theorem
  for K being distributive commutative left_unital non empty
    doubleLoopStr,
      R being Element of i-tuples_on the carrier of K holds
     1.K * R = R
proof
  let K be distributive commutative left_unital non empty doubleLoopStr,
      R be Element of i-tuples_on the carrier of K;
A1: rng R c= the carrier of K by FINSEQ_1:def 4;
  the_unity_wrt the multF of K = 1.K by Th5;
  hence 1.K * R = (id the carrier of K)*R by FINSEQOP:44
    .= R by A1,RELAT_1:53;
end;
