Theorems · Theorem · functional analysis
Submodule.reflection_sub
∀ {F : Type u_3} [inst : NormedAddCommGroup F] [inst_1 : InnerProductSpace ℝ F] {v w : F},
‖v‖ = ‖w‖ → (ℝ ∙ (v - w))ᗮ.reflection v = w- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- RingHom.idstatement and proof · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- Submodulestatement · cited by 7,192
- Norm.normstatement and proof · cited by 5,413
- InnerProductSpacestatement and proof · cited by 3,523
- Submodule.spanstatement and proof · cited by 1,504
- map_addproof · cited by 964
- LinearIsometryEquivstatement and proof · cited by 748
- map_subproof · cited by 565
Cited by1
Results whose statement or proof uses this declaration.
- LinearIsometryEquiv.reflections_generate_dim_auxproof · cited by 1