lTensor_comp — Mathlib

English

Left-tensoring commutes with composition: (g ∘ f).lTensor M = (g.lTensor M) ∘ (f.lTensor M).

Русский

Левотензорирование commute с композициeй: (g ∘ f).lTensor M = (g.lTensor M) ∘ (f.lTensor M).

LaTeX

$$$ (g \circ f).lTensor M = (g.lTensor M) \circ (f.lTensor M) $$$

Lean4

theorem lTensor_comp : (g.comp f).lTensor M = (g.lTensor M).comp (f.lTensor M) :=
  by
  ext m n
  simp only [compr₂_apply, mk_apply, comp_apply, lTensor_tmul]

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