Theorem: Arith.HSemiformula.val_emb (Arithmetization/Definability/Hierarchy.lean)

State before:
L : Language
inst✝⁷ : L.ORing
ξ : Type v
n : ℕ
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : Structure L M
inst✝ : Structure.ORing L M
Γ : HierarchySymbol
p : HSemiformula ℒₒᵣ ξ n Γ
⊢ (emb L p).val = (Semiformula.lMap Language.oringEmb) p.val
Tactic:
rcases Γ with ⟨Γ, m⟩
State after:
case mk
L : Language
inst✝⁷ : L.ORing
ξ : Type v
n : ℕ
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : Structure L M
inst✝ : Structure.ORing L M
Γ : SigmaPiDelta
m : ℕ
p : HSemiformula ℒₒᵣ ξ n (Γ, m)
⊢ (emb L p).val = (Semiformula.lMap Language.oringEmb) p.val

State before:
case mk
L : Language
inst✝⁷ : L.ORing
ξ : Type v
n : ℕ
M : Type u_1
inst✝⁶ : Zero M
inst✝⁵ : One M
inst✝⁴ : Add M
inst✝³ : Mul M
inst✝² : LT M
inst✝¹ : Structure L M
inst✝ : Structure.ORing L M
Γ : SigmaPiDelta
m : ℕ
p : HSemiformula ℒₒᵣ ξ n (Γ, m)
⊢ (emb L p).val = (Semiformula.lMap Language.oringEmb) p.val
Tactic:
rcases p with (_ | _ | ⟨⟨p, _⟩, ⟨q, _⟩⟩) <;> simp [rew, val]
State after:
no goals