Theorems · Theorem · functional analysis
RCLike.ofReal_eq_re_of_isSelfAdjoint
∀ {K : Type u_1} [inst : RCLike K] {x : K} {y : ℝ}, IsSelfAdjoint x → (y = RCLike.re x ↔ ↑y = x)- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 170 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.
Cites9
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.re_eq_ofReal_of_isSelfAdjointproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- Complex.ofReal_eq_re_of_isSelfAdjointproof · cited by 0