subst nDef
W : Type
M : KripkeModel W
w : W
N n : ℕ
IH :
  ∀ m < n,
    ∀ (XS : List (List Formula)), XS.length = m → (Evaluate (M, w) (discon XS) ↔ ∃ Y ∈ XS, ∀ f ∈ Y, Evaluate (M, w) f)
XS : List (List Formula)
nDef : XS.length = n
⊢ Evaluate (M, w) (discon XS) ↔ ∃ Y ∈ XS, ∀ f ∈ Y, Evaluate (M, w) f
W : Type
M : KripkeModel W
w : W
N : ℕ
XS : List (List Formula)
IH :
  ∀ m < 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 XS) ↔ ∃ Y ∈ XS, ∀ f ∈ Y, Evaluate (M, w) f