theorem Th9: :: OSAFREE:9

for S being OrderSortedSign
for X being non-empty ManySortedSet of S
for s being Element of S holds the Sorts of (ParsedTermsOSA X) . s = { a where a is Element of TS (DTConOSA X) : ( ex s1 being Element of S ex x being object st
( s1 <= s & x in X . s1 & a = root-tree [x,s1] ) or ex o being OperSymbol of S st
( [o, the carrier of S] = a . {} & the_result_sort_of o <= s ) ) }