Theorem: LO.FirstOrder.Rew.eq_and_iff (Logic/FirstOrder/Basic/Syntax/Rew.lean)

State before:
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
⊢ ω.hom p = q₁ ⋏ q₂ ↔ ∃ p₁ p₂, ω.hom p₁ = q₁ ∧ ω.hom p₂ = q₂ ∧ p = p₁ ⋏ p₂
Tactic:
cases p using Semiformula.rec' <;> simp[Rew.rel, Rew.nrel]
State after:
no goals