Theorems · Theorem · number theory
Int.coe_negOnePow
∀ (R : Type u_1) [inst : Ring R] (n : ℤ), ↑↑n.negOnePow = (-1) ^ n.natAbs
The cast of negOnePow n to a ring equals (-1) ^ n.natAbs.
- Defined in
- Mathlib.Algebra.Ring.NegOnePow
- Cited by
- 24 results in Mathlib
- Foundations
- Depth 72 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.
Cites9
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
- Units.valstatement and proof · cited by 1,966
- Int.cast_oneproof · cited by 371
- Int.cast_negproof · cited by 224
- Int.negOnePowstatement · cited by 156
- zpow_negSuccproof · cited by 92
- Int.cast_powproof · cited by 59
- Int.units_inv_eq_selfproof · cited by 5
- Int.cast_negOnePow_natCastproof · cited by 5
Cited by24
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.T_eval_negproof · cited by 4
- Polynomial.Chebyshev.U_eval_zeroproof · cited by 2
- PowerSeries.WithPiTopology.hasSum_pentagonalSeriesproof · cited by 2
- Polynomial.zero_lt_negOnePow_mul_eval_of_lt_roots_of_leadingCoeff_nonnegproof · cited by 2
- Polynomial.Chebyshev.T_eval_zeroproof · cited by 2
- Complex.one_div_one_sub_cpow_hasFPowerSeriesOnBall_zeroproof · cited by 2
- Polynomial.Chebyshev.one_lt_abs_eval_T_realproof · cited by 1
- Polynomial.Chebyshev.U_eval_zero_of_evenproof · cited by 1
- Polynomial.Chebyshev.sumZeroes_T_of_not_dvdproof · cited by 1
- PowerSeries.WithPiTopology.hasSum_pow_pentagonal_sub_pentagonalSeriesproof · cited by 1
- PowerSeries.coeff_pentagonalSeries_pentagonalproof · cited by 1
- Polynomial.Chebyshev.T_eval_zero_of_evenproof · cited by 1