1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | language Essence 1.3 $ prob003: quasigroup existence QG7 given n : int (1..100) letting g be domain int (0..n-1) find quasigroup : function ( total ) tuple (g,g) --> g such that $ Latin square-ness forAll v : g . injective (restrict(quasigroup,` tuple ( int (v),g)`)), forAll v : g . injective (restrict(quasigroup,` tuple (g, int (v))`)), $ qg7 (b*a)*b = a*(b*a) forAll a,b : g . quasigroup((quasigroup((b,a)),b)) = quasigroup((a,quasigroup((b,a)))) |