Theorem: Arith.HSemiformula.ofZero_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
k : ℕ
Γ' : SigmaPiDelta
p : HSemiformula L ξ k (Γ', 0)
Γ : HierarchySymbol
⊢ (p.ofZero Γ).val = p.val
Tactic:
match Γ with
| (𝚺, _) => simp [ofZero]
| (𝚷, _) => simp [ofZero]
| (𝚫, _) => simp [ofZero]
State after:
no goals

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
k : ℕ
Γ' : SigmaPiDelta
p : HSemiformula L ξ k (Γ', 0)
Γ : HierarchySymbol
snd✝ : ℕ
⊢ (p.ofZero (𝚺, snd✝)).val = p.val
Tactic:
simp [ofZero]
State after:
no goals

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
k : ℕ
Γ' : SigmaPiDelta
p : HSemiformula L ξ k (Γ', 0)
Γ : HierarchySymbol
snd✝ : ℕ
⊢ (p.ofZero (𝚷, snd✝)).val = p.val
Tactic:
simp [ofZero]
State after:
no goals

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
k : ℕ
Γ' : SigmaPiDelta
p : HSemiformula L ξ k (Γ', 0)
Γ : HierarchySymbol
snd✝ : ℕ
⊢ (p.ofZero (𝚫, snd✝)).val = p.val
Tactic:
simp [ofZero]
State after:
no goals