chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
7,100 | lean_file_chunk | 2cd030e0880332eda292857cb0aa001f36e2da99d06f394da6dd3412fadc918c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Shaopeng Zhu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shaopeng Zhu
-/
module
public import Physlib.SpaceAndTime.Space.Origin
public import Physlib.SpaceAndTime.Space.EuclideanGroup.AffineGroup
/-!
# The action of the Euclidean group on `S... |
10,195 | lean_file_chunk | c5879a9042370b5f7b7a914835fa037ad3e5a0a9a56848b9ca3160f4bde58c3f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Shaopeng Zhu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shaopeng Zhu
-/
module
public import Physlib.SpaceAndTime.Space.EuclideanGroup.Basic
/-!
# The inclusion of the Euclidean group into the affine automorphism group
This file has two pa... |
15,397 | lean_file_chunk | c4e41f024e37412ffd19e8544fde8b3e01dd7e8bd3d63d2d8b418dfdb8990c50 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Shaopeng Zhu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shaopeng Zhu
-/
module
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# Euclidean group
This file defines the Euclidean group as translations composed with orthogonal maps,... |
9,581 | lean_file_chunk | 3952413a1b74508750eec673b75a8c4b69475ef9d563722f68b3fde2029d2ea5 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Module
public import Mathlib.MeasureTheory.Measure.Lebesgue.VolumeOfBalls
/-!
# Integrals in Space
## i. Ov... |
9,331 | lean_file_chunk | ffb7f8582f62e3fa6988cdec1e10bcc0b1702584eece1a5ee9640c3288834f02 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Gregory J. Loges. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gregory J. Loges
-/
module
public import Physlib.SpaceAndTime.Space.IsDistBounded
public import Physlib.SpaceAndTime.Space.Module
public import Mathlib.MeasureTheory.Constructions.H... |
8,352 | lean_file_chunk | 2b08844a8f20555588aa0eec1e73d9b984b9394ef28e95d6a2d797b7899c9f79 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Integrals.Basic
/-!
# The radial angular measure on Space
## i. Overview
The normal measure on `Space d` i... |
23,999 | lean_file_chunk | 8f27299eee9f8bee62072f97d31abe5ad0fdbccd6ef6ac36fa339f7ea44bd7ca | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Integrals.RadialAngularMeasure
public import Physlib.SpaceAndTime.Time.Basic
public import Physlib.Relativity... |
13,162 | lean_file_chunk | 3cd4de20d577ca83e3ddbf15ab568e4bccbdcf5a5ca215a9f8a90e8a2e5625e2 | lean_source_file | physlib_source_file_chunks | ### D.7. Monotonicity with respect to the norm
-/
omit [NormedSpace ℝ F'] in
lemma mono {d : ℕ} {f : Space d → F}
{g : Space d → F'}
(hf : IsDistBounded f) (hae : AEStronglyMeasurable g)
(hfg : ∀ x, ‖g x‖ ≤ ‖f x‖) : IsDistBounded g := by
rcases hf with ⟨hae1, ⟨n1, c1, g1, p1, c1_nonneg, p1_bound, bound1... |
7,704 | lean_file_chunk | 4545648def3c5ba3e3b2bd4c9f7dd20d48a692183c79d3176524cc74d2d7895c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Basic
/-!
# Units on Length
A unit of length corresponds to a choice of translationall... |
23,038 | lean_file_chunk | 074aac0fe126c984f5f8cad86b79888e2b96f4b9eac95511cd62e21645ec4325 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Basic
public import Physlib.SpaceAndTime.Space.Origin
public import Mathlib.Geometry.Manifold.Diffeomorph
pub... |
23,965 | lean_file_chunk | bb10456e9a5288053271f22a616b24e02ed6bc77c8b0876cefd9c444cd637cdf | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Laplacian
public import Physlib.SpaceAndTime.Space.Integrals.NormPow
public import Physlib.Mathem... |
22,839 | lean_file_chunk | 2f718602d7d06427e97d8725d91148bffcb7cf90308f8095919d1d3e5d46c2f8 | lean_source_file | physlib_source_file_chunks | (𝓝 (⟪distOfFunction (fun x : Space d => (‖x‖ ^ (- 2 : ℤ)) • basis.repr x) (by
refine (IsDistBounded.zpow_smul_repr_self _ ?_)
omega) η, y⟫_ℝ)) := by
haveI : NeZero d := ⟨by omega⟩
simp only [gradient_dist_normPowerSeries_log, distOfFunction_inner]
have h1 (n : ℕ) (x : Space d) :
η x * ⟪(normPowerSeri... |
5,467 | lean_file_chunk | 91ac3a3defdc9ae771b373b1104cd7635b336a3f3caa20a5b84ff6223d9bcb57 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Lazar Milikic. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lazar Milikic
-/
module
public import Physlib.SpaceAndTime.Space.Norm.Basic
/-!
