specialize repl_imp_rho W M u
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
u v : W
v_rho : (M, v)⊨ρ
u_β_v : relate M β u v
u_ : (M, u)⊨(~⌈β⌉~ρ)
u_2 : evaluate M u ρ ∧ evaluate M u (repl_in_F x ρ σ0) ∨ evaluate M u (repl_in_F x ρ σ1)
⊢ (M, u)⊨ρ
β : Program
σ0 σ1 ρ ψ : Formula
x : ℕ
x_notin_beta : x ∉ voc β
beta_equiv : (~⌈β⌉~·x)≡(·x)⋀σ0⋁σ1
notPsi_imp_rho : (~ψ)⊨ρ
W : Type
M : KripkeModel W
u v : W
v_rho : (M, v)⊨ρ
u_β_v : relate M β u v
u_ : (M, u)⊨(~⌈β⌉~ρ)
u_2 : evaluate M u ρ ∧ evaluate M u (repl_in_F x ρ σ0) ∨ evaluate M u (repl_in_F x ρ σ1)
repl_imp_rho : (∀ φ ∈ [repl_in_F x ρ σ1], evaluate M u φ) → ∀ ψ ∈ [ρ], evaluate M u ψ
⊢ (M, u)⊨ρ