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
  Product<* a,b,c *> = a * b * c & Product<* a,b,c *> = a * (b * c)
proof
A1: Product<* a *> = a & Product<* c *> = c by FINSOP_1:11;
A2: Product<* a,b *> = a * b & Product<* b,c *> = b * c by FINSOP_1:12;
  <* a,b,c *> = <* a *> ^ <* b,c *> & <* a,b,c *> = <* a,b *> ^ <* c *> by
FINSEQ_1:43;
  hence thesis by A1,A2,FINSOP_1:5;
end;
