induction' X with f X IH
W : Type
M : KripkeModel W
X : List Formula
w : W
⊢ Evaluate (M, w) (bigCon X) ↔ ∀ f ∈ X, Evaluate (M, w) f
case nil
W : Type
M : KripkeModel W
w : W
⊢ Evaluate (M, w) (bigCon []) ↔ ∀ f ∈ [], Evaluate (M, w) f

case cons
W : Type
M : KripkeModel W
w : W
f : Formula
X : List Formula
IH : Evaluate (M, w) (bigCon X) ↔ ∀ f ∈ X, Evaluate (M, w) f
⊢ Evaluate (M, w) (bigCon (f :: X)) ↔ ∀ f_1 ∈ f :: X, Evaluate (M, w) f_1