Theorems · Theorem · commutative algebra
Ring.multichoose_succ_neg_natCast
∀ {R : Type u_1} [inst : NonAssocRing R] [inst_1 : Pow R ℕ] [inst_2 : BinomialRing R] [NatPowAssoc R] (n : ℕ),
Ring.multichoose (-↑n) (n + 1) = 0- Defined in
- Mathlib.RingTheory.Binomial
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- smul_zeroproof · cited by 665
- Nat.factorialproof · cited by 616
- NonAssocRingstatement and proof · cited by 483
- Int.cast_zeroproof · cited by 188
- ascPochhammerproof · cited by 80
- Nat.factorial_ne_zeroproof · cited by 56
- NatPowAssocstatement and proof · cited by 53
- BinomialRingstatement and proof · cited by 46
- Ring.multichoosestatement and proof · cited by 25
- nsmul_right_injproof · cited by 21
- Ring.factorial_nsmul_multichoose_eq_ascPochhammerproof · cited by 12
- Ring.smeval_ascPochhammer_succ_negproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Ring.choose_zero_succproof · cited by 1