Theorem: LO.FirstOrder.Arith.Model.seq_defined (Arithmetization/ISigmaOne/HFS/Seq.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
⊢ 𝚺₀-Predicate Seq via seqDef
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* 𝐈𝚺₁
v : Fin 1 → M
⊢ (fun v => Seq (v 0)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val seqDef)

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
v : Fin 1 → M
⊢ (fun v => Seq (v 0)) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val seqDef)
Tactic:
simp [seqDef, seq_iff]
State after:
no goals