# Iterated Laplacians of norm distributions
## i. Overview
This file proves the distributional identi... |
2,632 | lean_file_chunk | c48770adc6902b40a8e821a75f2fa5948d436388e7e218b664e13b6185b59cca | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Gregory J. Loges. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gregory J. Loges
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Basic
public import Physlib.SpaceAndTime.Space.Integrals.NormPow
/-!
# Regularized powers of the nor... |
2,161 | lean_file_chunk | a77fa32b00024fe07c52fd6148bd224788c9a478040aa3e6ca679bd10679c0fd | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Shaopeng Zhu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Shaopeng Zhu, Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Basic
public import Mathlib.Analysis.Normed.Affine.Isometry
/-!
# The origin of `Space` and the Eucl... |
7,432 | lean_file_chunk | a7532655dbb8d26d88eea65ac26b42d397b192f2e8c4271737dac292dbb4b1ba | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Module
/-!
# Slices of space
## i. Overview
In this module we will define the equivalence between `Space d... |
5,526 | lean_file_chunk | 6c2ac098d3b46f9b83b0032fe9285a11da6b2f3017aac341072af5c6c9012928 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Div
/-!
# Translations on space
We define translations on space, and how translations act on di... |
16,984 | lean_file_chunk | f93bf8c2ec8d3fbeb2537907364b0ce67e0cd97455e4f8e8291b33e311e9fda5 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.SpeedOfLight
public import Physlib.Relativity.Tensors.RealTensor.Vector.Tensorial
public import Physlib.SpaceAndTime.... |
2,734 | lean_file_chunk | 383cf47886e48da4012aec0a2bc69c2fb8d5fa090f6fca3328d68b30529b78f6 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.LorentzGroup.Boosts.Basic
public import Physlib.SpaceAndTime.SpaceTime.Basic
/-!
# Boosts of space time
## i. Overv... |
22,785 | lean_file_chunk | 0bb3ec0bde59263a89cd41ebe61811cf133d1d30debb3376c0c7c03a71f3c33f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2024 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.SpaceTime.LorentzAction
public import Physlib.Relativity.Tensors.RealTensor.CoVector.Tensorial
public import Mathli... |
5,223 | lean_file_chunk | 7c08c77a914fb071fd4681c1d3626c1b2538e20f38e1e4470bc0effaedf8a571 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.SpaceTime.Basic
public import Physlib.Mathematics.Distribution.Basic
/-!
# Lorentz group actions related to SpaceT... |
8,458 | lean_file_chunk | 801adbfa4ce5af3f6f24db26bb9ddeb67f5a055e2d3506dab991ad1bf52f91ca | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.SpaceTime.Derivatives
public import Physlib.SpaceAndTime.TimeAndSpace.Basic
/-!
# Time slice
Time slicing function... |
10,562 | lean_file_chunk | b3962e1ee6389de8f44d773567635ef4073cf449cd68ba42e0c21341550fee1d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Linear
public import Mathlib.MeasureTheory.Measure.Haar.InnerProductSpace
/-!
# Time
## i. Overview
I... |
7,994 | lean_file_chunk | 743a943da796823d1a99228ef0b37704035bd691f0a14f4c5976343e89f5144f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nikolai Kashcheev, Joseph Tooby-Smith
-/
module
public import Physlib.Relativity.Tensors.RealTensor.Vector.Basic
public import Physlib.SpaceAndTime.Space.Module
public import Phys... |
3,262 | lean_file_chunk | 1514eb1146080754e893b4de45e59ac90130740664762022bbe0abc10c6ed8f5 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Giuseppe Sorge. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Giuseppe Sorge
-/
module
public import Physlib.SpaceAndTime.Time.Derivatives
public import Mathlib.Analysis.Matrix.Normed
/-!
# Time derivatives of matrix-valued functions
General l... |
4,253 | lean_file_chunk | 92e6598fbb9a7e5455444d5110dc5254ae4d8d16d4d1933d7ac98e9c2d903bf6 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.InnerProductSpace.Basic
public import Mathlib.Geometry.Manifold.Diffeomorph
/-!
