show me your report pls
Any model uploaded without the technical report should be banned (kidding
Tried this prompt (with the problem from the new combi bench) and seems no thinking process ...?
"Can you help solving the following lean 4 code? \n\n import Mathlib structure Square where (pos : ℝ × ℝ) (side_length : ℕ) def Square.vertices (s: Square) : List (ℝ × ℝ) := let x := s.pos.1; let y := s.pos.2; let n : ℝ := s.side_length; [(x, y), (x + n, y), (x, y + n), (x + n, y + n)] def Square.contains (s : Square) (p : ℝ × ℝ) : Prop := let x := s.pos.1; let y := s.pos.2; let n : ℝ := s.side_length; x ≤ p.1 ∧ p.1 ≤ x + n ∧ y ≤ p.2 ∧ p.2 ≤ y + n def touches (s1: Square) (s2: Square): Prop := ∃ v ∈ s1.vertices, s2.contains v def touches_interior_or_edge (s1: Square) (s2: Square): Prop := ∃ v ∈ s1.vertices, s2.contains v ∧ v ∉ s2.vertices /-- Let $n \geq 5$ be an integer. Consider $n$ squares with side lengths $1,2, \ldots, n$, respectively. The squares are arranged in the plane with their sides parallel to the $x$ and $y$ axes. Suppose that no two squares touch, except possibly at their vertices.\nShow that it is possible to arrange these squares in a way such that every square touches exactly two other squares. -/ theorem apmo_2023_p1 (n : ℕ) (h_n: n ≥ 5) : ∃ position: Fin n → ℝ × ℝ, (∀ n1 n2 : Fin n, n1 ≠ n2 → ¬ touches_interior_or_edge ⟨position n1, n1 + 1⟩ ⟨position n2, n2 + 1⟩) ∧ ∀m : Fin n, ∃ l k, m ≠ l ∧ m ≠ k ∧ l ≠ k ∧ touches ⟨position m, m + 1⟩ ⟨position l, l + 1⟩ ∧ touches ⟨position m, m + 1⟩ ⟨position k, k + 1⟩ ∧ (∀ j : Fin n, j ∉ [m, l, k] → ¬ touches ⟨position m, m + 1⟩ ⟨position j, j + 1⟩) := by sorry"