
theorem Th10:
  for a,b,c being Real st a * (- b) = c & a * c = b holds
  c = 0 & b = 0
  proof
    let a,b,c be Real;
    assume that
A1: a * (-b) = c and
A2: a * c = b;
    a * (- a * c) = c by A1,A2; then
A3: (-a * a) * c = c;
    thus c = 0
    proof
      assume c <> 0;
      then - a^2 = 1 by A3,XCMPLX_1:7;
      hence contradiction;
    end;
    hence b = 0 by A2;
  end;
