split_ifs at a1
v t x y : VarName
binders : Finset VarName
h1_left : t ≠ x
h1_right : t ≠ y
a1 : ((t = if v = x ∧ x ∉ binders then t else x) ∨ t = if v = y ∧ y ∉ binders then t else y) ∧ t ∉ binders
⊢ v ∉ binders
case pos
v t x y : VarName
binders : Finset VarName
h1_left : t ≠ x
h1_right : t ≠ y
h✝¹ : v = x ∧ x ∉ binders
h✝ : v = y ∧ y ∉ binders
a1 : (t = t ∨ t = t) ∧ t ∉ binders
⊢ v ∉ binders

case neg
v t x y : VarName
binders : Finset VarName
h1_left : t ≠ x
h1_right : t ≠ y
h✝¹ : v = x ∧ x ∉ binders
h✝ : ¬(v = y ∧ y ∉ binders)
a1 : (t = t ∨ t = y) ∧ t ∉ binders
⊢ v ∉ binders

case pos
v t x y : VarName
binders : Finset VarName
h1_left : t ≠ x
h1_right : t ≠ y
h✝¹ : ¬(v = x ∧ x ∉ binders)
h✝ : v = y ∧ y ∉ binders
a1 : (t = x ∨ t = t) ∧ t ∉ binders
⊢ v ∉ binders

case neg
v t x y : VarName
binders : Finset VarName
h1_left : t ≠ x
h1_right : t ≠ y
h✝¹ : ¬(v = x ∧ x ∉ binders)
h✝ : ¬(v = y ∧ y ∉ binders)
a1 : (t = x ∨ t = y) ∧ t ∉ binders
⊢ v ∉ binders