2.5.10. Implies

If constraint C π‘’π‘›π‘‘π‘Ÿπ‘¦ holds and if all restrictions of constraint C π‘Žπ‘™π‘ π‘œ hold then constraint C π‘Žπ‘™π‘ π‘œ 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 TableΒ 3.5.1.

EXAMPLE: As an example, constraint C π‘’π‘›π‘‘π‘Ÿπ‘¦ = πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš implies constraint C π‘Žπ‘™π‘ π‘œ = πš—πš˜πš_πšŠπš•πš•_πšŽπššπšžπšŠπš•. Note that the case of an πšŠπš•πš•πšπš’πšπšπšŽπš›πšŽπš—πš constraint with one single variable does not imply a πš—πš˜πš_πšŠπš•πš•_πšŽπššπšžπšŠπš• constraint since its restriction (i.e.,Β the number of variables of a πš—πš˜πš_πšŠπš•πš•_πšŽπššπšžπšŠπš• constraint should be strictly greater than one) does not hold.