### 2.6.13. Negation

If constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ holds then constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ does not hold. Reciprocally, if constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ holds then constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ does not hold. Note that constraints ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ and ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ must also have exactly the same parameters, but not necessarily the same parameters restrictions.

EXAMPLE: As an example, the constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}=$ $\mathrm{𝚗𝚘𝚝}_\mathrm{𝚊𝚕𝚕}_\mathrm{𝚎𝚚𝚞𝚊𝚕}$ (i.e., prevent all variables to be assigned the same value) is the negation of constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}=$ $\mathrm{𝚊𝚕𝚕}_\mathrm{𝚎𝚚𝚞𝚊𝚕}$ (i.e., enforce all variables to be assigned the same value).

Note that negation is also directly available for constraints which are defined by: