Theorem: LO.FirstOrder.Arith.Model.Exponential.Seq₀.append (Arithmetization/ISigmaZero/Exponential/Exp.lean)

State before:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚫₀
X Y i x y : M
H : Seq₀ X Y
ppi : PPow2 i
hi : 4 < i
⊢ Seq₀ (Exponential.append i X x) (Exponential.append i Y y)
Tactic:
rw [Seq₀, ext_append_of_lt, ext_append_of_lt] <;> try simp [ppi, hi]
State after:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚫₀
X Y i x y : M
H : Seq₀ X Y
ppi : PPow2 i
hi : 4 < i
⊢ ext 4 X = 1 ∧ ext 4 Y = 2

State before:
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚫₀
X Y i x y : M
H : Seq₀ X Y
ppi : PPow2 i
hi : 4 < i
⊢ ext 4 X = 1 ∧ ext 4 Y = 2
Tactic:
exact H
State after:
no goals

State before:
case hij
M : Type u_1
inst✝⁵ : Zero M
inst✝⁴ : One M
inst✝³ : Add M
inst✝² : Mul M
inst✝¹ : LT M
inst✝ : M ⊧ₘ* 𝐈𝚫₀
X Y i x y : M
H : Seq₀ X Y
ppi : PPow2 i
hi : 4 < i
⊢ 4 < i
Tactic:
simp [ppi, hi]
State after:
no goals