Theorems · Theorem · commutative algebra
Ring.add_choose_eq
∀ {R : Type u_1} [inst : Ring R] [inst_1 : BinomialRing R] {r s : R} (k : ℕ),
Commute r s →
Ring.choose (r + s) k = ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal k, Ring.choose r ij.1 * Ring.choose s ij.2The Chu-Vandermonde identity for binomial rings
- Defined in
- Mathlib.RingTheory.Binomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 115 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RingBinomialRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- Finset.sumstatement and proof · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- mul_assocproof · cited by 1,667
- Commutestatement and proof · cited by 639
- Nat.factorialproof · cited by 616
- Nat.chooseproof · cited by 494
- nsmul_eq_mulproof · cited by 369
- Nat.cast_mulproof · cited by 309
- Finset.HasAntidiagonal.antidiagonalstatement and proof · cited by 218
- Finset.smul_sumproof · cited by 88
- Polynomial.smevalproof · cited by 65
Cited by1
Results whose statement or proof uses this declaration.
- PowerSeries.binomialSeries_addproof · cited by 1