theorem
  for Y for f,g be Y-valued Function st f c= g
  for x st x in dom f holds f/.x = g/.x
proof let Y; let f,g be Y-valued Function;
    assume
A1: f c= g;
    then
A2: dom f c= dom g by GRFUNC_1:2;
    let x;
    assume
A3: x in dom f;
    then f.x = g.x by A1,GRFUNC_1:2;
    then f/.x = (g qua Function).x by A3,PARTFUN1:def 6;
    hence thesis by A2,A3,PARTFUN1:def 6;
end;
