for S being locally_directed OrderSortedSign
for X being V2() ManySortedSet of S
for t being Element of TS (DTConOSA X) holds
( ( for s being Element of S holds
( t in the Sorts of (ParsedTermsOSA X) . s iff [t,s] in (PTClasses X) . t ) ) & ( for s being Element of S
for y being Element of TS (DTConOSA X) st [y,s] in (PTClasses X) . t holds
[t,s] in (PTClasses X) . y ) )