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 Th1:
  (s/t)*(u*x)=(s*u)/t*x & (1/t)*(u*x)= u/t*x
proof
  thus (s/t)*(u*x) = ((s/t)*u)*x by EUCLID_4:4
    .= (s*u)/t*x by XCMPLX_1:74;
  thus (1/t)*(u*x) = ((1/t)*u)*x by EUCLID_4:4
    .= u/t*x by XCMPLX_1:99;
end;
