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 Th2:
  [a,b,c]+[f,g,h]=[a+f,b+g,c+h]
proof
  set abc = [a,b,c] ,fgh = [f,g,h];
A1: abc`3_3=c & fgh`1_3=f;
A2: fgh`2_3=g & fgh`3_3=h;
  abc`1_3=a & abc`2_3=b;
  hence thesis by A1,A2,Def1;
end;
