reserve a,x,y for object, A,B for set,
  l,m,n for Nat;
reserve X,Y for set, x for object,
  p,q for Function-yielding FinSequence,
  f,g,h for Function;
reserve m,n,k for Nat, R for Relation;
reserve i,j for Nat;
reserve F for Function,
  e,x,y,z for object;

theorem Th101:
  x in dom F implies y in rng(F+*(x,y))
proof
  assume x in dom F;
  then x in dom (F+*(x,y)) & (F+*(x,y)).x = y by Th29,Th30;
  hence thesis by FUNCT_1:3;
end;
