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

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

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

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

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

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

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

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

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