ι : Type u_1
inst✝³ : LinearOrder ι
inst✝² : SuccOrder ι
inst✝¹ : IsSuccArchimedean ι
inst✝ : PredOrder ι
i0 i : ι
hi : i0 ≤ i
⊢ 0 ≤ ↑(Nat.find (_ : ∃ n, (succ^[n]) i0 = i))
ι : Type u_1
inst✝³ : LinearOrder ι
inst✝² : SuccOrder ι
inst✝¹ : IsSuccArchimedean ι
inst✝ : PredOrder ι
i0 i : ι
hi : i0 ≤ i
⊢ 0 ≤ toZ i0 i
rw [toZ_of_ge hi]
no goals
ι : Type u_1
inst✝³ : LinearOrder ι
inst✝² : SuccOrder ι
inst✝¹ : IsSuccArchimedean ι
inst✝ : PredOrder ι
i0 i : ι
hi : i0 ≤ i
⊢ 0 ≤ ↑(Nat.find (_ : ∃ n, (succ^[n]) i0 = i))
exact Nat.cast_nonneg _