induction δ generalizing v
W : Type
M : KripkeModel W
v : W
δ : List Program
ξ : Formula
⊢ evaluate M v (~⌈⌈δ⌉⌉ξ) → Nonempty (witness M v δ ξ)
case nil
W : Type
M : KripkeModel W
ξ : Formula
v : W
⊢ evaluate M v (~⌈⌈[]⌉⌉ξ) → Nonempty (witness M v [] ξ)

case cons
W : Type
M : KripkeModel W
ξ : Formula
head✝ : Program
tail✝ : List Program
tail_ih✝ : ∀ (v : W), evaluate M v (~⌈⌈tail✝⌉⌉ξ) → Nonempty (witness M v tail✝ ξ)
v : W
⊢ evaluate M v (~⌈⌈head✝ :: tail✝⌉⌉ξ) → Nonempty (witness M v (head✝ :: tail✝) ξ)