Theorems · Definition · complex analysis
RCLike.complexRingEquiv
{𝕜 : Type u_2} → [inst : RCLike 𝕜] → RCLike.im RCLike.I = 1 → 𝕜 ≃+* ℂThe natural isomorphism between 𝕜 satisfying RCLike 𝕜 and ℂ when
RCLike.im RCLike.I = 1.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 161 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.
Cites15
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 and proof · cited by 5,565
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- Complex.ofRealproof · cited by 1,654
- RingEquivstatement · cited by 1,147
- Complex.reproof · cited by 882
- Complex.Iproof · cited by 866
- Complex.improof · cited by 591
- RCLike.ofRealproof · cited by 350
- AddMonoid.toZerostatement · cited by 325
Cited by11
Results whose statement or proof uses this declaration.
- RCLike.complexRingEquiv_applystatement and proof · cited by 5
- RCLike.complexLinearIsometryEquivproof · cited by 4
- RCLike.sqrt_eq_itestatement and proof · cited by 4
- RCLike.sqrt_neg_of_nonnegproof · cited by 1
- RCLike.sqrt_of_nonnegproof · cited by 1
- RCLike.complexRingEquiv_symm_applystatement and proof · cited by 1
- RCLike.sqrt_neg_Iproof · cited by 0
- RCLike.complexRingEquiv.congr_simpstatement and proof · cited by 0
- RCLike.complexLinearIsometryEquiv_applystatement · cited by 0
- RCLike.complexLinearIsometryEquiv_symm_applystatement · cited by 0
- RCLike.sqrt_Iproof · cited by 0