Theorems · Theorem · complex analysis
Real.cos_abs
∀ (x : ℝ), Real.cos |x| = Real.cos x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 149 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
- absstatement · cited by 1,814
- Real.cosstatement and proof · cited by 424
- le_totalproof · cited by 294
- abs_of_nonnegproof · cited by 279
- abs_of_nonposproof · cited by 53
- Real.cos_negproof · cited by 27
Cited by4
Results whose statement or proof uses this declaration.
- Complex.angle_eq_abs_argproof · cited by 4
- selfAdjoint.norm_sq_expUnitary_sub_oneproof · cited by 3
- Real.Angle.cos_nonneg_iff_abs_toReal_le_pi_div_twoproof · cited by 3
- Complex.norm_exp_mul_exp_add_exp_neg_le_of_abs_im_leproof · cited by 1