Theorems · Theorem · functional analysis
RCLike.real_smul_eq_coe_smul
∀ {K : Type u_1} {E : Type u_2} [inst : RCLike K] [inst_1 : AddCommGroup E] [inst_2 : Module K E] [inst_3 : Module ℝ E]
[IsScalarTower ℝ K E] (r : ℝ) (x : E), r • x = ↑r • x- Defined in
- Mathlib.Analysis.RCLike.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Realstatement and proof · cited by 25,697
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- IsScalarTowerstatement and proof · cited by 3,896
- RCLikestatement and proof · cited by 2,829
- RCLike.ofRealstatement · cited by 350
- smul_one_smulproof · cited by 43
- RCLike.ofReal_algproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Matrix.IsHermitian.mulVec_eigenvectorBasisproof · cited by 3
- Matrix.IsHermitian.conjStarAlgAut_star_eigenvectorUnitaryproof · cited by 1
- CFC.abs_smulproof · cited by 1
- gauge_norm_smulproof · cited by 1
- SchwartzMap.smulLeftCLM_real_smulproof · cited by 0