Acknowledgements

Problems submitted by

Armaël Guéneau

Fabian Huch

Problem committee

Floris van Doorn

Maximilian P. L. Haslbeck

Anton Trunov

Simon Wimmer

Final Leaderboard

Solutions

Github repository with solutions: https://github.com/wimmers/proofground2021-solutions

Send us a pull request with your own!

Fourier-Motzkin Elimination

Submitted by: Simon Wimmer

Originally from a student project, kudos to Alexander Gehrlein

Group Theory

Submitted by: Floris van Doorn

lemma group_theory_problem {G H : Type*} [group G] [group H] (f : G →* H)
  (h1 : ∀ a b, a * b * a⁻¹ * b⁻¹ ∈ center G) (h2 : ∀ x ∈ center G, f x = 1 → x = 1) :
    injective f :=
begin
  suffices : ∀ (a : G), f a = 1 → a = 1,
  { rwa [monoid_hom.injective_iff] },
  intros a ha,
  have : a ∈ center G,
  { intro b,
    have : f (a * b * a⁻¹ * b⁻¹) = 1,
    { simp [ha] },
    have : a * b * a⁻¹ * b⁻¹ = 1,
    { refine h2 _ (h1 a b) this },
    rw [eq_comm],
    simpa [mul_inv_eq_iff_eq_mul] using this },
  exact h2 a this ha
end

No group theory in Coq stdlib :(

SAT Solver

Submitted by: Armaël Guéneau

Interval Lists

Submitted by: Fabian Huch

From a course @TUM

Kadane’s Algorithm

Submitted by: Simon Wimmer

Thought of it while working on dynamic programming algorithms.

Had to reformulate for Coq to avoid indices and sets.

Help Wanted

We are looking for:

• organizers
• problem committee members
• problems