rintro ⟨p₁, rfl, p₂, rfl, rfl⟩
case mpr
L : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ₁ : Type u_2
ξ₂ : Type u_3
ξ₃ : Type u_4
n n₁ n₂✝ n₂ m m₁ m₂ m₃ : ℕ
ω : Rew L ξ₁ n₁ ξ₂ n₂
p : Semiformula L ξ₁ n₁
q₁ q₂ : Semiformula L ξ₂ n₂
⊢ (∃ p₁, ω.hom p₁ = q₁ ∧ ∃ x, ω.hom x = q₂ ∧ p = ~p₁ ⋎ x) → ∃ p₁, ω.hom p₁ = ~q₁ ∧ ∃ x, ω.hom x = q₂ ∧ p = p₁ ⋎ x
case mpr.intro.intro.intro.intro
L : Language
L₁ : Language
L₂ : Language
L₃ : Language
ξ : Type u_1
ξ₁ : Type u_2
ξ₂ : Type u_3
ξ₃ : Type u_4
n n₁ n₂✝ n₂ m m₁ m₂ m₃ : ℕ
ω : Rew L ξ₁ n₁ ξ₂ n₂
p₁ p₂ : Semiformula L ξ₁ n₁
⊢ ∃ p₁_1, ω.hom p₁_1 = ~ω.hom p₁ ∧ ∃ x, ω.hom x = ω.hom p₂ ∧ ~p₁ ⋎ p₂ = p₁_1 ⋎ x