lift_comp — Mathlib

English

For x ∈ R and y ∈ M, the equality lift hg (mk'(S, x, y)) = g(x) · (g(y))^{-1} is compatible with the general lift specification.

Русский

Для x ∈ R и y ∈ M равенство lift hg (mk'(S, x, y)) = g(x) · (g(y))^{-1} согласуется с общей спецификацией лифта.

LaTeX

$$$ \\mathrm{lift}\\;hg\\ (mk'\\ S\\ x\\ y) = g(x) \\cdot (g(y))^{-1}. $$$

Lean4

@[simp]
theorem lift_comp : (lift hg).comp (algebraMap R S) = g :=
  RingHom.ext <| (DFunLike.ext_iff (F := MonoidHom _ _)).1 <| (toLocalizationMap M S).lift_comp _

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