# The time manifold
In this module we ... |
13,895 | lean_file_chunk | 03cc6a7f8a8f45f1dcba9a632ac63721dfc72abd1b424a769fdd795baa99b57a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Geometry.Manifold.Diffeomorph
public import Physlib.SpaceAndTime.Time.Basic
public import Physlib.SpaceAndTime.Time.TimeUnit
/-!... |
6,477 | lean_file_chunk | 517fa8eed21fa57b888651958f2560727f97124d58e37db7ecea4bef94794f9e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.RCLike.Basic
/-!
# Units on time
A unit of time corresponds to a choice of translationally-invariant
metric on the ti... |
19,899 | lean_file_chunk | 7ea3495768e8c1bdfaf882a8e38e355af7af84a6447ffcee7b4a50e24e71bb66 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhi Kai Pong, Joseph Tooby-Smith, Rob Sneiderman
-/
module
public import Physlib.SpaceAndTime.Space.Derivatives.Curl
/-!
# Functions and distributions on Time and Space d
## i. ... |
23,989 | lean_file_chunk | 7582e2e7d90a7eb622d3bcae7e47dc6949e13c5c088342b601573924fc2014fa | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.TimeAndSpace.Basic
public import Mathlib.Analysis.Calculus.ContDiff.FiniteDimension
/-!
# Distributions which are ... |
12,603 | lean_file_chunk | 82a245407cb7bf4b98f83d72aff217a59eb7059e1a5e8c10ed611cbf7940c7dd | lean_source_file | physlib_source_file_chunks | clear x y
clear ih
induction n with
| zero => simp
| succ n ih2 =>
intro x y
rw [iteratedFDeriv_succ_eq_comp_left, iteratedFDeriv_succ_eq_comp_left]
simp only [Function.comp_apply,
continuousMultilinearCurryLeftEquiv_symm_apply]
trans ((fderiv ℝ (fun x =... |
5,366 | lean_file_chunk | 42a2241117f2ee02709f51690ca391f3218a1a204cf72c76d42f03c32076ee48 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Rob Sneiderman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rob Sneiderman
-/
module
public import Physlib.SpaceAndTime.Space.EuclideanGroup.Action
public import Physlib.SpaceAndTime.TimeAndSpace.Basic
/-!
# The action of the Euclidean group ... |
4,501 | lean_file_chunk | 4dcc67ac3438867b87df33118790aa80400f03805be6e56b5c7a8fc0cf42e258 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Rob Sneiderman. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rob Sneiderman
-/
module
public import Mathlib.RepresentationTheory.Continuous.Basic
public import Physlib.SpaceAndTime.TimeAndSpace.EuclideanGroup.Action
/-!
# The Euclidean group a... |
1,236 | lean_file_chunk | b60213d6d8514669c1a5a922be0c3116f5004807119fdbbeed7906ed92789ee2 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Boltzmann constant
The Boltzmann constant is a constant `kB` of dimension `m² kg s⁻² K⁻¹`, that is
`Ene... |
23,953 | lean_file_chunk | 2595a882c278bab606680d0386188b1e7d00407a7ecbb809a9e311e37503bd9e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Mathlib.MeasureTheory.Integral.Prod
public import Physlib.Thermodynamics.Temperature.Basic
/-!
# Canonical Ensemble: C... |
8,054 | lean_file_chunk | 36173c5078acda00b265ccec6f81a9fd8262c0842a585dd8445ac7b2034b64f2 | lean_source_file | physlib_source_file_chunks | div_pos (𝓒.mathematicalPartitionFunction_pos T) (pow_pos 𝓒.hPos _)
lemma partitionFunction_congr
(𝓒 : CanonicalEnsemble ι) (e : ι1 ≃ᵐ ι) (T : Temperature) :
(𝓒.congr e).partitionFunction T = 𝓒.partitionFunction T := by
simp [partitionFunction]
lemma partitionFunction_add
(𝓒 : CanonicalEnsemble ι) ... |
21,694 | lean_file_chunk | fb5093d5a74e216dff1821b996bcbedda6a6528fb887f61aba8753557c006f5f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.StatisticalMechanics.CanonicalEnsemble.Lemmas
/-!
