Theorem: LO.FirstOrder.Arith.Model.Exponential.defined (Arithmetization/ISigmaZero/Exponential/Exp.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
⊢ 𝚺₀-Relation Exponential via exponentialDef
Tactic:
intro v
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
v : Fin 2 → M
⊢ (fun v => Exponential (v 0) (v 1)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val exponentialDef)

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
v : Fin 2 → M
⊢ (fun v => Exponential (v 0) (v 1)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val exponentialDef)
Tactic:
simp [Exponential.graph_iff, exponentialDef, ppow2_defined.df.iff, ext_defined.df.iff,
Exponential.Seqₛ.defined.df.iff, ←le_iff_lt_succ, pow_four, sq, numeral_eq_natCast]
State after:
no goals