reserve x,y,X,Y for set,
  k,l,n for Nat,
  i,i1,i2,i3,j for Integer,
  G for Group,
  a,b,c,d for Element of G,
  A,B,C for Subset of G,
  H,H1,H2, H3 for Subgroup of G,
  h for Element of H,
  F,F1,F2 for FinSequence of the carrier of G,
  I,I1,I2 for FinSequence of INT;

theorem Th8:
  for G being unital non empty multMagma holds Product <*> the
  carrier of G = 1_G
proof
  let G be unital non empty multMagma;
  set g = the multF of G;
  len <*> the carrier of G = 0 & g is having_a_unity;
  hence Product <*> the carrier of G = the_unity_wrt g by FINSOP_1:def 1
    .= 1_G by GROUP_1:22;
end;
