Theorems · Theorem · complex analysis
RCLike.complexRingEquiv_apply
∀ {𝕜 : Type u_2} [inst : RCLike 𝕜] (h : RCLike.im RCLike.I = 1) (x : 𝕜),
(RCLike.complexRingEquiv h) x = ↑(RCLike.re x) + ↑(RCLike.im x) * Complex.I- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- RCLike
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Realstatement · cited by 25,697
- Complexstatement · cited by 5,565
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Complex.ofRealstatement · cited by 1,654
- RingEquivstatement · cited by 1,147
- Complex.Istatement · cited by 866
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement · cited by 319
- RCLike.imstatement and proof · cited by 161
- RCLike.Istatement and proof · cited by 100
Cited by5
Results whose statement or proof uses this declaration.
- RCLike.sqrt_eq_iteproof · cited by 4
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- RCLike.sqrt_of_nonnegproof · cited by 1
- RCLike.sqrt_neg_Iproof · cited by 0
- RCLike.sqrt_Iproof · cited by 0