induction l
case mpr
W : Type
l : List Formula
M : KripkeModel W
w : W
satOne : ∃ φ ∈ l, Evaluate (M, w) φ
⊢ Evaluate (M, w) (bigDis l)
case mpr.nil
W : Type
M : KripkeModel W
w : W
satOne : ∃ φ ∈ [], Evaluate (M, w) φ
⊢ Evaluate (M, w) (bigDis [])

case mpr.cons
W : Type
M : KripkeModel W
w : W
head✝ : Formula
tail✝ : List Formula
tail_ih✝ : (∃ φ ∈ tail✝, Evaluate (M, w) φ) → Evaluate (M, w) (bigDis tail✝)
satOne : ∃ φ ∈ head✝ :: tail✝, Evaluate (M, w) φ
⊢ Evaluate (M, w) (bigDis (head✝ :: tail✝))