set G = DTConOSA X;
set D = bool [:(TS (DTConOSA X)), the carrier of S:];
deffunc H₁( Symbol of (DTConOSA X)) -> Subset of [:(TS (DTConOSA X)), the carrier of S:] = @ $1;
deffunc H₂( Symbol of (DTConOSA X), set , FinSequence of bool [:(TS (DTConOSA X)), the carrier of S:]) -> Subset of [:(TS (DTConOSA X)), the carrier of S:] = @ ($1,$3);
thus ex f being Function of (TS (DTConOSA X)),(bool [:(TS (DTConOSA X)), the carrier of S:]) st
( ( for t being Symbol of (DTConOSA X) st t in Terminals (DTConOSA X) holds
f . (root-tree t) = H₁(t) ) & ( for nt being Symbol of (DTConOSA X)
for ts being FinSequence of TS (DTConOSA X) st nt ==> roots ts holds
f . (nt -tree ts) = H₂(nt, roots ts,f * ts) ) ) from DTCONSTR:sch 8(); :: thesis: verum