rcases Fδ_in with ⟨l, ⟨Gs, γ, ⟨Gγ_in, def_l⟩⟩, Gγ_in_l⟩
case mpr.intro.mk.intro
ψ : Formula
W : Type
M : KripkeModel W
w : W
α β : Program
Fs : List Formula
δ : List Program
w_Con : evaluate M w (Con (Yset (Fs, δ) ψ))
Fδ_in :
  ∃ l,
    (∃ a b,
        (a, b) ∈ H α ∧ (if b = [] then (List.map (fun x => [(a ∪ x.1, x.2)]) (H β)).join else [(a, b ++ [β])]) = l) ∧
      (Fs, δ) ∈ l
⊢ ∃ Fδ ∈ H α, evaluate M w (Con (Yset Fδ (⌈β⌉ψ)))
case mpr.intro.mk.intro.intro.intro.intro.intro.intro
ψ : Formula
W : Type
M : KripkeModel W
w : W
α β : Program
Fs : List Formula
δ : List Program
w_Con : evaluate M w (Con (Yset (Fs, δ) ψ))
l : List (List Formula × List Program)
Gγ_in_l : (Fs, δ) ∈ l
Gs : List Formula
γ : List Program
Gγ_in : (Gs, γ) ∈ H α
def_l : (if γ = [] then (List.map (fun x => [(Gs ∪ x.1, x.2)]) (H β)).join else [(Gs, γ ++ [β])]) = l
⊢ ∃ Fδ ∈ H α, evaluate M w (Con (Yset Fδ (⌈β⌉ψ)))