intro v_
W : Type
M : KripkeModel W
ξ : Formula
α : Program
γs : List Program
IH : ∀ (v : W), evaluate M v (~⌈⌈γs⌉⌉ξ) → Nonempty (witness M v γs ξ)
v : W
⊢ evaluate M v (~⌈⌈α :: γs⌉⌉ξ) → Nonempty (witness M v (α :: γs) ξ)
W : Type
M : KripkeModel W
ξ : Formula
α : Program
γs : List Program
IH : ∀ (v : W), evaluate M v (~⌈⌈γs⌉⌉ξ) → Nonempty (witness M v γs ξ)
v : W
v_ : evaluate M v (~⌈⌈α :: γs⌉⌉ξ)
⊢ Nonempty (witness M v (α :: γs) ξ)