# Documentation

Mathlib.Data.Int.Order.Lemmas

# Further lemmas about the integers #

The distinction between this file and Data.Int.Order.Basic is not particularly clear. They are separated by now to minimize the porting requirements for tactics during the transition to mathlib4. After data.rat.order has been ported, please feel free to reorganize these two files.

### nat abs #

theorem Int.natAbs_eq_iff_mul_self_eq {a : } {b : } :
a * a = b * b
theorem Int.natAbs_lt_iff_mul_self_lt {a : } {b : } :
a * a < b * b
theorem Int.natAbs_le_iff_mul_self_le {a : } {b : } :
a * a b * b
theorem Int.dvd_div_of_mul_dvd {a : } {b : } {c : } (h : a * b c) :
b c / a

### units #

theorem Int.eq_zero_of_abs_lt_dvd {m : } {x : } (h1 : m x) (h2 : abs x < m) :
x = 0