kim-em

import Mathlib

open Set

theorem mem_convexHull_finset_extremePoints_of_mem_compact_convex {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E] [FiniteDimensional ℝ E]
    {s : Set E} {x : E}
    (hscomp : IsCompact s)
    (hsconv : Convex ℝ s)
    (hx : x ∈ s) :
    ∃ t : Finset E,

kim-em

import ChallengeDeps

open LeanEval.Combinatorics
open scoped BigOperators

theorem dvd_card_connectedComponent_markoffGraph {p : ℕ} (hp : Nat.Prime p) (hgt : 3 < p) :
    ∀ c : (markoffGraph p).ConnectedComponent, p ∣ Nat.card c := by
  sorry

kim-em

import Mathlib

theorem pi1_circle_mulEquiv_int :
    Nonempty (HomotopyGroup.Pi 1 Circle (1 : Circle) ≃* Multiplicative ℤ) := by
  sorry

kim-em

import ChallengeDeps

open LeanEval.NumberTheory
open scoped ArithmeticFunction.sigma

theorem riemann_hypothesis_iff_lagarias_elementary_criterion :
    RiemannHypothesis ↔ LagariasElementaryCriterion := by
  sorry

kim-em

import Mathlib

open PowerSeries

theorem substInv_X_sub_X_sq_eq_catalan (n : ℕ) :
    haveI : Invertible (coeff 1 ((X : ℚ⟦X⟧) - X ^ 2)) := by
      simp [coeff_X, coeff_X_pow]; exact invertibleOne
    coeff (n + 1) (substInv ((X : ℚ⟦X⟧) - X ^ 2)) =
      (Nat.choose (2 * n) n : ℚ) / (↑n + 1) := by
  sorry

kim-em

import Mathlib

theorem ci_regenerate_main_check : True := by
  sorry

kim-em

import Mathlib

theorem mulCayley_connected_iff_closure_eq_top {G : Type*} [Group G]
    (S : Set G) :
    (SimpleGraph.mulCayley S).Connected ↔ Subgroup.closure S = ⊤ := by
  sorry

kim-em

import Mathlib

open SimpleGraph

theorem finite_graph_ramsey_theorem :
    ∀ r s : ℕ, 2 ≤ r → 2 ≤ s → ∃ n : ℕ, ∀ G : SimpleGraph (Fin n), ¬ G.CliqueFree r ∨ ¬ Gᶜ.CliqueFree s := by
  sorry

kim-em

import Mathlib

theorem list_append_singleton_length :
    (([1, 2] : List Nat).append [3]).length = 3 := by
  sorry

kim-em

import Mathlib

theorem two_plus_two_eq_four : (2 : Nat) + 2 = 4 := by
  sorry