Theorems · Theorem · functional analysis
RCLike.smul_re
∀ {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
- 4 results in Mathlib
- Foundations
- Depth 161 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.
Cites8
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
- AddMonoid.toZerostatement · cited by 325
- RCLike.restatement and proof · cited by 319
- RCLike.re_ofReal_mulproof · cited by 10
- RCLike.real_smul_eq_coe_mulproof · cited by 8
Cited by6
Results whose statement or proof uses this declaration.
- RCLike.reLmproof · cited by 6
- ConvexOn.exists_affine_le_of_ltproof · cited by 4
- LinearMap.IsPositive.nonneg_eigenvaluesproof · cited by 3
- RCLike.conj_smulproof · cited by 2
- RCLike.realLinearIsometryEquivproof · cited by 2
- Matrix.IsHermitian.eigenvalues_eqproof · cited by 1