## 5.188. leq

Origin

Arithmetic.

Constraint

$\mathrm{𝚕𝚎𝚚}\left(\mathrm{𝚅𝙰𝚁}\mathtt{1},\mathrm{𝚅𝙰𝚁}\mathtt{2}\right)$

Synonyms

$\mathrm{𝚛𝚎𝚕}$, $\mathrm{𝚡𝚕𝚝𝚎𝚚𝚢}$.

Arguments
 $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ $\mathrm{𝚍𝚟𝚊𝚛}$ $\mathrm{𝚅𝙰𝚁}\mathtt{2}$ $\mathrm{𝚍𝚟𝚊𝚛}$
Purpose

Enforce the fact that the first variable is less than or equal to the second variable.

Example
$\left(1,8\right)$

The $\mathrm{𝚕𝚎𝚚}$ constraint holds since 1 is greater than or equal to 8.

Symmetries
• $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ can be replaced by any value $\le \mathrm{𝚅𝙰𝚁}\mathtt{2}$.

• $\mathrm{𝚅𝙰𝚁}\mathtt{2}$ can be replaced by any value $\ge \mathrm{𝚅𝙰𝚁}\mathtt{1}$.

Systems

leq in Choco, rel in Gecode, xlteqy in JaCoP, #=< in SICStus.

generalisation: $\mathrm{𝚕𝚎𝚚}_\mathrm{𝚌𝚜𝚝}$ ($\mathrm{𝚌𝚘𝚗𝚜𝚝𝚊𝚗𝚝}$ added).