reserve a,b,c for set;

theorem
  for D being non empty set,f being FinSequence of D st f=<*a,b,c*>
  holds f/^2=<*c*>
proof
  let D be non empty set,f be FinSequence of D;
  assume
A1: f = <*a,b,c*>;
  then reconsider a2=a,b2=b,c2=c as Element of D by Th10;
  f/^2 = (<*a2*>^<*b2,c2*>)/^(1+1) by A1,FINSEQ_1:43
    .= (<*a2*>^<*b2,c2*>)/^(len <*a2*> +1) by FINSEQ_1:40
    .= <*b2,c2*>/^1 by FINSEQ_5:36
    .= <*c2*> by FINSEQ_6:46;
  hence thesis;
end;
