lift_comp_lift — Mathlib

English

Lifting along i and then j is the same as lifting along the composite i then k: lift j k p ∘ lift i j p = lift i k p.

Русский

Подъём по i затем j равен подъёму по композиции i∘k: lift j k p ∘ lift i j p = lift i k p.

LaTeX

$$$ (\mathrm{lift}\, j\, k\, p) \circ (\mathrm{lift}\, i\, j\, p) = \mathrm{lift}\, i\, k\, p $$$

Lean4

@[simp]
theorem lift_comp_lift : (lift j k p).comp (lift i j p) = lift i k p :=
  IsPRadical.injective_comp_of_perfect _ i p (by ext; simp)

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