intro h₁ hm₁ h₂ hm₂
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐏𝐀⁻
k n✝ : ℕ
c : Code (n✝ + 1)
ih :
  ∀ {v : Fin (n✝ + 1) → M} {z z' : M},
    (Semiformula.Evalfm M (z :> v)) (codeAux c) → (Semiformula.Evalfm M (z' :> v)) (codeAux c) → z = z'
v : Fin n✝ → M
z z' : M
⊢ (Semiformula.Eval (standardModel M) ![] (Semiterm.Operator.val (goedelNumber 0) ![] :> fun i => (z :> v) i))
      (codeAux c) →
    (∀ x < z, ∃ x_1, ¬x_1 = 0 ∧ (Semiformula.Eval (standardModel M) ![] (x_1 :> x :> fun i => v i)) (codeAux c)) →
      (Semiformula.Eval (standardModel M) ![] (Semiterm.Operator.val (goedelNumber 0) ![] :> fun i => (z' :> v) i))
          (codeAux c) →
        (∀ x < z', ∃ x_1, ¬x_1 = 0 ∧ (Semiformula.Eval (standardModel M) ![] (x_1 :> x :> fun i => v i)) (codeAux c)) →
          z = z'
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐏𝐀⁻
k n✝ : ℕ
c : Code (n✝ + 1)
ih :
  ∀ {v : Fin (n✝ + 1) → M} {z z' : M},
    (Semiformula.Evalfm M (z :> v)) (codeAux c) → (Semiformula.Evalfm M (z' :> v)) (codeAux c) → z = z'
v : Fin n✝ → M
z z' : M
h₁ :
  (Semiformula.Eval (standardModel M) ![] (Semiterm.Operator.val (goedelNumber 0) ![] :> fun i => (z :> v) i))
    (codeAux c)
hm₁ : ∀ x < z, ∃ x_1, ¬x_1 = 0 ∧ (Semiformula.Eval (standardModel M) ![] (x_1 :> x :> fun i => v i)) (codeAux c)
h₂ :
  (Semiformula.Eval (standardModel M) ![] (Semiterm.Operator.val (goedelNumber 0) ![] :> fun i => (z' :> v) i))
    (codeAux c)
hm₂ : ∀ x < z', ∃ x_1, ¬x_1 = 0 ∧ (Semiformula.Eval (standardModel M) ![] (x_1 :> x :> fun i => v i)) (codeAux c)
⊢ z = z'