apply IH
f : Formula
S : Finset Formula
f_not_in_S : f ∉ S
IH : lengthOfSet (projection S) ≤ lengthOfSet S
insert_comm_proj : ∀ (X : Finset Formula) (f : Formula), projection (insert f X) = projection {f} ∪ projection X
⊢ (projection S).sum lengthOfFormula ≤ S.sum lengthOfFormula
no goals