Theorem: Arith.HSemiformula.sigma_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
m : ℕ
p : HSemiformula ℒₒᵣ ξ n (𝚫, m)
⊢ (emb L p).sigma = emb L p.sigma
Tactic:
cases p
State after:
case mkDelta
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
a✝¹ : HSemiformula ℒₒᵣ ξ n (𝚺, m)
a✝ : HSemiformula ℒₒᵣ ξ n (𝚷, m)
⊢ (emb L (a✝¹.mkDelta a✝)).sigma = emb L (a✝¹.mkDelta a✝).sigma

State before:
case mkDelta
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
a✝¹ : HSemiformula ℒₒᵣ ξ n (𝚺, m)
a✝ : HSemiformula ℒₒᵣ ξ n (𝚷, m)
⊢ (emb L (a✝¹.mkDelta a✝)).sigma = emb L (a✝¹.mkDelta a✝).sigma
Tactic:
rfl
State after:
no goals