Mathlib Map

Theorems · Definition · functional analysis

PreInnerProductSpace.Core.toInner

{𝕜 : Type u_4} →
  {F : Type u_5} →
    [inst : RCLike 𝕜] → [inst_1 : AddCommGroup F] → [inst_2 : Module 𝕜 F] → PreInnerProductSpace.Core 𝕜 F → Inner 𝕜 F
Defined in
Mathlib.Analysis.InnerProductSpace.Defs
Cited by
9 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Quot.sound
Assumes
RCLikeAddCommGroupModule
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

InnerProductSpace.Core.toPreInner' · cited by 32Core.toPreInner'PreInnerProductSpace.Core.re_inner_nonneg · cited by 2Core.re_inner_nonnegInnerProductSpace.Core.toInner' · cited by 2Core.toInner'InnerProductSpace.Core.mk.noConfusion · cited by 1mk.noConfusionPreInnerProductSpace.Core.conj_inner_symm · cited by 1Core.conj_inner_symmPreInnerProductSpace.Core.smul_left · cited by 1Core.smul_leftInnerProductSpace.Core.definite · cited by 1Core.definiteInnerProductSpace.Core.mk.inj · cited by 1mk.injPreInnerProductSpace.Core.add_left · cited by 1Core.add_leftInnerProductSpace.ofCoreOfTopology · cited by 0InnerProductSpace.ofCoreO…InnerProductSpace.Core.casesOn · cited by 0Core.casesOnInnerProductSpace.Core.recOn · cited by 0Core.recOnInnerProductSpace.Core.toNormedAddCommGroupOfTopology · cited by 0Core.toNormedAddCommGroup…InnerProductSpace.Core.toNormedSpaceOfTopology · cited by 0Core.toNormedSpaceOfTopol…InnerProductSpace.Core.mk.injEq · cited by 0mk.injEqModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRCLike · cited by 2829RCLikePreInnerProductSpace.Core · cited by 46PreInnerProductSpace.CoreInner · cited by 14InnerCore.toInnerCITED BYCITES

Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by17

Results whose statement or proof uses this declaration.