reserve i, x, I for set,
  A, B, M for ManySortedSet of I,
  f, f1 for Function;
reserve SF, SG for SubsetFamily of M;
reserve E, T for Element of Bool M;

theorem Th20:
  i in I & SF = {f,f1} implies |:SF:|.i = { f.i, f1.i }
proof
  assume that
A1: i in I and
A2: SF = {f,f1};
  dom |:SF:| = I & |:SF:| = |.SF.| by A2,Def3,PARTFUN1:def 2;
  hence thesis by A1,A2,Th19;
end;
