. intro h Γ hΓ;
  by_contra hC;
  have : L ⊬! p ⋏ List.conj' Γ ⟶ ⊥ := implyLeft_cons_conj'!.not.mp $ @h (p :: Γ) (by
    rintro q hq;
    simp at hq;
    cases hq with
    | inl h => subst h; simp;
    | inr h => simp; right; exact hΓ q h;
  );
  contradiction;
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
⊢ (L)-Consistent insert p T → ∀ {Γ : List (Formula α)}, (∀ q ∈ Γ, q ∈ T) → L ⊬! p ⋏ Γ.conj' ⟶ ⊥

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
⊢ (∀ {Γ : List (Formula α)}, (∀ q ∈ Γ, q ∈ T) → L ⊬! p ⋏ Γ.conj' ⟶ ⊥) → (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
⊢ (∀ {Γ : List (Formula α)}, (∀ q ∈ Γ, q ∈ T) → L ⊬! p ⋏ Γ.conj' ⟶ ⊥) → (L)-Consistent insert p T