Theorem: LO.FirstOrder.Arith.Model.PR.Construction.CSeq.initial (Arithmetization/ISigmaOne/HFS/PRF.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
k : ℕ
p : Formulae k
c : Construction M p
v : Fin k → M
⊢ Seq (∅ ⁀' c.zero v)
Tactic:
simp
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
k : ℕ
p : Formulae k
c : Construction M p
v : Fin k → M
⊢ ⟪0, c.zero v⟫ ∈ ∅ ⁀' c.zero v
Tactic:
simp [seqCons]
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
k : ℕ
p : Formulae k
c : Construction M p
v : Fin k → M
⊢ ∀ i < lh (∅ ⁀' c.zero v) - 1, ∀ (z : M), ⟪i, z⟫ ∈ ∅ ⁀' c.zero v → ⟪i + 1, c.succ v i z⟫ ∈ ∅ ⁀' c.zero v
Tactic:
simp
State after:
no goals