. intro h;
  apply iff_insert_notParametricConsistent.mpr;
  obtain ⟨Γ, hΓ₁, hΓ₂⟩ := Context.provable_iff.mp h;
  existsi Γ;
  constructor;
  . exact hΓ₁;
  . apply andImplyIffImplyImply'!.mpr;
    apply imp_swap'!;
    exact imp_trans! (FiniteContext.toDef'! hΓ₂) dni!;
case mp
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
T : Theory α
p : Formula α
⊢ T *⊢[L]! p → ¬(L)-Consistent insert (~p) T

case mpr
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
T : Theory α
p : Formula α
⊢ ¬(L)-Consistent insert (~p) T → T *⊢[L]! p
case mpr
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
T : Theory α
p : Formula α
⊢ ¬(L)-Consistent insert (~p) T → T *⊢[L]! p