Theorems · Theorem · field theory
Complex.conj_eq_iff_re
∀ {z : ℂ}, (starRingEnd ℂ) z = z ↔ ↑z.re = z- Defined in
- Mathlib.Data.Complex.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Realproof · cited by 25,697
- RingHomstatement · cited by 10,189
- Complexstatement and proof · cited by 5,565
- Complex.ofRealstatement and proof · cited by 1,654
- Complex.restatement and proof · cited by 882
- starRingEndstatement · cited by 671
- Complex.conj_eq_iff_realproof · cited by 1
Cited by12
Results whose statement or proof uses this declaration.
- Complex.Gamma_ofRealproof · cited by 9
- Complex.ofReal_cos_ofReal_reproof · cited by 3
- Complex.ofReal_sin_ofReal_reproof · cited by 3
- Complex.ofReal_exp_ofReal_reproof · cited by 3
- Complex.eq_re_of_ofReal_leproof · cited by 2
- Complex.ofReal_cosh_ofReal_reproof · cited by 2
- isSelfAdjoint_iff_isStarNormal_and_quasispectrumRestrictsproof · cited by 2
- Complex.ofReal_sinh_ofReal_reproof · cited by 2
- Complex.ofReal_tan_ofReal_reproof · cited by 2
- Complex.ofReal_tanh_ofReal_reproof · cited by 2
- Complex.ofReal_cot_ofReal_reproof · cited by 1
- PositiveLinearMap.preGNS_norm_sqproof · cited by 0