theorem Th10:
  for G being add-associative Abelian non empty addLoopStr, x,y,
  z,t being Element of G holds (x+y)+(z+t) = (x+z)+(y+t)
proof
  let G be add-associative Abelian non empty addLoopStr, x,y,z,t be Element
  of G;
  thus (x+y)+(z+t) = x+(y+(z+t)) by RLVECT_1:def 3
    .= x+(z+(y+t)) by RLVECT_1:def 3
    .= (x+z)+(y+t) by RLVECT_1:def 3;
end;
