## 5.218. leq_cst

Origin

Arithmetic.

Constraint

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

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

Enforce the fact that the first variable is less than or equal to the sum of the second variable and the constant.

Example
$\left(5,2,4\right)$

The $\mathrm{𝚕𝚎𝚚}_\mathrm{𝚌𝚜𝚝}$ constraint holds since 5 is less than or equal to $2+4$.

Typical
 $\mathrm{𝙲𝚂𝚃}\mathtt{2}\ne 0$ $\mathrm{𝚅𝙰𝚁}\mathtt{1}<\mathrm{𝚅𝙰𝚁}\mathtt{2}+\mathrm{𝙲𝚂𝚃}\mathtt{2}$
Symmetries
• Arguments are permutable w.r.t. permutation $\left(\mathrm{𝚅𝙰𝚁}\mathtt{1}\right)$ $\left(\mathrm{𝚅𝙰𝚁}\mathtt{2},\mathrm{𝙲𝚂𝚃}\mathtt{2}\right)$.

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

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

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

specialisation: $\mathrm{𝚕𝚎𝚚}$ ($\mathrm{𝚌𝚘𝚗𝚜𝚝𝚊𝚗𝚝}$ set to 0).