`exp` preserves congruence through degree `n` (on series with zero constant term).
ProvedTypeDensity.SCongr.expSertype-density
exp preserves congruence through degree n (on series with zero constant term).
Preamble
import Definitions.Def_TypeDensity_Basic import Definitions.Def_TypeDensity_Reciprocity_Defs import Definitions.Def_TypeDensity_Reciprocity_Quantum import Theorems.Thm_TypeDensity_scongr_subst 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
Formal statement
theorem TypeDensity.SCongr.expSer {n : ℕ} {f g : Ser} (hf : PowerSeries.constantCoeff f = 0)
(hg : PowerSeries.constantCoeff g = 0) (h : SCongr n f g) :
SCongr n (TypeDensity.expSer f) (TypeDensity.expSer g) := by sorrySource
TypeDensity/Reciprocity/Quantum.lean#L907-L911