reserve i,j,k for Nat;
reserve K for non empty addLoopStr,
  a for Element of K,
  p for FinSequence of the carrier of K,
  R for Element of i-tuples_on the carrier of K;
reserve K for left_zeroed right_zeroed add-associative right_complementable
  non empty addLoopStr,
  R,R1,R2 for Element of i-tuples_on the carrier of K;
reserve K for non empty addLoopStr,
  a1,a2 for Element of K,
  p1,p2 for FinSequence of the carrier of K,
  R1,R2 for Element of i-tuples_on the carrier of K;

theorem
  (i|->a1) - (i|->a2) = i|->(a1-a2)
proof
  thus (i|->a1) - (i|->a2) = i|->((diffield(K)).(a1,a2)) by FINSEQOP:17
    .= i|->(a1-a2) by Th11;
end;
