Theorem: LO.FirstOrder.Arith.Model.le_under (Arithmetization/ISigmaOne/Bit.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* 𝐈𝚺₁
a : M
⊢ a < under a + 1
Tactic:
simp [under, show exp a - 1 + 1 = exp a from sub_add_self_of_le (by 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* 𝐈𝚺₁
a : M
⊢ 1 ≤ exp a
Tactic:
simp
State after:
no goals