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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 curated research declarations and 119,070 complete package declarations. Search 10,000 more complete Mathlib declarations.

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Showing 541 to 546 of 2,569 results.

Project-declaredLean 4.32.0

Conj T contr T

ConjTensorSpecies.conjT_contrT

Mathematical statement

Conjugation commutes with contraction: conjugating a contracted tensor equals contracting the conjugate on the bar-images of the same two slots.

physicsquantum field theoryrelativity

Source project: Physlib

Person-level attribution pending.

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Project-declaredLean 4.28.0

Conj Transpose isometry mul isometry le one

conjTranspose_isometry_mul_isometry_le_one

Project documentation

The operator norm of the conjugate transpose is equal to the operator norm. -/ theorem Matrix.opNorm_conjTranspose_eq_opNorm {m n : Type*} [Fintype m] [Fintype n] [DecidableEq m] [DecidableEq n] (A : Matrix m n 𝕜) : Matrix.opNorm Aᴴ = Matrix.opNorm A := by unfold Matrix.opNorm rw [← ContinuousLinearMap.adjoint.norm_map (toEuclideanLin A).toContinuousLine...

quantum informationentropyquantum channels

Source project: quantumInfo

Person-level attribution pending.

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Project-declaredLean 4.21.0-rc3

Smul near Litter of smul litter

ConNF.BaseAction.smul_nearLitter_of_smul_litter

Project documentation

The main lemma about how approximations interact with actions.

set theoryconsistencyfoundations

Source project: Con(NF)

Person-level attribution pending.

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Project-declaredLean 4.21.0-rc3

Smul interference

ConNF.BasePerm.smul_interference

Mathematical statement

Base permutations commute with the interference of near-litters.

set theoryconsistencyfoundations

Source project: Con(NF)

Person-level attribution pending.

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Project-declaredLean 4.21.0-rc3

Card t Set le

ConNF.card_tSet_le

Mathematical statement

Note that we cannot prove the reverse implication because all of our hypotheses at this stage are about permutations, not objects.

set theoryconsistencyfoundations

Source project: Con(NF)

Person-level attribution pending.

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