# Finite Canonical Ensemble
This file specializes the gener... |
19,698 | lean_file_chunk | 5ab68ab1be6cff24dca5bd1e3f90f87ff16a41f7443fea0e5a5c2187d2c0bc92 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Matteo Cipollina. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.StatisticalMechanics.CanonicalEnsemble.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.Deriv
/-!
# Can... |
4,961 | lean_file_chunk | dfb3d09935040435d3237efa4da2d1a0df3ed3bbe0a959fff63c1fca25e77f8f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Physlib.StatisticalMechanics.CanonicalEnsemble.Finite
public import Physlib.Meta.Informal.Basic
/-!
# Two-state canon... |
2,161 | lean_file_chunk | 91e088342ca7d21f2a4a0f034f1f67af322d8a6173896c1ab862b91decf93b0f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Mathlib.MeasureTheory.Constructions.Pi
public import Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop
public import Physlib.Meta.Sorry
/-!
##... |
9,386 | lean_file_chunk | b2fbe4d34283d307104706da0c39fd17ef6190feec383f2cd0ef0edd410c5525 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Physlib.StatisticalMechanics.MicroCanonicalEnsemble.ThermoQuantities
public import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
/-!
... |
8,488 | lean_file_chunk | 8c0ca1b38693692944c8882ebd511881591dcdeec248e48fa2709a03f30a5453 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Physlib.StatisticalMechanics.MicroCanonicalEnsemble.Basic
public import QuantumInfo.ForMathlib.ComplexLaplaceTransform
/-!
## The theormodynamical ... |
430 | lean_file_chunk | 9546cc12488240c9b7b49cae0881b392c825401b00b9e5e1dd6729e7529a511f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
/-!
# String Theory
This directory is currently a place holder.
Please feel free to contribute!
Some directories which are NOT currently place hold... |
2,481 | lean_file_chunk | 203b14ba79bf96ddef33b97229c8af49829825c9704b411a5fcfcca194423a63 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
/-!
# F-theory with a SU(5) gauge group
This module contains the details of F-theory with a SU(5) gauge group, with possible
additional charges. Thi... |
4,069 | lean_file_chunk | 4e825e58c7468f640747cabf64c62e2e248de7d0ec5f158e48d58f31366acf21 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.StringTheory.FTheory.SU5.Quanta.Basic
public import Physlib.Particles.SuperSymmetry.SU5.ChargeSpectrum.Map
public import Physlib... |
4,382 | lean_file_chunk | f278e3aa020023549cdf94738a5a0b987c7cde54bc2dd7703916cb948f02d541 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Meta.TODO.Basic
public import Mathlib.Data.Fintype.Sets
/-!
# Allowed charges
## i. Overview
Within SU(5) F-theory with 10d a... |
23,849 | lean_file_chunk | c7cfb494c435f276ba884c49967838660b8daa249dc7e4d7b0bdbb67877ff05a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Particles.SuperSymmetry.SU5.ChargeSpectrum.PhenoClosed
public import Physlib.StringTheory.FTheory.SU5.Charges.OfRationalSection
... |
15,668 | lean_file_chunk | 70faa8cf3ac117e5195e8bdb7e2e39f0892b26666b78904febc019d2d71a6616 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.Normed.Ring.Lemmas
/-!
# Fluxes of representations
## i. Overview
Associated with each matter curve `Σ` are `G₄`-flu... |
15,351 | lean_file_chunk | 71d6abdeda1e90adfe08c60456b4e8681e63e75949f80396435a0cabea7565e4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.StringTheory.FTheory.SU5.Fluxes.Basic
/-!
# Constraints on chiral indices from the condition of no chiral exotics
## i. Overvi... |
17,786 | lean_file_chunk | bf62eb7ee890d23345f2567ddbcbf0cdab79800b76add6af5486d32eb4791726 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.StringTheory.FTheory.SU5.Fluxes.NoExotics.ChiralIndices
public import Physlib.StringTheory.FTheory.SU5.Fluxes.NoExotics.Elems
/-... |
6,694 | lean_file_chunk | 910c286b526e306f4fca6aa764a5c8493d298755c12ef204b904613e11e1ffee | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.StringTheory.FTheory.SU5.Fluxes.Basic
/-!
# Terms of `FluxesFive` and `FluxesTen` with no chiral exotics
## i. Overview
In th... |
8,474 | lean_file_chunk | 7ac7698a607ecb10711abb3e789cc5b49a9acc6731be3b8cbee6b9714a2b39c9 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.StringTheory.FTheory.SU5.Quanta.FiveQuanta
public import Physlib.StringTheory.FTheory.SU5.Quanta.TenQuanta
/-!
