intro _ h
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
T : Theory α
consisT : (L)-Consistent T
T₁ T₂ : Theory α
h : ∀ {Γ₁ Γ₂ : List (Formula α)}, (∀ p ∈ Γ₁, p ∈ T₁) → (∀ p ∈ Γ₂, p ∈ T₂) → L ⊬! Γ₁.conj' ⋏ Γ₂.conj' ⟶ ⊥
Δ : List (Formula α)
hΔ : ∀ p ∈ Δ, p ∈ T₁ ∨ p ∈ T₂
Δ₁ : List (Formula α) := List.filter (fun x => decide (x ∈ T₁)) Δ
Δ₂ : List (Formula α) := List.filter (fun x => decide (x ∈ T₂)) Δ
⊢ ∀ p ∈ Δ₂, p ∈ T₂
α : Type u_1
inst✝² : DecidableEq α
inst✝¹ : Inhabited α
L : DeductionParameter α
inst✝ : L.Normal
T : Theory α
consisT : (L)-Consistent T
T₁ T₂ : Theory α
h✝ : ∀ {Γ₁ Γ₂ : List (Formula α)}, (∀ p ∈ Γ₁, p ∈ T₁) → (∀ p ∈ Γ₂, p ∈ T₂) → L ⊬! Γ₁.conj' ⋏ Γ₂.conj' ⟶ ⊥
Δ : List (Formula α)
hΔ : ∀ p ∈ Δ, p ∈ T₁ ∨ p ∈ T₂
Δ₁ : List (Formula α) := List.filter (fun x => decide (x ∈ T₁)) Δ
Δ₂ : List (Formula α) := List.filter (fun x => decide (x ∈ T₂)) Δ
p✝ : Formula α
h : p✝ ∈ Δ₂
⊢ p✝ ∈ T₂