Theorem: LO.FirstOrder.Arith.Model.Exponential.lt_iff_log_lt (Arithmetization/ISigmaZero/Exponential/Log.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 a : M
H : Exponential x y
pos : 0 < a
⊢ ¬a < y ↔ ¬log a < x
Tactic:
simpa using le_iff_le_log_of_exp H pos
State after:
no goals