mathlib documentation

data.int.sqrt

Square root of integers #

This file defines the square root function on integers. int.sqrt z is the greatest integer r such that r * r ≤ z. If z ≤ 0, then int.sqrt z = 0.

def int.sqrt (z : ) :

sqrt z is the square root of an integer z. If z is positive, it returns the largest integer r such that r * r ≤ n. If it is negative, it returns 0. For example, sqrt (-1) = 0, sqrt 1 = 1, sqrt 2 = 1

Equations
theorem int.sqrt_eq (n : ) :
theorem int.exists_mul_self (x : ) :
(∃ (n : ), n * n = x) (int.sqrt x) * int.sqrt x = x
theorem int.sqrt_nonneg (n : ) :