Theorems · Theorem · functional analysis
CStarModule.inner_smul_left_real
∀ {A : Type u_1} {E : Type u_2} [inst : NonUnitalRing A] [inst_1 : StarRing A] [inst_2 : AddCommGroup E]
[inst_3 : Module ℂ A] [inst_4 : Module ℂ E] [inst_5 : PartialOrder A] [inst_6 : SMul A E] [inst_7 : Norm A]
[inst_8 : Norm E] [inst_9 : CStarModule A E] [StarModule ℂ A] {z : ℝ} {x y : E}, inner A (z • x) y = z • inner A x y- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
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
- PartialOrderstatement and proof · cited by 6,410
- Complexstatement and proof · cited by 5,565
- StarRingstatement and proof · cited by 1,686
- Complex.ofRealproof · cited by 1,654
- Inner.innerstatement and proof · cited by 1,089
- Star.starproof · cited by 1,082
- StarModulestatement and proof · cited by 570
- Normstatement and proof · cited by 512
- NonUnitalRingstatement and proof · cited by 422
Cited by2
Results whose statement or proof uses this declaration.
- CStarModule.inner_mul_inner_swap_leproof · cited by 1
- CStarModule.norm_eq_csSupproof · cited by 0