Theorems · Theorem · functional analysis
RCLike.re_eq_ofReal_of_isSelfAdjoint
∀ {K : Type u_1} [inst : RCLike K] {x : K} {y : ℝ}, IsSelfAdjoint x → (RCLike.re x = y ↔ x = ↑y)- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 169 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
- IsSelfAdjointstatement and proof · cited by 545
- RCLike.ofRealstatement and proof · cited by 350
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- RCLike.improof · cited by 161
- RCLike.ofReal_reproof · cited by 60
- RCLike.ofReal_improof · cited by 41
- RCLike.ext_iffproof · cited by 13
Cited by2
Results whose statement or proof uses this declaration.
- RCLike.ofReal_eq_re_of_isSelfAdjointproof · cited by 1
- Complex.re_eq_ofReal_of_isSelfAdjointproof · cited by 0