Theorems · Theorem · functional analysis
cfc_re_id
∀ {A : Type u_1} [inst : TopologicalSpace A] [inst_1 : Ring A] [inst_2 : StarRing A] [inst_3 : Algebra ℂ A]
[inst_4 : StarModule ℂ A] [inst_5 : ContinuousFunctionalCalculus ℂ A IsStarNormal] (a : A),
autoParam (IsStarNormal a) cfc_re_id._auto_1 → cfc (fun x => ↑x.re) a = ↑(realPart a)- Cited by
- 4 results in Mathlib
- Foundations
- Depth 169 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
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
- TopologicalSpacestatement and proof · cited by 24,529
- RingHom.idstatement · cited by 18,349
- Algebrastatement and proof · cited by 11,388
- LinearMapstatement · cited by 10,215
- Ringstatement and proof · cited by 7,463
- Complexstatement and proof · cited by 5,565
- mul_oneproof · cited by 3,885
- AddSubgroupstatement · cited by 3,232
- StarRingstatement and proof · cited by 1,686
- Complex.ofRealstatement and proof · cited by 1,654
Cited by4
Results whose statement or proof uses this declaration.
- cfc_im_idproof · cited by 3
- spectrum_realPartproof · cited by 2
- cfc_realPartproof · cited by 0
- cfc_comp_reproof · cited by 0