The Adams substitution commutes with `q ↦ q⁻¹`.

import Definitions.Def_TypeDensity_Basic
import Definitions.Def_TypeDensity_Reciprocity_Defs
import Theorems.Thm_TypeDensity_recipRat_algebraMap
import Theorems.Thm_TypeDensity_adamsRat_X
import Theorems.Thm_TypeDensity_recipRat_X
import Mathlib.FieldTheory.RatFunc.Basic
import Mathlib.MeasureTheory.Measure.Haar.Unique
import Mathlib.NumberTheory.ArithmeticFunction.Moebius
import Mathlib.NumberTheory.Padics.PadicIntegers
import Mathlib.RingTheory.IntegralClosure.IntegralRestrict
import Mathlib.RingTheory.MvPowerSeries.Basic
import Mathlib.RingTheory.RamificationInertia.Basic
import Mathlib.Topology.Algebra.Nonarchimedean.AdicTopology
import Mathlib.FieldTheory.RatFunc.AsPolynomial
import Mathlib.RingTheory.PowerSeries.Expand
import Mathlib.RingTheory.PowerSeries.Log
set_option autoImplicit false

open TypeDensity

theorem TypeDensity.adamsRat_recipRat (δ : ℕ) (hδ : 0 < δ) (f : RatFunc ℚ) :
    adamsRat δ (recipRat f) = recipRat (adamsRat δ f) := by sorry