Theorems · Theorem · functional analysis
RCLike.im_eq_conj_sub
∀ {K : Type u_1} [inst : RCLike K] (z : K), ↑(RCLike.im z) = RCLike.I * ((starRingEnd K) z - z) / 2- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 165 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.
Cites22
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
- map_mulproof · cited by 1,137
- sub_eq_add_negproof · cited by 1,023
- starRingEndstatement and proof · cited by 671
- neg_mulproof · cited by 654
- mul_negproof · cited by 590
- RCLike.ofRealstatement and proof · cited by 350
- AddMonoid.toZerostatement · cited by 325
Cited by3
Results whose statement or proof uses this declaration.
- RCLike.is_real_TFAEproof · cited by 5
- InnerProductSpace.Core.inner_self_improof · cited by 3
- inner_self_improof · cited by 2