specialize IH XS.length (by simp) XS (by rfl)
case cons
W : Type
M : KripkeModel W
w : W
N : ℕ
X : List Formula
XS : List (List Formula)
IH :
  ∀ m < (X :: XS).length,
    ∀ (XS : List (List Formula)), XS.length = m → (evaluate M w (discon XS) ↔ ∃ Y ∈ XS, ∀ f ∈ Y, evaluate M w f)
⊢ evaluate M w (discon (X :: XS)) ↔ ∃ Y ∈ X :: XS, ∀ f ∈ Y, evaluate M w f
case cons
W : Type
M : KripkeModel W
w : W
N : ℕ
X : List Formula
XS : List (List Formula)
IH : evaluate M w (discon XS) ↔ ∃ Y ∈ XS, ∀ f ∈ Y, evaluate M w f
⊢ evaluate M w (discon (X :: XS)) ↔ ∃ Y ∈ X :: XS, ∀ f ∈ Y, evaluate M w f