-- Module: Mathlib.NumberTheory.LSeries.HurwitzZetaEven
Goal:
e_f :
  WeakFEPair.g
      { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
        f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
        hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
        WeakFEPair ℂ } =
    ofReal ∘ evenKernel 0
e_g :
  WeakFEPair.f
      { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
        f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
        hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
        WeakFEPair ℂ } =
    ofReal ∘ cosKernel 0
e_ε :
  (WeakFEPair.ε
        { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
          f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
          hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
          WeakFEPair ℂ })⁻¹ =
    1
e_f₀ :
  WeakFEPair.g₀
      { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
        f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
        hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
        WeakFEPair ℂ } =
    if Eq (α := UnitAddCircle) 0 0 then 1 else 0
e_g₀ :
  WeakFEPair.f₀
      { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
        f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
        hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
        WeakFEPair ℂ } =
    1
⊢ {
      f :=
        WeakFEPair.g
          { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
            f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
            hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
            WeakFEPair ℂ },
      g :=
        WeakFEPair.f
          { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
            f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
            hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
            WeakFEPair ℂ },
      k :=
        WeakFEPair.k
          { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
            f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
            hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
            WeakFEPair ℂ },
      ε :=
        (WeakFEPair.ε
            { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
              f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
              hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
              WeakFEPair ℂ })⁻¹,
      f₀ :=
        WeakFEPair.g₀
          { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
            f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
            hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
            WeakFEPair ℂ },
      g₀ :=
        WeakFEPair.f₀
          { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
            f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
            hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ :
            WeakFEPair ℂ },
      hf_int := ⋯, hg_int := ⋯, hk := ⋯, hε := ⋯, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ : WeakFEPair ℂ } =
    { f := ofReal ∘ evenKernel 0, g := ofReal ∘ cosKernel 0, k := 1 / 2, ε := 1,
      f₀ := if Eq (α := UnitAddCircle) 0 0 then 1 else 0, g₀ := 1, hf_int := ⋯, hg_int := ⋯,
      hk := hurwitzEvenFEPair._proof_7, hε := hurwitzEvenFEPair._proof_8, h_feq := ⋯, hf_top := ⋯, hg_top := ⋯ }

Tactic:
congr 1