 reserve a for non empty set;
 reserve b, x, o for object;
reserve R for right_zeroed add-associative right_complementable Abelian
  well-unital distributive associative non trivial non trivial doubleLoopStr;

theorem Th20:
    Leading-Monomial(1_1(R)) = 1_1(R)
    proof
A1:   1 in dom(0_.(R));
A2:   len 1_1(R) = 1+1 by NIVEN:20;
      Leading-Monomial(1_1(R))
      = 0_.(R)+*(len(1_1(R))-'1,(1_1(R)).(len(1_1(R))-'1)) by POLYNOM4:11
      .= 1_1(R) by A2,A1,FUNCT_7:31;
      hence thesis;
    end;
