Theorem: LO.FirstOrder.Arith.Model.PR.Construction.result_zero (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
⊢ c.result v 0 = c.zero v
Tactic:
rcases c.result_spec v 0 with ⟨s, Hs, _, h0⟩
State after:
case intro.intro.intro
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
s : M
Hs : c.CSeq v s
left✝ : 0 + 1 = lh s
h0 : ⟪0, c.result v 0⟫ ∈ s
⊢ c.result v 0 = c.zero v

State before:
case intro.intro.intro
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
s : M
Hs : c.CSeq v s
left✝ : 0 + 1 = lh s
h0 : ⟪0, c.result v 0⟫ ∈ s
⊢ c.result v 0 = c.zero v
Tactic:
exact Hs.seq.isMapping.uniq h0 Hs.zero
State after:
no goals