Theorems · Theorem · functional analysis
InnerProductSpace.Core.inner_conj_symm
∀ {𝕜 : Type u_1} {F : Type u_3} [inst : RCLike 𝕜] [inst_1 : AddCommGroup F] [inst_2 : Module 𝕜 F]
[c : PreInnerProductSpace.Core 𝕜 F] (x y : F), (starRingEnd 𝕜) (inner 𝕜 y x) = inner 𝕜 x y- Defined in
- Mathlib.Analysis.InnerProductSpace.Defs
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 48 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Modulestatement and proof · cited by 20,661
- AddCommGroupstatement and proof · cited by 12,871
- RingHomstatement · cited by 10,189
- RCLikestatement and proof · cited by 2,829
- Inner.innerstatement · cited by 1,089
- starRingEndstatement · cited by 671
- PreInnerProductSpace.Corestatement and proof · cited by 46
- InnerProductSpace.Core.toPreInner'statement · cited by 32
- PreInnerProductSpace.Core.conj_inner_symmproof · cited by 1
Cited by10
Results whose statement or proof uses this declaration.
- InnerProductSpace.Core.inner_self_improof · cited by 3
- InnerProductSpace.Core.inner_smul_rightproof · cited by 3
- InnerProductSpace.Core.inner_add_rightproof · cited by 2
- InnerProductSpace.Core.norm_inner_symmproof · cited by 2
- InnerProductSpace.Core.cauchy_schwarz_auxproof · cited by 1
- InnerProductSpace.Core.inner_neg_rightproof · cited by 1
- InnerProductSpace.Core.inner_re_symmproof · cited by 1
- InnerProductSpace.Core.inner_zero_rightproof · cited by 0
- InnerProductSpace.Core.inner_im_symmproof · cited by 0
- InnerProductSpace.Core.inner_mul_symm_re_eq_normproof · cited by 0