:: deftheorem defines associative ALTCAT_1:def 5 :
for I being non empty set
for G being ManySortedSet of [:I,I:]
for IT being BinComp of G holds
( IT is associative iff for i, j, k, l being Element of I
for f, g, h being set st f in G . (i,j) & g in G . (j,k) & h in G . (k,l) holds
(IT . (i,k,l)) . (h,((IT . (i,j,k)) . (g,f))) = (IT . (i,j,l)) . (((IT . (j,k,l)) . (h,g)),f) );