:: deftheorem defines @ OSAFREE:def 20 :
for S being OrderSortedSign
for X being V2() ManySortedSet of S
for nt being Symbol of (DTConOSA X)
for x being FinSequence of bool [:(TS (DTConOSA X)), the carrier of S:] holds @ (nt,x) = { [((Den (o2,(ParsedTermsOSA X))) . x2),s3] where o2 is OperSymbol of S, x2 is Element of Args (o2,(ParsedTermsOSA X)), s3 is Element of S : ( ex o1 being OperSymbol of S st
( nt = [o1, the carrier of S] & o1 ~= o2 & len (the_arity_of o1) = len (the_arity_of o2) & the_result_sort_of o1 <= s3 & the_result_sort_of o2 <= s3 ) & ex w3 being Element of the carrier of S * st
( dom w3 = dom x & ( for y being Nat st y in dom x holds
[(x2 . y),(w3 /. y)] in x . y ) ) ) } ;