ext1
X : Finset Formula
ϕ : Formula
in_X : ϕ ∈ X
claim : lengthOfSet (insert ϕ (X \ {ϕ})) = lengthOfSet (X \ {ϕ}) + lengthOfFormula ϕ
⊢ insert ϕ (X \ {ϕ}) = X
case a
X : Finset Formula
ϕ : Formula
in_X : ϕ ∈ X
claim : lengthOfSet (insert ϕ (X \ {ϕ})) = lengthOfSet (X \ {ϕ}) + lengthOfFormula ϕ
a✝ : Formula
⊢ a✝ ∈ insert ϕ (X \ {ϕ}) ↔ a✝ ∈ X