have hmono : StrictMono s := strictMono_nat_of_lt_succ hs
s : ℕ → ℤ
hs : ∀ (i : ℕ), s i < s (i + 1)
z : ℤ
hs0 : s 0 < z
⊢ ∃! i, s i < z ∧ z ≤ s (i + 1)
s : ℕ → ℤ
hs : ∀ (i : ℕ), s i < s (i + 1)
z : ℤ
hs0 : s 0 < z
hmono : StrictMono s
⊢ ∃! i, s i < z ∧ z ≤ s (i + 1)