subtype_compMultilinearMap_codRestrict

English

If a renaming σ of indices is applied to the domain, the composition commutes with this domain renaming: (g.compMultilinearMap f).domDomCongr σ = g.compMultilinearMap (f.domDomCongr σ).

Русский

При перестановке индексов в домене композиция commute-ится с этой перестановкой: (g.compMultilinearMap f).domDomCongr σ = g.compMultilinearMap (f.domDomCongr σ).

LaTeX

$$$$ (g \circMultilinearMap f).domDomCongr \sigma = g.compMultilinearMap (f.domDomCongr σ). $$$$

Lean4

/-- The multilinear version of `LinearMap.subtype_comp_codRestrict` -/
@[simp]
theorem subtype_compMultilinearMap_codRestrict (f : MultilinearMap R M₁ M₂) (p : Submodule R M₂) (h) :
    p.subtype.compMultilinearMap (f.codRestrict p h) = f :=
  rfl

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