{"id":"palomar/PALOMAR-2026-08-26-000008","url":"https://github.com/sneed-and-feed/lean-theorems-1/tree/38161dacae52fb604fb26933140dd4c3a129369d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-26-000008-v1.json","repo":"https://github.com/sneed-and-feed/lean-theorems-1","tags":["math.CO","msc:05D05","msc:05C35","extremal-combinatorics","set-systems","lean","formal-verification"],"score":0,"title":"sneed-and-feed/lean-theorems-1","trust":"high","domain":"math.CO","source":"palomar","authors":["Sneed & Feed Formalization Team"],"reviews":0,"subject":"math.CO","summary":"A complete machine-checked Lean 4 formalization of Béla Bollobás's 1965 Two Families Theorem (Set Pairs Inequality) in extremal set theory. Proves the skew LYM-type inequality for pairs of disjoint subsets (A_i, B_i) satisfying cross-intersection conditions A_i ∩ B_j ≠ ∅ for i ≠ j, and deduces the uniform bound m ≤ C(a+b, a) for uniform families of sizes a and b. To the maintainers' knowledge, the theorem was not found in an exact declaration, docstring, and type signature search of the pinned Mathlib revision (Mathlib v4.34.0-rc1).","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-08-26","reactions":{},"formalized":true,"formalizes":[{"title":"On generalized graphs","identifier":"","relationship":"formalizes"}]}