constructor
v u x y : VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v = x ∨ v = y → u ∉ binders
⊢ (x ∈ binders ↔ (if v = x then u else x) ∈ binders) ∧ (y ∈ binders ↔ (if v = y then u else y) ∈ binders)
case left
v u x y : VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v = x ∨ v = y → u ∉ binders
⊢ x ∈ binders ↔ (if v = x then u else x) ∈ binders

case right
v u x y : VarName
binders : Finset VarName
h1 : v ∉ binders
h2 : v = x ∨ v = y → u ∉ binders
⊢ y ∈ binders ↔ (if v = y then u else y) ∈ binders