Theorem: LO.FirstOrder.Arith.Model.log_defined (Arithmetization/ISigmaZero/Exponential/Log.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-Function₁ log via logDef
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 1) → M
⊢ (fun v => v 0 = (fun v => log (v 0)) fun x => v x.succ) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val logDef)

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 1) → M
⊢ (fun v => v 0 = (fun v => log (v 0)) fun x => v x.succ) v ↔ (Semiformula.Evalbm M v) (HSemiformula.val logDef)
Tactic:
simp [logDef, log_graph, ←le_iff_lt_succ, numeral_eq_natCast]
State after:
no goals