all_goals
  tauto
case pred_const_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders

case pred_var_
v u : VarName
a✝¹ : PredName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders

case eq_
v u a✝¹ a✝ : VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : (v = a✝¹ ∨ v = a✝) ∧ v ∉ binders → u ∉ binders
⊢ v = a✝¹ ∨ v = a✝ → u ∉ binders

case not_
v u : VarName
a✝ : Formula
a_ih✝ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝ → fastAdmitsAux v u binders a✝
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders a✝
⊢ fastAdmitsAux v u binders a✝

case imp_
v u : VarName
a✝¹ a✝ : Formula
a_ih✝¹ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝¹ → fastAdmitsAux v u binders a✝¹
a_ih✝ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝ → fastAdmitsAux v u binders a✝
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders a✝¹ ∧ admitsAux v u binders a✝
⊢ fastAdmitsAux v u binders a✝¹ ∧ fastAdmitsAux v u binders a✝

case and_
v u : VarName
a✝¹ a✝ : Formula
a_ih✝¹ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝¹ → fastAdmitsAux v u binders a✝¹
a_ih✝ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝ → fastAdmitsAux v u binders a✝
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders a✝¹ ∧ admitsAux v u binders a✝
⊢ fastAdmitsAux v u binders a✝¹ ∧ fastAdmitsAux v u binders a✝

case or_
v u : VarName
a✝¹ a✝ : Formula
a_ih✝¹ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝¹ → fastAdmitsAux v u binders a✝¹
a_ih✝ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝ → fastAdmitsAux v u binders a✝
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders a✝¹ ∧ admitsAux v u binders a✝
⊢ fastAdmitsAux v u binders a✝¹ ∧ fastAdmitsAux v u binders a✝

case iff_
v u : VarName
a✝¹ a✝ : Formula
a_ih✝¹ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝¹ → fastAdmitsAux v u binders a✝¹
a_ih✝ : ∀ (binders : Finset VarName), v ∉ binders → admitsAux v u binders a✝ → fastAdmitsAux v u binders a✝
binders : Finset VarName
h1 : v ∉ binders
h2 : admitsAux v u binders a✝¹ ∧ admitsAux v u binders a✝
⊢ fastAdmitsAux v u binders a✝¹ ∧ fastAdmitsAux v u binders a✝

case def_
v u : VarName
a✝¹ : DefName
a✝ : List VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v ∈ a✝ ∧ v ∉ binders → u ∉ binders
⊢ v ∈ a✝ → u ∉ binders
no goals