# Quanta of repr... |
23,996 | lean_file_chunk | e832392b98ee89e028c830d936716105920a73352f757cda19d84158a0357d80 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Particles.SuperSymmetry.SU5.ChargeSpectrum.MinimallyAllowsTerm.OfFinset
public import Physlib.StringTheory.FTheory.SU5.Fluxes.No... |
5,894 | lean_file_chunk | a6bd93a1174d9d731a113d31e4311f5f17562fbac42eb97d566437168c8d75b5 | lean_source_file | physlib_source_file_chunks | x.filter (fun y => y.2 = v) := by
intro v
refine (Multiset.map_congr rfl fun y hy => ?_).trans (Multiset.map_id _)
simp [← (Multiset.mem_filter.mp hy).2]
have hx : Multiset.filter (fun y => y.2 = ⟨0, 1⟩) x
= Multiset.filter (fun y => ¬ y.2 = ⟨1, -1⟩) x := by
refine Multiset.filter_congr ?_
... |
11,885 | lean_file_chunk | dbdad4100feb1e215de06e54edcf58e1cc9488089f72e321037a62e7b18354f3 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.StringTheory.FTheory.SU5.Charges.AnomalyFree
public import Mathlib.Data.ZMod.Defs
/-!
# Viable Quanta with Yukawa
## i. Overvi... |
23,995 | lean_file_chunk | f734027ac77d3c9bbbff81f6b6dd4e855a3614cba5dbc01791bf7285a2602b60 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Particles.SuperSymmetry.SU5.ChargeSpectrum.MinimallyAllowsTerm.OfFinset
public import Physlib.StringTheory.FTheory.SU5.Fluxes.No... |
9,821 | lean_file_chunk | 2e75dc6e398029342111afa893eb76ed409fe1f8796ed49707ac8237a8aa896b | lean_source_file | physlib_source_file_chunks | /-!
### D.2. TenQuanta in `liftCharge c` have a finite set of charges `c`
-/
lemma toCharge_toFinset_of_mem_liftCharge (c : Finset 𝓩)
{x : TenQuanta 𝓩} (h : x ∈ liftCharge c) :
x.toCharges.toFinset = c := by
rw [liftCharge, Multiset.mem_map] at h
obtain ⟨a, h, rfl⟩ := h
rw [reduce_toCharges]
simp a... |
431 | lean_file_chunk | b0aef76c3a30f3bf6ad2d3d26b3aecc13c9a566ba3d2d0358d8236fb29111bd4 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
/-!
# Thermodynamics
This directory is currently a place holder.
Please feel free to contribute!
Some directories which are NOT currently place hol... |
3,090 | lean_file_chunk | b8fc00ab0a53ef5466a4e0e4a9de6b1229c254356df61123e051d84a1780303c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Fabio Anza. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mitch Scheffer, Fabio Anza
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real -- for Real.rpow_def_of_pos
/-!
# Ideal gas: basic entropy and adiabatic relations
In this ... |
8,747 | lean_file_chunk | 9801602d9b04fd1584cd4b17a02ab9c6492b157e8e6cf2d935517cdbf36d2a7d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Matteo Cipollina, Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.Calculus.Deriv.Inv
public import Mathlib.Analysis.InnerProductSpace.Basic
public import Physlib.Stati... |
4,954 | lean_file_chunk | e784fde7379f49bee7c2b6c425b7253787b6629d1cbddf9629ecd8b25bbc384e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.RCLike.Basic
/-!
# Units on Temperature
A unit of temperature corresponds to a choice of translationally-invariant
me... |
12,609 | lean_file_chunk | 10ad60fdef1b84849ddfc077419f9af62cb7f68cdcbd36f8ac7593010fa00e78 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.SpaceAndTime.Time.TimeUnit
public import Physlib.SpaceAndTime.Space.LengthUnit
public import Physlib.ClassicalMechanics.Mass.Mas... |
7,767 | lean_file_chunk | 2df21546d42bb339032bf1a8cda31e16cd5b77df22d3a631770c6e6f875763d5 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Mathlib.Analysis.Normed.Field.Lemmas
public import Mathlib.Tactic.DeriveFintype
/-!
# Dimension
In this module we define the type `Dim... |
7,891 | lean_file_chunk | 819762e2f5e1ab3b257b21c7fcb936bca758b4f1d5b5bc4c8ba523bb4c63a5a9 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.WithDim.Speed
public import Physlib.Units.FDeriv
/-!
