reserve a,b,r for Real;
reserve A for non empty set;
reserve X,x for set;
reserve f,g,F,G for PartFunc of REAL,REAL;
reserve n for Element of NAT;

theorem Th11:
  F is_integral_of f,X implies X c= dom F
proof
  assume F is_integral_of f,X;
  then F in IntegralFuncs(f,X); then
  ex G be PartFunc of REAL,REAL st F = G & G is_differentiable_on X & G`|X
  = f|X by Def1;
  hence thesis;
end;
