apply intro_union_ParametricConsistent
α : Type u_1
Λ : AxiomSet α
inst✝³ : Inhabited α
inst✝² : DecidableEq α
t : Axioms.Geach.Taple
L : DeductionParameter α
inst✝¹ : L.HasNecOnly
includeK : L.IncludeK
inst✝ : Inhabited (MCT L)
hAx : 𝗴𝗲(t) ⊆ Ax(L)
this : L.Normal
Ω₁ Ω₂ Ω₃ : (CanonicalFrame L).World
r₁₂ : Ω₁ ≺^[t.i] Ω₂
r₁₃ : Ω₁ ≺^[t.j] Ω₃
⊢ (L)-Consistent (□''⁻¹^[t.m]Ω₂.theory ∪ □''⁻¹^[t.n]Ω₃.theory)
case h
α : Type u_1
Λ : AxiomSet α
inst✝³ : Inhabited α
inst✝² : DecidableEq α
t : Axioms.Geach.Taple
L : DeductionParameter α
inst✝¹ : L.HasNecOnly
includeK : L.IncludeK
inst✝ : Inhabited (MCT L)
hAx : 𝗴𝗲(t) ⊆ Ax(L)
this : L.Normal
Ω₁ Ω₂ Ω₃ : (CanonicalFrame L).World
r₁₂ : Ω₁ ≺^[t.i] Ω₂
r₁₃ : Ω₁ ≺^[t.j] Ω₃
⊢ ∀ {Γ₁ Γ₂ : List (Formula α)},
    (∀ p ∈ Γ₁, p ∈ □''⁻¹^[t.m]Ω₂.theory) → (∀ p ∈ Γ₂, p ∈ □''⁻¹^[t.n]Ω₃.theory) → L ⊬! Γ₁.conj' ⋏ Γ₂.conj' ⟶ ⊥