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Theorems · Theorem · functional analysis

Submodule.orthogonalProjectionFn.congr_simp

∀ {𝕜 : Type u_1} {E : Type u_2} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E] [inst_2 : InnerProductSpace 𝕜 E]
  {K K_1 : Submodule 𝕜 E} (e_K : K = K_1) [inst_3 : K.HasOrthogonalProjection] (x x_1 : E),
  x = x_1 → Submodule.orthogonalProjectionFn x = Submodule.orthogonalProjectionFn x_1
Defined in
Mathlib.Analysis.InnerProductSpace.Projection.Basic
Cited by
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Foundations
Depth 178 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RCLikeNormedAddCommGroupInnerProductSpaceSubmodule.HasOrthogonalProjection
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NormedAddCommGroup · cited by 15752NormedAddCommGroupSubmodule · cited by 7192SubmoduleInnerProductSpace · cited by 3523InnerProductSpaceRCLike · cited by 2829RCLikeSubmodule.HasOrthogonalProjection · cited by 245Submodule.HasOrthogonalPr…Submodule.orthogonalProjectionFn · cited by 3Submodule.orthogonalProje…orthogonalProjectionFn.congr_…CITED BYCITES

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