Theorems · Theorem · complex analysis
Real.cos_neg
∀ (x : ℝ), Real.cos (-x) = Real.cos x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 27 results in Mathlib
- Foundations
- Depth 148 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- Complex.ofRealproof · cited by 1,654
- Complex.reproof · cited by 882
- Real.cosstatement · cited by 424
- Complex.cosproof · cited by 279
- Complex.ofReal_negproof · cited by 130
- Complex.cos_negproof · cited by 17
Cited by27
Results whose statement or proof uses this declaration.
- Real.cos_pi_div_two_subproof · cited by 8
- Real.sin_pi_div_two_subproof · cited by 6
- Real.sin_eq_zero_iffproof · cited by 5
- Complex.sin_argproof · cited by 4
- Real.cos_absproof · cited by 4
- Real.cos_pi_subproof · cited by 4
- Real.cos_arcsinproof · cited by 4
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- Complex.arg_of_im_negproof · cited by 3
- Real.cos_sub_pi_div_twoproof · cited by 3
- Real.cos_nat_mul_pi_subproof · cited by 2
- Real.cos_subproof · cited by 2