let i be object ; :: according to PBOOLE:def 13 :: thesis: ( not i in the carrier of S or not (StabCl R) . i is empty )
assume i in the carrier of S ; :: thesis: not (StabCl R) . i is empty
then reconsider s = i as SortSymbol of S ;
set x = the Element of R . s;
R c= StabCl R by Def12;
then A2: R . s c= (StabCl R) . s ;
the Element of R . s in R . s ;
hence not (StabCl R) . i is empty by A2; :: thesis: verum