Theorems · Theorem · functional analysis
Submodule.reflection_mem_subspace_eq_self
∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
{K : Submodule 𝕜 E} [inst_3 : K.HasOrthogonalProjection] {x : E}, x ∈ K → K.reflection x = x- Cited by
- 4 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, 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
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement and proof · cited by 7,192
- InnerProductSpacestatement and proof · cited by 3,523
- RCLikestatement and proof · cited by 2,829
- LinearIsometryEquivstatement · cited by 748
- Submodule.HasOrthogonalProjectionstatement and proof · cited by 245
- Submodule.reflectionstatement · cited by 31
- Submodule.reflection_eq_self_iffproof · cited by 3
Cited by4
Results whose statement or proof uses this declaration.
- Submodule.det_reflectionproof · cited by 1
- Submodule.reflection_subproof · cited by 1
- LinearIsometryEquiv.reflections_generate_dim_auxproof · cited by 1
- EuclideanGeometry.hasFDerivAt_inversionproof · cited by 0