specialize notPsi_imp_rho W M u1
β : Program
σ0 σ1 ρ ψ : Formula
x : ℕ
x_notin_beta : x ∉ voc β
beta_equiv : (~⌈β⌉~·x)≡(~(~(·x)⋀σ0)⋀(~σ1))
repl_imp_rho : repl_in_F x ρ σ1⊨ρ
notPsi_imp_rho : (~ψ)⊨ρ
W : Type
M : KripkeModel W
w v : W
v_Psi : ¬evaluate M v ψ
u1 u2 : W
u1_b_u2 : relate M β u1 u2
h✝ : Relation.ReflTransGen (relate M β) u2 v
IH : evaluate M u2 ρ
claim : (M, u2)⊨ρ → relate M β u1 u2 → (M, u1)⊨ρ
⊢ evaluate M u1 ρ
β : Program
σ0 σ1 ρ ψ : Formula
x : ℕ
x_notin_beta : x ∉ voc β
beta_equiv : (~⌈β⌉~·x)≡(~(~(·x)⋀σ0)⋀(~σ1))
repl_imp_rho : repl_in_F x ρ σ1⊨ρ
W : Type
M : KripkeModel W
w v : W
v_Psi : ¬evaluate M v ψ
u1 u2 : W
u1_b_u2 : relate M β u1 u2
h✝ : Relation.ReflTransGen (relate M β) u2 v
IH : evaluate M u2 ρ
claim : (M, u2)⊨ρ → relate M β u1 u2 → (M, u1)⊨ρ
notPsi_imp_rho : (∀ φ ∈ [~ψ], evaluate M u1 φ) → ∀ ψ ∈ [ρ], evaluate M u1 ψ
⊢ evaluate M u1 ρ