brualdi-ch10-34

open

difficulty 4

credited

Run this goal:./swarm/run.sh --goal brualdi-ch10-34

What it runs

The Lean statement the swarm must prove — kernel-verified at Gate A. The trailing sorry is the open obligation a proof replaces.

goals/brualdi-ch10-34.lean

import Mathlib

structure SteinerTripleSystemOfIndOne (t k n : ℕ) where
  carrier : Fin n
  blocks : Finset (Finset (Fin n))
  card_blocks : ∀ b ∈ blocks, b.card = k
  block_inner : ∀ s : (Finset (Fin n)), s.card = t → ∃! b ∈ blocks, s ⊆ b
structure SteinerTripleSystem (t k n I : ℕ) where
  carrier : Fin n
  blocks : Finset (Finset (Fin n))
  card_blocks : ∀ b ∈ blocks, b.card = k
  block_inner : ∀ s : (Finset (Fin n)), s.card = t → ∃ f : Fin I ↪ blocks, ∀ i, s ⊆ f i

theorem brualdi_ch10_34 (t v : ℕ) (ht : t > 0) : Nonempty (SteinerTripleSystemOfIndOne 2 3 v) →
    ∃ I, Nonempty (SteinerTripleSystem 2 3 (v ^ t) I) := by
  sorry

Runs (0)

No runs recorded for this suite yet — they appear here as the swarm attempts the benchmarks.