English
The pthRoot map induces an isomorphism; specifically, the coefficient at 0 of the lift equals the original coefficient.
Русский
kotорая вызывает изоморфизм: коэффициент нулевого порядка лифта равен исходному коэффициенту.
LaTeX
$$$\\text{coeff } R p 0 (\\mathrm{lift}~p~P~R~f) = \\text{coeff } R p 0 f$$$
Lean4
/-- The canonical perfection map from the perfection of a ring. -/
theorem of : PerfectionMap p (Perfection.coeff R p 0) :=
mk' (RingEquiv.refl _) <| (Equiv.apply_eq_iff_eq_symm_apply _).2 rfl