reserve FS for non empty doubleLoopStr;
reserve F for Field;
reserve R for Abelian add-associative right_zeroed right_complementable non
  empty addLoopStr,
  x, y, z for Scalar of R;
reserve SF for Skew-Field,
  x, y, z for Scalar of SF;

theorem Th6:
  for SF being non degenerated almost_left_invertible associative
add-associative right_zeroed right_complementable well-unital distributive non
  empty doubleLoopStr, x being Element of SF holds x<>0.SF implies ex y being
  Element of SF st x*y = 1.SF
proof
  let SF be non degenerated almost_left_invertible associative add-associative
  right_zeroed right_complementable well-unital right_unital distributive non
  empty doubleLoopStr, x be Element of SF;
  assume x<>0.SF;
  then consider y be Element of SF such that
A1: y*x = 1.SF by VECTSP_1:def 9;
  take y;
  y<>0.SF by A1;
  then consider z be Element of SF such that
A2: z*y = 1.SF by VECTSP_1:def 9;
  z = z*(y*x) by A1
    .= 1.SF*x by A2,GROUP_1:def 3
    .= x;
  hence thesis by A2;
end;
