Theorems · Theorem · complex analysis
Complex.sin_neg
∀ (x : ℂ), Complex.sin (-x) = -Complex.sin x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Complexstatement and proof · cited by 5,565
- sub_eq_add_negproof · cited by 1,023
- neg_negproof · cited by 960
- Complex.Iproof · cited by 866
- neg_mulproof · cited by 654
- Complex.expproof · cited by 612
- add_mulproof · cited by 363
- Complex.sinstatement · cited by 258
- neg_add_revproof · cited by 236
- DivisionMonoidproof · cited by 201
- neg_divproof · cited by 161
- HasDistribNegproof · cited by 114
Cited by17
Results whose statement or proof uses this declaration.
- Real.sin_negproof · cited by 34
- Complex.tan_negproof · cited by 5
- Complex.cos_sub_pi_div_twoproof · cited by 4
- Complex.Gamma_mul_Gamma_one_subproof · cited by 3
- Complex.sin_add_sinproof · cited by 2
- Complex.cos_subproof · cited by 2
- Complex.sin_pi_div_two_subproof · cited by 2
- Complex.arctan_tanproof · cited by 1
- Complex.exp_neg_pi_div_two_mul_Iproof · cited by 1
- Complex.arg_eq_neg_pi_div_two_iffproof · cited by 1
- Complex.sin_subproof · cited by 1
- integral_exp_mul_I_eq_sinproof · cited by 1