
theorem Th19:
  for A being non-empty partial UAStr
  for R being Relation of the carrier of A holds R|^A c= R
proof
  let A be non-empty partial UAStr;
  let R be Relation of the carrier of A;
  let x,y be object;
  assume
A1: [x,y] in R|^A;
  then
A2: x in the carrier of A by ZFMISC_1:87;
  y in the carrier of A by A1,ZFMISC_1:87;
  hence thesis by A1,A2,Def5;
end;
