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

theorem Th18:
  for x,y,z being Element of REAL st x <> 0 & *(x,y) = 1 & *(x,z)
  = 1 holds y = z
proof
  let x,y,z be Element of REAL;
  assume that
A1: x <> 0 and
A2: *(x,y) = 1 and
A3: *(x,z) = 1;
  thus y = inv x by A1,A2,Def4
    .= z by A1,A3,Def4;
end;
