### 2.6.12. Implies (items to collection)

Given two constraints ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ and ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ where:

• ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}$ has a single argument ${\mathrm{𝚊𝚛𝚐}}_{1}$ corresponding to a collection of $k$ items, each attribute of type $\mathrm{𝚒𝚗𝚝}$ or $\mathrm{𝚍𝚟𝚊𝚛}$.

• ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}$ has a single argument ${\mathrm{𝚊𝚛𝚐}}_{2}$ corresponding to a collection of collections of $\mathrm{𝚍𝚟𝚊𝚛}$, each of them having the same number of items $k$.

If constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}\left({\mathrm{𝚊𝚛𝚐}}_{1}\right)$ holds then constraint ${C}_{\mathrm{𝑎𝑙𝑠𝑜}}\left({\mathrm{𝚊𝚛𝚐}}_{2}\right)$ also holds.

EXAMPLE: As an example, we can go from constraint ${C}_{\mathrm{𝑒𝑛𝑡𝑟𝑦}}=$ $\mathrm{𝚌𝚒𝚛𝚌𝚞𝚒𝚝}$ to constraint $\mathrm{𝚕𝚎𝚡}_\mathrm{𝚊𝚕𝚕𝚍𝚒𝚏𝚏𝚎𝚛𝚎𝚗𝚝}$ if we create for each item “$\mathrm{𝚒𝚗𝚍𝚎𝚡}-i\mathrm{𝚜𝚞𝚌𝚌}-s$” of the $\mathrm{𝚌𝚒𝚛𝚌𝚞𝚒𝚝}$ constraint a collection $〈\mathrm{𝚟𝚊𝚛}-i,\mathrm{𝚟𝚊𝚛}-s〉$.