reserve x,y,z for set;
reserve f,f1,f2,f3 for FinSequence,
  p,p1,p2,p3 for set,
  i,k for Nat;
reserve D for non empty set,
  p,p1,p2,p3 for Element of D,
  f,f1,f2 for FinSequence of D;

theorem Th77:
  f1 <> {} implies (f1^f2)/^1 = (f1/^1)^f2
proof
  assume f1 <> {};
  then consider p being Element of D, df1 being FinSequence of D such that
  p = f1.1 and
A1: f1 = <*p*>^df1 by FINSEQ_3:102;
  thus (f1^f2)/^1 = (<*p*>^(df1^f2))/^1 by A1,FINSEQ_1:32
    .= df1^f2 by Th45
    .= (f1/^1)^f2 by A1,Th45;
end;
