Theorems · Theorem · number theory
Int.cast_negOnePow_natCast
∀ (R : Type u_1) [inst : Ring R] (n : ℕ), ↑↑(↑n).negOnePow = (-1) ^ n
- Defined in
- Mathlib.Algebra.Ring.NegOnePow
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Ring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Ringstatement and proof · cited by 7,463
- mul_oneproof · cited by 3,885
- Nat.cast_oneproof · cited by 2,501
- Units.valstatement and proof · cited by 1,966
- pow_zeroproof · cited by 1,094
- neg_negproof · cited by 960
- mul_negproof · cited by 590
- Nat.cast_addproof · cited by 586
- one_powproof · cited by 521
- pow_succproof · cited by 374
- Int.cast_oneproof · cited by 371
- Nat.cast_mulproof · cited by 309
Cited by5
Results whose statement or proof uses this declaration.
- Int.coe_negOnePowproof · cited by 24
- Polynomial.Chebyshev.eval_T_real_eq_neg_one_iffproof · cited by 3
- Polynomial.Chebyshev.eval_T_real_eq_one_iffproof · cited by 3
- Int.coe_negOnePow_natCastproof · cited by 0
- PowerSeries.rescale_neg_one_invOneSubPowproof · cited by 0