Theorem: LO.FirstOrder.Arith.Model.lt_hash_one_right (Arithmetization/OmegaOne/Basic.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
a : M
⊢ a < a # 1
Tactic:
have : Exponential ‖a‖ (a # 1) := by simpa using (exponential_hash a 1)
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 + 𝛀₁
a : M
this : Exponential ‖a‖ (a # 1)
⊢ a < a # 1

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
a : M
this : Exponential ‖a‖ (a # 1)
⊢ a < a # 1
Tactic:
exact lt_exponential_length this
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
a : M
⊢ Exponential ‖a‖ (a # 1)
Tactic:
simpa using (exponential_hash a 1)
State after:
no goals