Theorems · Theorem · commutative algebra
Ring.multichoose_succ_succ
∀ {R : Type u_2} [inst : NonAssocSemiring R] [inst_1 : Pow R ℕ] [NatPowAssoc R] [inst_3 : BinomialRing R] (r : R)
(k : ℕ), Ring.multichoose (r + 1) (k + 1) = Ring.multichoose r (k + 1) + Ring.multichoose (r + 1) k- Defined in
- Mathlib.RingTheory.Binomial
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 115 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.
- add_commproof · cited by 1,535
- NonAssocSemiringstatement and proof · cited by 805
- Nat.factorialproof · cited by 616
- smul_addproof · cited by 263
- ascPochhammerproof · cited by 80
- Polynomial.smevalproof · cited by 65
- 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
Cited by2
Results whose statement or proof uses this declaration.
- Ring.multichoose_oneproof · cited by 1
- Ring.multichoose_twoproof · cited by 0