Theorem: LO.FirstOrder.Arith.Model.not_mem_of_lt_exp (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
i a : M
h : a < exp i
H : i ∈ a
⊢ False
Tactic:
have := lt_of_le_of_lt (exp_le_of_mem H) h
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* 𝐈𝚺₁
i a : M
h : a < exp i
H : i ∈ a
this : exp i < exp i
⊢ False

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
i a : M
h : a < exp i
H : i ∈ a
this : exp i < exp i
⊢ False
Tactic:
simp at this
State after:
no goals