 reserve a for non empty set;
 reserve b, x, o for object;
reserve R for right_zeroed add-associative right_complementable Abelian
  well-unital distributive associative non trivial non trivial doubleLoopStr;
reserve R for non degenerated comRing;

theorem Th25:
    for R be non degenerated Ring holds
    ex PR be non degenerated Ring, X be set, h be Function,
    G be Function of Polynom-Ring R,PR
    st R is Subring of PR & G is RingIsomorphism & id R = G*(canHom R) &
    X /\ [#]R = {} & h is one-to-one &
    dom h = [#]Polynom-Ring R \ rng (canHom R) & rng h = X &
    [#]PR = X \/ [#]R
    proof
      let R be non degenerated Ring;
      consider PR be Ring, X be set, h be Function,
      G be Function of Polynom-Ring R,PR such that
A1:   X /\ [#]R = {} & h is one-to-one &
      dom h = [#]Polynom-Ring R \ rng (canHom R) & rng h = X &
      [#]PR = X \/ [#]R & R is Subring of PR &
      G is RingIsomorphism & id R = G*(canHom R) by Th24, Th9;
A2:   1.PR = 1.R & 0.PR = 0.R by A1,C0SP1:def 3;
      PR is non degenerated Ring by A2,STRUCT_0:def 8;
      hence thesis by A1;
    end;
