Theorems · Theorem · functional analysis
RCLike.conj_eq_iff_im
∀ {K : Type u_1} [inst : RCLike K] {z : K}, (starRingEnd K) z = z ↔ RCLike.im z = 0- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 167 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 and proof · cited by 25,697
- RingHomstatement · cited by 10,189
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- starRingEndstatement and proof · cited by 671
- IsSelfAdjointproof · cited by 545
- RCLike.ofRealproof · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.reproof · cited by 319
- List.TFAE.outproof · cited by 177
- RCLike.imstatement and proof · cited by 161
Cited by4
Results whose statement or proof uses this declaration.
- LinearMap.IsPositive.smul_of_nonnegproof · cited by 2
- RCLike.re_nonneg_of_nonnegproof · cited by 2
- RCLike.re_eq_self_of_leproof · cited by 1
- LinearMap.IsSymmetric.im_inner_apply_selfproof · cited by 1