Theorems · Theorem · combinatorics
sub_pow
∀ {R : Type u_1} [inst : CommRing R] (x y : R) (n : ℕ),
(x - y) ^ n = ∑ m ∈ Finset.range (n + 1), (-1) ^ (m + n) * x ^ m * y ^ (n - m) * ↑(n.choose m)A special case of the binomial theorem
- Defined in
- Mathlib.Data.Nat.Choose.Sum
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Finset.sumstatement and proof · cited by 5,195
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- sub_eq_add_negproof · cited by 1,023
- one_powproof · cited by 521
- Nat.choosestatement and proof · cited by 494
- pow_addproof · cited by 315
- Finset.mem_rangeproof · cited by 140
- Even.neg_powproof · cited by 99
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