
theorem Th7:
  for L being non empty transitive RelStr, C being non empty
  Subset of L, X being Subset of C st ex_sup_of X,L & "\/"(X,L) in C holds
  ex_sup_of X,subrelstr C & "\/"(X,L) = "\/"(X,subrelstr C)
proof
  let L be non empty transitive RelStr, C be non empty Subset of L, X be
  Subset of C such that
A1: ex_sup_of X,L and
A2: "\/"(X,L) in C;
  the carrier of subrelstr C = C by YELLOW_0:def 15;
  hence thesis by A1,A2,YELLOW_0:64;
end;
