reserve a,a1,a2,a3,b,b1,b2,b3,r,s,t,u for Real;
reserve n for Nat;
reserve x0,x,x1,x2,x3,y0,y,y1,y2,y3 for Element of REAL n;

theorem Th20:
  a*(x1+x2+x3)=a*x1+a*x2+a*x3
proof
  thus a*(x1+x2+x3) = a*(x1+x2)+a*x3 by EUCLID_4:6
    .= a*x1+a*x2+a*x3 by EUCLID_4:6;
end;
