let ⟨L,R,O⟩ := Δ
tabΔ : (Y : TNode) × (HistY : LoadHistory) × ClosedTableau HistY Y
W : Type
α : Program
w : W
Root Δ : TNode
tab : ClosedTableau ([], []) Root
path_to_Δ : List TNode
h : some tabΔ = tabInAt ⟨Root, ⟨([], []), tab⟩⟩ path_to_Δ
M : KripkeModel W
v : W
φ : AnyFormula
negLoad_in : NegLoadFormula_in_TNode (~'⌊α⌋φ) Δ
v_X : (M, v)⊨Δ
v_α_w : relate M α v w
w_φ : (M, w)⊨~''φ
⊢ ∃ path_Δ_to_Γ,
    ∃ Γ ∈ tabInAt ⟨Root, ⟨([], []), tab⟩⟩ (path_to_Δ ++ path_Δ_to_Γ), AnyNegFormula_in_TNode (~''φ) Γ.fst ∧ (M, w)⊨Γ.fst
tabΔ : (Y : TNode) × (HistY : LoadHistory) × ClosedTableau HistY Y
W : Type
α : Program
w : W
Root Δ : TNode
tab : ClosedTableau ([], []) Root
path_to_Δ : List TNode
h : some tabΔ = tabInAt ⟨Root, ⟨([], []), tab⟩⟩ path_to_Δ
M : KripkeModel W
v : W
φ : AnyFormula
v_α_w : relate M α v w
w_φ : (M, w)⊨~''φ
L R : List Formula
O : Option (NegLoadFormula ⊕ NegLoadFormula)
negLoad_in : NegLoadFormula_in_TNode (~'⌊α⌋φ) (L, R, O)
v_X : (M, v)⊨(L, R, O)
⊢ ∃ path_Δ_to_Γ,
    ∃ Γ ∈ tabInAt ⟨Root, ⟨([], []), tab⟩⟩ (path_to_Δ ++ path_Δ_to_Γ), AnyNegFormula_in_TNode (~''φ) Γ.fst ∧ (M, w)⊨Γ.fst