reserve x,y,y1,y2 for set,
  D for non empty set,
  d,d1,d2,d3 for Element of D,
  F,G,H,H1,H2 for FinSequence of D,
  f,f1,f2 for sequence of D,
  g for BinOp of D,
  k,n,i,l for Nat,
  P for Permutation of dom F;

theorem Th6:
  g is associative & (g is having_a_unity or len F >= 1) implies g
  "**" (<* d *> ^ F) = g.(d,g "**" F)
proof
A1: len<* d *> = 1 by FINSEQ_1:39;
  assume g is associative &( g is having_a_unity or len F >= 1);
  hence g "**" (<* d *> ^ F) = g.(g "**" <* d *>,g "**" F) by A1,Th5
    .= g.(d,g "**" F) by Lm4;
end;
