reserve F for Field,
  a,b,c,d,e,f,g,h for Element of F;
reserve x,y for Element of [:the carrier of F,the carrier of F,the carrier of
  F:];
reserve F for Field;
reserve PS for non empty ParStr;
reserve x for set,
  a,b,c,d,e,f,g,h,i,j,k,l for Element of [:the carrier of F,
  the carrier of F,the carrier of F:];
reserve a,b,c,d,p,q,r,s for Element of MPS(F);

theorem Th13:
  a,b '||' b,a
proof
  consider e,f such that
A1: [[e,f],[f,e]] = [[a,b],[b,a]];
A2: (e`2_3-f`2_3)*(f`3_3-e`3_3) - (f`2_3-e`2_3)*(e`3_3-f`3_3) = 0.F by Lm2;
  (e`1_3-f`1_3)*(f`2_3-e`2_3) - (f`1_3-e`1_3)*(e`2_3-f`2_3) = 0.F &
   (e`1_3-f`1_3)*(f`3_3-e`3_3) -
  (f`1_3 -e`1_3)*(e`3_3-f`3_3) = 0.F by Lm2;
  hence thesis by A1,A2,Th12;
end;
