Lean 4 · Mathlib v4.32.2 · kernel-checked

PDElib Atlas

Every result in the library is machine-checked: no sorry, no admitted lemma, no axiom beyond the three Lean itself assumes. This is the map of what is proved and what each proof rests on.

Modules
240
Declarations
1256
Theorems
1118
Non-classical axioms
0
sorry
0
Build
8905 jobs

lake build green FullAudit: propext · Classical.choice · Quot.sound only 8 witness files

The spine

How the results connect

Five chains carry the library. Each arrow is a real dependency — the target could not be stated or proved without the source. Solid nodes are verified; the dashed frontier is what is not yet proved.

123 45 weak ∂ᵢ on ℝⁿ WeakDerivPi mollification Young · ApproxIdentity Meyers–Serrin MeyersSerrinPi H = W on ℝⁿ memW12_iff_approx compact exhaustion OpenExhaustion partition of unity Telescope · Annuli domain Meyers–Serrin meyersSerrin_domain H = W on Ω memW12On_iff_approx 1-D mean Poincaré PoincareMean slab → cube L² and L¹, by induction mean form poincare_cube_mean Poincaré at W^1,2 poincare_cube_memW12 Caccioppoli energy on level sets step → recursion geometry-abstract key lemma → osc decay δ uniform in the solution interior Hölder deGiorgi_interior_holder translation estimate ‖u(·+v) − u‖ ≤ Σ|vⱼ|‖gⱼ‖ mollification rate first order in δ cells & lattice disjoint, corner-free constant Fréchet–Kolmogorov not yet proved Rellich–Kondrachov not yet proved localise density weak ∂ ∫|∇u| side cell Poincaré
Lanes 1–4 are complete and kernel-checked. Lane 5 is the live frontier: the translation estimate, the mollification rate, and the disjoint cell lattice are proved, and the two compactness theorems they feed are not. The dashed cross-links carry results between chains — density transfers a smooth-function inequality to weak derivatives, and the Poincaré lane supplies the ∫|∇u| term the De Giorgi isoperimetric argument consumes.
Explorer

Every module and what it rests on

Each dot is a module, placed left-to-right by how deep its dependency chain runs and grouped by area. Click one to see its theorems and light up everything it depends on, transitively.

Areas

Reading the map

Horizontal position is dependency depth: foundations at the left, endpoints at the right. The deepest chain runs 56 modules.

click a node · 240 modules · 357 dependencies

Module

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By area

Where the mass sits

Theorem counts are of named results in source. The audited figure (1118) is larger because it counts every constant in the compiled environment, including structure projections and instances.

AreaModulesTheoremsMax depth