theorem Th60:
  x in dom f & y in f.x implies x .--> y in sproduct f
proof
  assume that
A1: x in dom f and
A2: y in f.x;
A3: dom(x .--> y) c= dom f by A1,ZFMISC_1:31;
  now
    let z be object;
    assume z in dom(x .--> y);
    then z = x by TARSKI:def 1;
    hence (x .--> y).z in f.z by A2,FUNCOP_1:72;
  end;
  hence thesis by A3,Def9;
end;
