Theorem: LO.FirstOrder.Arith.Model.seqProduct_defined (Arithmetization/ISigmaOne/HFS/Supplemental.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
⊢ 𝚺₁-Function₂ seqProduct via seqProductDef
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 (Nat.succ 2) → M
⊢ (fun v => v 0 = (fun v => v 0 ×ˢ v 1) fun x => v x.succ) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val seqProductDef)

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 (Nat.succ 2) → M
⊢ (fun v => v 0 = (fun v => v 0 ×ˢ v 1) fun x => v x.succ) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val seqProductDef)
Tactic:
simp [seqProductDef, seqProduct_graph]
State after:
no goals