 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 Th24:
    for R be non degenerated Ring holds
    [#]Polynom-Ring R \ rng (canHom R) <> {}
    proof
      let R be non degenerated Ring;
reconsider p = 0_.(R) +*(1,1.R) as Polynomial of R;
      assume [#]Polynom-Ring R \ rng (canHom R) = {}; then
A2:   [#]Polynom-Ring R c= rng (canHom R) by XBOOLE_1:37;
      p in [#]Polynom-Ring R by POLYNOM3:def 10; then
      consider x be object such that
A4:   x in dom canHom R & (canHom R).x = p by A2,FUNCT_1:def 3;
      reconsider x0 = x as Element of R by A4;
A5:   p = x0|R by A4,RING_4:def 6
      .= 0_.(R) +*(0,x) by RING_4:def 5;
      1 in dom(0_.(R)); then
      1.R = (0_.(R) +*(0,x)).1 by A5,FUNCT_7:31
      .= (0_.(R)).1 by FUNCT_7:32 .= 0.R;
      hence contradiction;
    end;
