Theorems · Theorem · field theory
Complex.ofReal_add
∀ (r s : ℝ), ↑(r + s) = ↑r + ↑s
- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 94 results in Mathlib
- Foundations
- Depth 95 from the axioms, rests on 1,754 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- add_zeroproof · cited by 2,707
- Complex.ofRealstatement · cited by 1,654
- Complex.ext_iffproof · cited by 20
Cited by95
Results whose statement or proof uses this declaration.
- Real.exp_addproof · cited by 39
- Complex.ofRealHomproof · cited by 21
- Real.Gamma_add_oneproof · cited by 13
- Real.sin_addproof · cited by 12
- Real.sin_sq_add_cos_sqproof · cited by 12
- Real.cos_addproof · cited by 8
- periodic_circleMapproof · cited by 7
- Complex.arg_mem_Iocproof · cited by 6
- Complex.arg_mul_coe_angleproof · cited by 6
- Real.Gamma_nat_eq_factorialproof · cited by 5
- ProbabilityTheory.IndepFun.hasGaussianLawproof · cited by 4
- Real.inv_one_add_tan_sqproof · cited by 4