Theorems · Theorem · functional analysis
RCLike.im_eq_zero_iff_isSelfAdjoint
∀ {K : Type u_1} [inst : RCLike K] {x : K}, RCLike.im x = 0 ↔ IsSelfAdjoint x- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 1 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.
Cites12
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
- AddMonoidHomstatement · cited by 3,230
- RCLikestatement and proof · cited by 2,829
- starRingEndproof · cited by 671
- IsSelfAdjointstatement and proof · 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
- RCLike.is_real_TFAEproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- Complex.im_eq_zero_iff_isSelfAdjointproof · cited by 0