Theorem: LO.FirstOrder.Arith.Model.ext_defined (Arithmetization/ISigmaZero/Exponential/Exp.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
⊢ 𝚺₀-Function₂ fun a b => ext a b 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
v : Fin (Nat.succ 2) → M
⊢ (fun v => v 0 = (fun v => (fun a b => ext a b) (v 0) (v 1)) 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
v : Fin (Nat.succ 2) → M
⊢ (fun v => v 0 = (fun v => (fun a b => ext a b) (v 0) (v 1)) fun x => v x.succ) v ↔
    (Semiformula.Evalbm M v) (HSemiformula.val extDef)
Tactic:
simp [Matrix.vecHead, Matrix.vecTail, extDef,
ext_graph, Semiformula.eval_substs, div_defined.df.iff, rem_defined.df.iff, le_iff_lt_succ]
State after:
no goals