for S being non empty non void ManySortedSign
for s being SortSymbol of S
for X being V5() ManySortedSet of the carrier of S
for x being Element of X . s
for t, t1 being Element of (Free (S,X))
for xi being Element of dom t st t . xi = [x,s] & the_sort_of t1 = s holds
t with-replacement (xi,t1) is Element of (Free (S,X)),(the_sort_of t)