Theorem: LO.FirstOrder.Arith.Model.Seq.seqCons (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
s : M
h : Seq s
x : M
⊢ lh s ∉ domain s
Tactic:
simp [h.domain_eq]
State after:
no goals

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
s : M
h : Seq s
x : M
⊢ domain (s ⁀' x) = under (lh s + 1)
Tactic:
simp [seqCons, h.domain_eq]
State after:
no goals