Theorem: LO.FirstOrder.Arith.Model.hash_monotone (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
a₁ a₂ b₁ b₂ : M
h₁ : a₁ ≤ b₁
h₂ : a₂ ≤ b₂
⊢ 0 ≤ ‖a₂‖
Tactic:
simp
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
a₁ a₂ b₁ b₂ : M
h₁ : a₁ ≤ b₁
h₂ : a₂ ≤ b₂
⊢ 0 ≤ ‖b₁‖
Tactic:
simp
State after:
no goals