Inequalities · medium

Statement, exactly as the model and Lean see it

theorem lg_target {ι : Type u_1} [DecidableEq ι] {s : Finset ι} (n : ℕ) : (s.finsuppAntidiag n).card = s.card.multichoose n := by

Mathlib declaration: Finset.card_finsuppAntidiag_nat_eq_multichoose
Held-out module: Mathlib.Algebra.Order.Antidiag.FinsuppEquiv
Banned modules (itself + downstream): 1
Reference proof premises (reachable / held-out): 3 / 0

Traces

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No configuration has attempted this theorem yet.

Reference proof

Mathlib's own source for this declaration, shown for comparison. It may use lemmas the prover is not allowed to use.

theorem card_finsuppAntidiag_nat_eq_multichoose (n : ℕ) :
    #(s.finsuppAntidiag n) = (#s).multichoose n := by
  simp [card_eq_of_equiv_fintype (finsuppAntidiagEquiv s n), Sym.card_sym_eq_multichoose]