_mapM_index

Plain-language statement

Index-extraction for Vector.mapM: any component of a vector in the support of the sequenced computation lies in the support of the corresponding component computation.

program verificationseparation logiccryptography

Source project: VCVio

Person-level attribution pending.

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Project-declaredLean 4.8.0

Vera debate cost

vera_debate_cost

Plain-language statement

Vera makes few queries, regardless of Alice and Bob

probabilitycomplexity theoryinteractive protocols

Source project: debate

Person-level attribution pending.

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