### 2.5.10. Implies

If constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ holds and if all restrictions of constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ hold then constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ also holds. Note that we also consider all the implications depicted in the implication graphs mentioned in the tables associated with the normalised signature tree of global constraints arguments. For an example of such table see Table 3.5.1.

EXAMPLE: As an example, constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}=$ $\mathrm{𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝}$ implies constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}=$ $\mathrm{𝚗𝚘𝚝}_\mathrm{𝚊𝚕𝚕}_\mathrm{𝚎𝚚𝚞𝚊𝚕}$. Note that the case of an $\mathrm{𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝}$ constraint with one single variable does not imply a $\mathrm{𝚗𝚘𝚝}_\mathrm{𝚊𝚕𝚕}_\mathrm{𝚎𝚚𝚞𝚊𝚕}$ constraint since its restriction (i.e., the number of variables of a $\mathrm{𝚗𝚘𝚝}_\mathrm{𝚊𝚕𝚕}_\mathrm{𝚎𝚚𝚞𝚊𝚕}$ constraint should be strictly greater than one) does not hold.