Theorems · Theorem · combinatorics
Nat.cast_choose_two
∀ (K : Type u_1) [inst : DivisionRing K] [NeZero 2] (a : ℕ), ↑(a.choose 2) = ↑a * (↑a - 1) / 2
- Defined in
- Mathlib.Data.Nat.Choose.Cast
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRingNeZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- DivisionRingstatement and proof · cited by 1,062
- Nat.choosestatement and proof · cited by 494
- Nat.cast_mulproof · cited by 309
- two_ne_zeroproof · cited by 251
- Nat.cast_twoproof · cited by 32
- eq_div_iff_mul_eqproof · cited by 19
- Nat.descFactorial_eq_factorial_mul_chooseproof · cited by 12
- Nat.factorial_twoproof · cited by 6
- Nat.cast_descFactorial_twoproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- SimpleGraph.antitoneOn_extremalNumber_div_choose_twoproof · cited by 3