Theorems · Theorem · combinatorics
Nat.succ_mul_binomial
∀ {α : Type u_1} {f : α → ℕ} {a b : α} [inst : DecidableEq α],
a ≠ b →
(f a + f b).succ * Nat.multinomial {a, b} f = (f a).succ * Nat.multinomial {a, b} (Function.update f a (f a).succ)- Defined in
- Mathlib.Data.Nat.Choose.Multinomial
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- mul_commproof · cited by 2,262
- Function.updatestatement and proof · cited by 502
- Nat.chooseproof · cited by 494
- Function.update_selfproof · cited by 201
- Function.update_of_neproof · cited by 198
- Nat.multinomialstatement and proof · cited by 34
- Nat.add_one_mul_choose_eqproof · cited by 7
- Nat.binomial_eq_chooseproof · cited by 3
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