# Examples of units in Physlib
In this module we give some examples... |
3,057 | lean_file_chunk | 553c71268768c4a74b708cdaef7b5d68d510aafda1546016516098321534edcf | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.WithDim.Basic
public import Mathlib.Analysis.Calculus.FDeriv.Equiv
/-!
# Dimensional invariance of fderiv
In this module... |
6,514 | lean_file_chunk | 9b036022c5153cf47b1f7a1deb8b7a253a498b72bf84145e0f84a9cc5d136fc3 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicolas Rouquette. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rouquette
-/
module
public import Physlib.Units.LTMCTDimensionBase
public import Physlib.Units.ISQDimensionBase
/-!
# Bridging PhysLib's default basis and the ISQ basis
`... |
3,379 | lean_file_chunk | 8d20c833d1ff2cb3bc7c547034c13ddb25c9b871643d24aca8a227cf315d6b2d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicolas Rouquette. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rouquette
-/
module
public import Physlib.Units.Dimension
/-!
# The ISQ base quantities
The International System of Quantities (ISQ), specified in ISO/IEC 80000-1 and
des... |
4,524 | lean_file_chunk | 41cf8b6fc4c8b0d27c526ed95a3ee865377b83ae23c86f4b9dc30cd996a3e84e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.UnitDependent
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
/-!
# Dimensional invariance of the integral
In... |
8,292 | lean_file_chunk | c6c6f405df0ff9cffdb70585800f7ad13d5b7b0780ba66eb71afb75de8bb455a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.Dimension
/-!
# PhysLib's default dimension basis
`LTMCTDimensionBase` is PhysLib's default basis of base dimensions — l... |
3,646 | lean_file_chunk | 22d8c4afe3c2285673f880e69df50fe29c6839bda5866658b3e6f736ff8a6c35 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicolas Rouquette. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rouquette
-/
module
public import Physlib.Units.WithDim.Basic
/-!
# Examples: parametric dimensions and comparing dimensioned quantities
`Dimension B` is parameterised by... |
4,405 | lean_file_chunk | 3cb11629496629dc7c82c984455b7ac6d949862faf2ec2f5b9a1b5acaaa0f837 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicolas Rouquette. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rouquette
-/
module
public import Physlib.Units.Basic
/-!
# The unit side, parametrised in the same basis
The dimension basis is parametric (`Dimension B`), but the *unit... |
7,886 | lean_file_chunk | c834caf2e159a88a6bdb5060e57e81496749360bafc29b7973a9e93ba753b192 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicolas Rouquette. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rouquette
-/
module
public import Physlib.Units.UnitSystem
public import Physlib.Units.ISQDimensionBase
/-!
# A typed unit choice over the ISQ base quantities (the SI unit... |
19,213 | lean_file_chunk | b5a5f654606373d9d8c81cd1eb8ae390013ada97de18b7647121f435e6944484 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.Basic
public import Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap
/-!
## Types which depend on dimensions
I... |
10,552 | lean_file_chunk | b32c01fc474c2d4428d74a0f971ba569dcd619d0dc8e0b4bd8e7dc0f2bcfeac7 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Nicolas Rouquette. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Nicolas Rouquette
-/
module
public import Physlib.Units.ParametricUnits
/-!
# Unit systems, parametrised in a dimension basis
A **unit system** is the everyday physics object: a ... |
2,816 | lean_file_chunk | a3b3349d6f53689343abc140d4ca9a390b7b4c267127ba3cc90b98cf7be2f5a3 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.WithDim.Basic
/-!
# Area
In this module we define the dimensionful type corresponding to an area.
We define specific ins... |
8,752 | lean_file_chunk | c14f5de4bca851032c1614a150256391194c3a2ad461f658887a379d31d7d943 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.UnitDependent
/-!
## WithDim
WithDim is the type `M` which carrying the dimension `d`.
The dimension `d : Dimension B` ... |
1,213 | lean_file_chunk | 63ef28c7b45c78440852efb19a3ca0479c60fdf078e04727d1ae456a26c1563d | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.WithDim.Basic
/-!
# Energy
In this module we define the dimensionful type corresponding to an energy.
We define specific... |
336 | lean_file_chunk | 8bf96d1d2303f4ed2b07432806a9ce4e703b71f682649e54f8e7328c3598f5d7 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
/-!
