Theorem: LO.FirstOrder.Arith.Model.seqMap₀_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
p : 𝚺₀-Semisentence 2
f : M → M
hf : 𝚺₀-Function₁ f via p
⊢ 𝚺₀-Function₁ seqMap ⋯ via seqMap₀Def p
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
p : 𝚺₀-Semisentence 2
f : M → M
hf : 𝚺₀-Function₁ f via p
v : Fin (Nat.succ 1) → M
⊢ (fun v => v 0 = (fun v => seqMap ⋯ (v 0)) fun x => v x.succ) v ↔
    (Semiformula.Evalbm M v) (HSemiformula.val (seqMap₀Def p))

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
p : 𝚺₀-Semisentence 2
f : M → M
hf : 𝚺₀-Function₁ f via p
v : Fin (Nat.succ 1) → M
⊢ (fun v => v 0 = (fun v => seqMap ⋯ (v 0)) fun x => v x.succ) v ↔
    (Semiformula.Evalbm M v) (HSemiformula.val (seqMap₀Def p))
Tactic:
simp [seqMap₀Def, seqMap_graph, hf.df.iff]
State after:
no goals