compRightL_apply — Mathlib

English

A simple evaluation fact: for any α, i, and v, the i-th component of (Pi.compRightL f) v equals v composed with f at i, i.e., ((Pi.compRightL f) v)(i) = v(f(i)).

Русский

Эта же выпуклая равенность: для любого α, i и v, i-я компонента x := (Pi.compRightL f) v равна v(f(i)).

LaTeX

$$$$ (\Pi.compRightL\; f\; v)(i) = v(f(i)) $$$$

Lean4

@[simp]
theorem _root_.Pi.compRightL_apply {α : Type*} (f : α → ι) (v : (i : ι) → φ i) (i : α) :
    Pi.compRightL R φ f v i = v (f i) :=
  rfl

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