Theorem: Arith.HSemiformula.sigma_extd_val (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
m : ℕ
p : HSemiformula ℒₒᵣ ξ n (𝚺, m)
⊢ (extd L p).val = (Semiformula.lMap Language.oringEmb) p.val
Tactic:
rcases p
State after:
case mkSigma
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
m : ℕ
p✝ : Semiformula ℒₒᵣ ξ n
a✝ : Hierarchy 𝚺 m p✝
⊢ (extd L (mkSigma p✝ a✝)).val = (Semiformula.lMap Language.oringEmb) (mkSigma p✝ a✝).val

State before:
case mkSigma
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
m : ℕ
p✝ : Semiformula ℒₒᵣ ξ n
a✝ : Hierarchy 𝚺 m p✝
⊢ (extd L (mkSigma p✝ a✝)).val = (Semiformula.lMap Language.oringEmb) (mkSigma p✝ a✝).val
Tactic:
simp [extd]
State after:
no goals