# Mass
In this module we define the type `Mass`, which represents the mass of a particle,
in an arbitrary (but given) set of units.
-/
@[expose... |
667 | lean_file_chunk | e7ad11c9032ef9253475ea1006eb67b07af0edbfad722579c9cfd5584e9e2c04 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.WithDim.Basic
/-!
# Momentum
In this module we define the type `Momentum`, which represents the momentum of a particle
in... |
1,670 | lean_file_chunk | dcfa894ee3026ce334d3f699fc2a5f046143b61aed84c11e56d33cca86556102 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.WithDim.Basic
/-!
# Pressure
In this module we define the dimensionful type corresponding to an pressure.
We define spec... |
3,458 | lean_file_chunk | b2273c79f54b2ebf3c08d4951ee8a8fd3a777e73e9479b8e12ef9f5469d63a3e | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
public import Physlib.Units.WithDim.Basic
/-!
# Speed
In this module we define the dimensionful type corresponding to an speed.
We define specific i... |
373 | lean_file_chunk | dbd90f8592e0377298154478e804ed08abf5ceb2a68cf92392ae6968e0e7d02f | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Joseph Tooby-Smith. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Tooby-Smith
-/
module
/-!
# Velocity
In this module we define the type `Velocity`, which represents the velocity of a particle
in `d`-dimensional space, in an arbitrary (b... |
5,345 | lean_file_chunk | a0109a8b28a2c68eb71845e8686b8f05da8b774bef5dd74271eec7c89d7ddae7 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
/-!
# Defining Quantum Capacity
Quantum capacity is defined in different reference works in at least seven meaningfully different ways:
(1) https://www.uio.no/s... |
18,256 | lean_file_chunk | 45cb77b447c6df7a4bf496b2618267a11788c0e51505e042a97c7c40d96c3ba7 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.Channels.Unbundled
public import QuantumInfo.States.Mixed.MState
public import Mathlib.Topology.Order.Hom.Basic
/-! # Classes of Matri... |
23,996 | lean_file_chunk | a36662a32cb03bf2f9458bbf7d06464a3bbda6664dd164ce1bab811c47a4c89b | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.Channels.Bundled
public import QuantumInfo.Operators.Unitary
/-! # Completely Positive Trace Preserving maps
A `CPTPMap` is a `ℂ`-line... |
11,877 | lean_file_chunk | 7a5372a78147a96e46fd3c0b5d9e7a7d3e0501561cb53ed526cf7e9c37df1bb5 | lean_source_file | physlib_source_file_chunks | fun ⟨a, b, d⟩ a' => (K (b, a)) d a'
V.conjTranspose * V = 1 := by
rw [← hTP]
ext1 i j
simp only [Matrix.mul_apply, Fintype.sum_prod_type];
rw [Finset.sum_comm]
simp [Matrix.sum_apply, Matrix.mul_apply]
private lemma purify_MState_pure_basis_default_entry (i j : dOut × dOut) :
(MState.pure (Ket.basis ... |
2,440 | lean_file_chunk | 5e221ecf64364f894a04b3f2bb1e6425b28ee67b868c91cfc17db95f4721634b | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.Channels.Bundled
public import QuantumInfo.Channels.CPTP
public import QuantumInfo.Channels.Dual
public import QuantumInfo.Channels.Matr... |
23,794 | lean_file_chunk | 091e990a26bf975dedb6cc00c2dc1c2c7e4f463059723053c4963017c6a3f064 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg, Dennj Osele
-/
module
public import QuantumInfo.Channels.Bundled
public import Mathlib.LinearAlgebra.Matrix.FiniteDimensional
/-! # Duals of matrix map
Definitions and t... |
21,124 | lean_file_chunk | 6f44b08455a6a7868305f9ba1888b006f6ae0f1578b63a00f2a22c41a0ee3327 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Mathlib.LinearAlgebra.TensorProduct.Matrix
public import Mathlib.LinearAlgebra.PiTensorProduct.Basic
public import Mathlib.LinearAlgebra.PiTensorPro... |
19,426 | lean_file_chunk | 9c10cc9e93f5634f4a9028b3157e50a77953e95780aeb75d473e53e4a208de4a | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Leonardo A Lessa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo A Lessa, Alex Meiburg
-/
module
public import QuantumInfo.Channels.Bundled
public import QuantumInfo.Channels.CPTP
public import QuantumInfo.Channels.Dual
public import Qua... |
23,977 | lean_file_chunk | 184acac25562e52f0035890bdffc9ea2bb95bed761d6d9fab804d4e4c86e583b | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.Channels.MatrixMap
public import QuantumInfo.ForMathlib.MatrixNorm.TraceNorm
/-! # Properties of Matrix Maps
Building on `MatrixMap`s,... |
18,098 | lean_file_chunk | b87d4ee8b90c372b47f415ad89e85630b2661797a515f261efab2d9f7e5dce81 | lean_source_file | physlib_source_file_chunks | convert congruence_CP ( K k ) using 1;
-- Since B is a finite type, we can use the fact that finite types have decidable equality.
