### 2.6.8. Hard version

Constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ is a hard version of constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ (i.e., constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ is a soft variant of constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$).

EXAMPLE: As an example, constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}=$ $\mathrm{𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝}$ is a hard version of constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}=$ $\mathrm{𝚜𝚘𝚏𝚝}_\mathrm{𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝}$, which restricts the minimum number of variables that should be assigned differently in order that all variables take a distinct value.