reserve x,y,z, X,Y,Z for set,
  n for Element of NAT;
reserve A for set,
  D for non empty set,
  a,b,c,l,r for Element of D,
  o,o9 for BinOp of D,
  f,g,h for Function of A,D;
reserve G for non empty multMagma;
reserve A for non empty set,
  a for Element of A,
  p for FinSequence of A,
  m1,m2 for Multiset of A;
reserve p,q for FinSequence of A;
reserve fm for Element of finite-MultiSet_over A;
reserve a,b,c for Element of D;

theorem
  for G being unital non empty multMagma holds 1.bool G = {
  the_unity_wrt the multF of G}
proof
  let G be unital non empty multMagma;
  bool G = multLoopStr(#bool carr(G), op(G).:^2,{the_unity_wrt op(G)}#) by Def9
;
  hence thesis;
end;
