Theorems · Theorem · complex analysis
Complex.ofReal_tan
∀ (x : ℝ), ↑(Real.tan x) = Complex.tan ↑x
- Defined in
- Mathlib.Analysis.Complex.Trigonometric
- Cited by
- 9 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Complexstatement · cited by 5,565
- Complex.ofRealstatement · cited by 1,654
- Real.tanstatement · cited by 100
- Complex.tanstatement · cited by 77
- Complex.ofReal_tan_ofReal_reproof · cited by 2
Cited by9
Results whose statement or proof uses this declaration.
- Real.tan_eq_sin_div_cosproof · cited by 15
- Real.inv_one_add_tan_sqproof · cited by 4
- Real.tendsto_abs_tan_of_cos_eq_zeroproof · cited by 2
- Real.tan_addproof · cited by 1
- Real.tan_subproof · cited by 1
- Real.tan_inv_eq_cotproof · cited by 0
- Real.isAlgebraic_tan_rat_mul_piproof · cited by 0
- Complex.ofReal_arctanproof · cited by 0
- Real.cot_inv_eq_tanproof · cited by 0