apply Classical.decEq);
exact h_sum_congruence.symm ▸ IsCompletelyPositive.finset_sum h_congruence_CP
theorem exists_kraus_of_choi_PSD
(C : Matrix (B × A) (B × A) 𝕜) (hC : C... |
2,530 | lean_file_chunk | c5d2d93054a0230151677bdcbcb023c7deafe234283ab0fe3315fb7af9d85ab8 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.ClassicalInfo.Distribution
public import Mathlib.MeasureTheory.Measure.MeasureSpaceDef
@[expose] public section
open BigOperators
/- ... |
12,405 | lean_file_chunk | 42db0ab4d9ec4a38b0be7b2b366578c59f005b58fcf8efd95a0cdb8df9dd99cb | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.ClassicalInfo.Prob
public import Mathlib.Analysis.Convex.Combination
/-! # Distributions on finite sets
We define the type `Distribut... |
5,177 | lean_file_chunk | 2bfa9a70009ab8e3151f4e2fd1ed7de62ce9fad2e8964a10975cc7447ee6a654 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.ClassicalInfo.Distribution
public import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
public import Mathlib.Analysis.SpecialFunctions... |
1,441 | lean_file_chunk | e11874b17540233a13db5d3e09f910eebd7f724124c843031e8aa32074e78779 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.NegMulLog
@[expose] public section
noncomputable section
open NNReal
namespace Real
theorem negMulLog_stri... |
17,895 | lean_file_chunk | 7c0a1781ed33d0a0ca7e49506f46da3bd57f3919211b4044ef75be38154a08e3 | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2025 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import Mathlib.Analysis.Convex.Mul
public import Mathlib.Analysis.SpecialFunctions.Log.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.ENNRealLog... |
23,970 | lean_file_chunk | 8d05bf42770147f21ea8983d89298ca47f5e809ca8309c7721cc294af94b2f2c | lean_source_file | physlib_source_file_chunks | /-
Copyright (c) 2026 Alex Meiburg. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Meiburg
-/
module
public import QuantumInfo.Entropy.Relative
public import QuantumInfo.ForMathlib.HermitianMat.Sqrt
public import QuantumInfo.ForMathlib.HermitianMat.LiebConcavity
... |
23,995 | lean_file_chunk | cc020abe54aee167efe05f2c31da411d2c9340379665772d3e47a06c15156fcb | lean_source_file | physlib_source_file_chunks | apply f_alpha_jointly_convex hα H.1 H.2 w hw_nonneg hw_sum ρs σs ρ_mix σ_mix hρ_mix hσ_mix
exact h_sum.trans (Finset.sum_le_sum fun i _ => mul_le_mul_of_nonneg_left
(le_ciSup (f_alpha_bddAbove hα (ρs i) (σs i) (hker i)) H) (hw_nonneg i))
/-- If for all i, ker(σs i) ≤ ker(ρs i), then ker(∑ w i • σs i) ≤ ker(∑ w i... |
23,998 | lean_file_chunk | 5e5b213ba92bec51a2c2e7da06e16de6df28eda16cc374d4577295730fb0432f | lean_source_file | physlib_source_file_chunks | The proof uses the twirling argument:
1. By unitary invariance, `Q̃_α(ρ_AB‖σ_AB) = Q̃_α(V_i ρ_AB V_i†‖V_i σ_AB V_i†)` for each `i`.
2. Averaging: `Q̃_α(ρ_AB‖σ_AB) = (1/|κ|) Σ_i Q̃_α(V_i ρ_AB V_i†‖V_i σ_AB V_i†)`.
3. By joint convexity (α > 1): `≥ Q̃_α((1/|κ|) Σ_i V_i ρ_AB V_i†‖(1/|κ|) Σ_i V_i σ_AB V_i†)`.
4. By twirlin... |
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