Theorems · Theorem · functional analysis
Submodule.reflection_trans_reflection
∀ {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],
K.reflection.trans K.reflection = LinearIsometryEquiv.refl 𝕜 EReflection is involutive.
- Cited by
- 1 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- LinearIsometryEquiv.transstatement · cited by 45
- LinearIsometryEquiv.extproof · cited by 35
- Submodule.reflectionstatement · cited by 31
- LinearIsometryEquiv.reflstatement · cited by 23
- Submodule.reflection_involutiveproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- Submodule.reflection_mul_reflectionproof · cited by 1