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 4.32.0

Wick Term insert some

WickContraction.wickTerm_insert_some

Plain-language statement

For a list φs = φ₀…φₙ of 𝓕.FieldOp, a Wick contraction φsΛ of φs, an element φ of 𝓕.FieldOp, i ≤ φs.length and a k in φsΛ.uncontracted, such that all 𝓕.FieldOp in φ₀…φᵢ₋₁ have time strictly less than φ and φ has a time greater than or equal to all FieldOp in φ₀…φₙ, then (φsΛ ↩Λ φ i (some k)).staticWickTerm is equal to th...

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.32.0

W Inner one dddconv

wInner_one_dddconv

Plain-language statement

An adjointness identity for difference convolution. The inner product of ff with ghg\mathbin{\circleddash}h equals the inner product of g\overline g with fh\overline f*\overline h.

additive combinatoricsarithmetic progressionsFourier analysis

Source project: Arithmetic Progressions Almost Periodicity

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U cauchy Seq derivto Lp

WkpU.cauchySeq_derivtoLp

Plain-language statement

A Cauchy sequence in W^{k,p}(U) induces a Cauchy sequence in Lp for each weak derivative component.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U deriv ELp Norm add le

WkpU.derivELpNorm_add_le

Plain-language statement

Triangle inequality for a single weak-derivative eLpNorm.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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Project-declaredLean 4.30.0

Wkp U deriv ELp Norm le e Norm

WkpU.derivELpNorm_le_eNorm

Plain-language statement

Each weak-derivative eLpNorm is bounded by the Sobolev eNorm.

partial differential equationsSobolev spacesanalysis

Source project: PDE

Person-level attribution pending.

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