## 5.150. eq_cst

Origin

Arithmetic.

Constraint

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

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 equal to the sum of the second variable and the constant.

Example
$\left(8,2,6\right)$

The $\mathrm{𝚎𝚚}_\mathrm{𝚌𝚜𝚝}$ constraint holds since 8 is equal to $2+6$.

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

• One and the same constant can be added to $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ and $\mathrm{𝚅𝙰𝚁}\mathtt{2}$.

• One and the same constant can be added to $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ and $\mathrm{𝙲𝚂𝚃}\mathtt{2}$.

Arg. properties
• Functional dependency: $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ determined by $\mathrm{𝚅𝙰𝚁}\mathtt{2}$ and $\mathrm{𝙲𝚂𝚃}\mathtt{2}$.

• Functional dependency: $\mathrm{𝚅𝙰𝚁}\mathtt{2}$ determined by $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ and $\mathrm{𝙲𝚂𝚃}\mathtt{2}$.

• Functional dependency: $\mathrm{𝙲𝚂𝚃}\mathtt{2}$ determined by $\mathrm{𝚅𝙰𝚁}\mathtt{1}$ and $\mathrm{𝚅𝙰𝚁}\mathtt{2}$.

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