reserve x,y,X,Y for set;
reserve C,D,E for non empty set;
reserve SC for Subset of C;
reserve SD for Subset of D;
reserve SE for Subset of E;
reserve c,c1,c2 for Element of C;
reserve d,d1,d2 for Element of D;
reserve e for Element of E;
reserve f,f1,g for PartFunc of C,D;
reserve t for PartFunc of D,C;
reserve s for PartFunc of D,E;
reserve h for PartFunc of C,E;
reserve F for PartFunc of D,D;

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;
