Theorems · Theorem · functional analysis
CStarModule.inner_smul_left_complex
∀ {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 : ℂ} {x y : E},
inner A (z • x) y = star z • inner A x y- Cited by
- 2 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- 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
- Inner.innerstatement and proof · cited by 1,089
- Star.starstatement and proof · cited by 1,082
- starRingEndproof · cited by 671
- 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.normedSpaceCoreproof · cited by 1
- CStarModule.inner_smul_right_realproof · cited by 1