theorem Th51: f c= g iff for x st x in dom f holds (x in dom g & f.x = g.x)
proof
defpred Q1[] means for x being object st x in dom f holds x in dom g;
defpred Q2[] means for x being object st x in dom f holds f.x=g.x;
Q1[] & Q2[] iff dom f c= dom g & Q2[];
hence thesis by GRFUNC_1:2;
end;
