{"id":"palomar/PALOMAR-2026-08-26-000007","url":"https://github.com/sneed-and-feed/lean-theorems-1/tree/1fbfff16eb01c3640f48194de9690baf0c07a01d","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-08-26-000007-v1.json","repo":"https://github.com/sneed-and-feed/lean-theorems-1","tags":["math.CO","msc:05D05","msc:05C65","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 J. A. Bondy's 1972 theorem on induced subsets. Proves that for any family F of n distinct subsets of an arbitrary finite ground set X, there exists a distinguishing subset S ⊆ X of cardinality at most n - 1 such that the restriction map s ↦ s ∩ S is injective on F. 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":"Induced subsets","identifier":"","relationship":"formalizes"}]}