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:];

theorem
  x+y = [x`1_3+y`1_3,x`2_3+y`2_3,x`3_3+y`3_3] by Def1;
