reserve x,y for Element of REAL;
reserve i,j,k for Element of NAT;
reserve a,b for Element of REAL;

theorem Th21:
  for x,y st *(x,y) = 0 holds x = 0 or y = 0
proof
  reconsider jj = 1 as Element of REAL by NUMBERS:19;
  let x,y such that
A1: *(x,y) = 0 and
A2: x <> 0;
A3: *(x, inv x) = 1 by A2,Def4;
  thus y = *(jj,y) by Th19
    .= *(*(x,y),inv x) by A3,Th13
    .= 0 by A1,Th12;
end;
