Theorem: LO.FirstOrder.Arith.Model.Nuon.ext_defined (Arithmetization/OmegaOne/Nuon.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* 𝐈𝚫₀ + 𝛀₁
⊢ 𝚺₀-Function₃ ext via extDef
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* 𝐈𝚫₀ + 𝛀₁
v : Fin (Nat.succ 3) → M
⊢ (fun v => v 0 = (fun v => v 1{v 0}[v 2]) fun x => v x.succ) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val extDef)

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* 𝐈𝚫₀ + 𝛀₁
v : Fin (Nat.succ 3) → M
⊢ (fun v => v 0 = (fun v => v 1{v 0}[v 2]) fun x => v x.succ) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val extDef)
Tactic:
simp [extDef, length_defined.df.iff, Exponential.defined.df.iff,
div_defined.df.iff, rem_defined.df.iff, lt_succ_iff_le, ext_graph, numeral_eq_natCast]
State after:
no goals