reserve X,Y for set;
reserve R for domRing-like commutative Ring;
reserve c for Element of R;

theorem Th10:
  for R being non degenerated domRing-like commutative Ring
  for a being Element of R holds a/1.R = a
proof
  let R be non degenerated domRing-like commutative Ring;
  let a be Element of R;
  set A = a/1.R;
  1.R * a = a;
  then
A1: 1.R <> 0.R & 1.R divides a;
  A = A * 1.R
    .= a by A1,Def4;
  hence thesis;
end;
