Theorem: Arith.HSemiformula.val_ball (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
t : Semiterm L ξ n
p : HSemiformula L ξ (n + 1) Γ
⊢ (ball t p).val = (“(∀[#0 < !!(Rew.bShift t)] !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
t : Semiterm L ξ n
Γ : SigmaPiDelta
m : ℕ
p : HSemiformula L ξ (n + 1) (Γ, m)
⊢ (ball t p).val = (“(∀[#0 < !!(Rew.bShift t)] !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
t : Semiterm L ξ n
Γ : SigmaPiDelta
m : ℕ
p : HSemiformula L ξ (n + 1) (Γ, m)
⊢ (ball t p).val = (“(∀[#0 < !!(Rew.bShift t)] !p.val)”)
Tactic:
rcases Γ <;> simp [val, val_sigma]
State after:
no goals