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

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

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

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

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

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

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

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

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