Theorems · Theorem · field theory
Int.cast_negOnePow
∀ (K : Type u_1) (n : ℤ) [inst : DivisionRing K], ↑↑n.negOnePow = (-1) ^ n
- Defined in
- Mathlib.Algebra.Field.NegOnePow
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_oneproof · cited by 3,885
- Units.valstatement and proof · cited by 1,966
- DivisionRingstatement and proof · cited by 1,062
- mul_negproof · cited by 590
- one_powproof · cited by 521
- Int.cast_oneproof · cited by 371
- Int.cast_negproof · cited by 224
- Int.negOnePowstatement and proof · cited by 156
- zpow_ofNatproof · cited by 144
- Even.neg_powproof · cited by 99
- one_zpowproof · cited by 44
- zpow_mulproof · cited by 27
Cited by10
Results whose statement or proof uses this declaration.
- Polynomial.Chebyshev.eval_T_real_cos_int_mul_pi_divproof · cited by 2
- Real.cos_add_int_mul_piproof · cited by 1
- Real.cos_sub_int_mul_piproof · cited by 1
- Polynomial.Chebyshev.sumZeroes_T_of_not_dvdproof · cited by 1
- Polynomial.Chebyshev.one_le_negOnePow_mul_eval_T_realproof · cited by 0
- Real.sin_sub_int_mul_piproof · cited by 0
- Polynomial.Chebyshev.one_lt_negOnePow_mul_eval_T_realproof · cited by 0
- Real.sin_add_int_mul_piproof · cited by 0
- Real.sin_int_mul_pi_subproof · cited by 0
- Real.cos_int_mul_pi_subproof · cited by 0