lTensor_smul_action — Mathlib

English

The map map f g interacts with rTensor: map f g (f'.rTensor x) = map (f ∘ f') g x for suitable x.

Русский

Отображение map f g взаимодействует с rTensor: map f g (f'.rTensor x) = map (f ∘ f') g x.

LaTeX

$$$\text{map } f\, g\ (f'.\mathrm{rTensor}\ _\ x) = \text{map } (f \circ f')\, g\ x$$$

Lean4

@[simp]
theorem lTensor_smul_action (r : R) :
    (DistribMulAction.toLinearMap R N r).lTensor M = DistribMulAction.toLinearMap R (M ⊗[R] N) r :=
  (lTensor_smul M r LinearMap.id).trans (congrArg _ (lTensor_id M N))

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