theorem Th47:
   |.a1*b2-a2*b1.|<>0 & a2/b2 is irrational implies
   ex x,y be Element of INT st
   |.LF(a2,b2,c2).(x,y).|*|.LF(a1,b1,c1).(x,y).|<|.a1*b2-a2*b1.|/4 &
   |.LF(a2,b2,c2).(x,y).| < eps
   proof
     |.a2*b1-a1*b2.| = |.-(a1*b2-a2*b1).| .=|.a1*b2-a2*b1.| by COMPLEX1:52;
     hence thesis by Th46;
   end;
