Theorems · Theorem · functional analysis
RCLike.re_ofReal_mul
∀ {K : Type u_1} [inst : RCLike K] (r : ℝ) (z : K), RCLike.re (↑r * z) = r * RCLike.re z- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 160 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.
Cites13
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
- MulZeroClass.zero_mulproof · cited by 1,625
- sub_zeroproof · cited by 938
- 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
Cited by10
Results whose statement or proof uses this declaration.
- RCLike.smul_reproof · cited by 4
- RCLike.inv_reproof · cited by 3
- InnerProductSpace.Core.inner_mul_inner_self_leproof · cited by 2
- RCLike.re_mul_ofRealproof · cited by 1
- ContinuousLinearMap.opNorm_le_of_re_inner_leproof · cited by 1
- InnerProductSpace.Core.cauchy_schwarz_aux'proof · cited by 1
- RCLike.ofReal_mul_pos_iffproof · cited by 1
- ContinuousLinearMap.IsPositive.spectrumRestrictsproof · cited by 0
- RCLike.div_re_ofRealproof · cited by 0
- RCLike.ofNat_mul_reproof · cited by 0