Theorem: LO.FirstOrder.Arith.Model.Exponential.Seqₛ.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-Relation₃ Seqₛ via def
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 3 → M
⊢ (fun v => Seqₛ (v 0) (v 1) (v 2)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val def)

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