induction Y using Finset.induction_on
X Y : Finset Formula
h : Y ⊆ X
⊢ lengthOfSet (X \ Y) + lengthOfSet Y = lengthOfSet X
case empty
X : Finset Formula
h : ∅ ⊆ X
⊢ lengthOfSet (X \ ∅) + lengthOfSet ∅ = lengthOfSet X

case insert
X : Finset Formula
a✝² : Formula
s✝ : Finset Formula
a✝¹ : a✝² ∉ s✝
a✝ : s✝ ⊆ X → lengthOfSet (X \ s✝) + lengthOfSet s✝ = lengthOfSet X
h : insert a✝² s✝ ⊆ X
⊢ lengthOfSet (X \ insert a✝² s✝) + lengthOfSet (insert a✝² s✝) = lengthOfSet X