Theorem: LO.FirstOrder.Arith.Model.Nuon.SeriesSegment.initial (Arithmetization/OmegaOne/Nuon.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 + 𝛀₁
L✝ A✝ U I L A : M
Upos : 0 < U
⊢ 0 ≤ 0
Tactic:
rfl
State after:
no goals

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 + 𝛀₁
L✝ A✝ U I L A : M
Upos : 0 < U
⊢ IsSeries U I L A (0 / ‖I‖) 0 ∧ 0{L}[0] = 0 ∧ 0{L}[0 / ‖I‖] = 0
Tactic:
simp [IsSeries]
State after:
no goals

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 + 𝛀₁
L✝ A✝ U I L A : M
Upos : 0 < U
⊢ IsSegment L A (‖I‖ * (0 / ‖I‖)) (0 % ‖I‖) 0 ∧ 0{L}[0] = 0 ∧ 0{L}[0 % ‖I‖] = 0
Tactic:
simp [IsSegment]
State after:
no goals