Formal target: Corpus.Erdos617.erdos_617
Let $r\geq 3$.
Exact formal statement
∀ (r : Nat),
GE.ge.{0} r 3 →
∀ {V : Type} [inst : Fintype.{0} V] [DecidableEq.{1} V],
Eq.{1} (Fintype.card.{0} V) (HAdd.hAdd.{0, 0, 0} (HPow.hPow.{0, 0, 0} r 2) 1) →
∀ (coloring : Sym2.{0} V → Fin r),
Exists.{1} fun S =>
Exists.{1} fun k =>
And (Eq.{1} (Finset.card.{0} S) (HAdd.hAdd.{0, 0, 0} r 1))
(∀ (u : V),
Membership.mem.{0, 0} S u →
∀ (v : V), Membership.mem.{0, 0} S v → Ne.{1} u v → Ne.{1} (coloring (Sym2.mk.{0} u v)) k)This target is a formal statement, not a proof of the problem.
Environment availability: available.