theorem Th10:
  CQC_Subst(ll,Sub) is CQC-variable_list of k,Al
proof
  reconsider ll as FinSequence of bound_QC-variables(Al) by SUBSTUT1:34;
  reconsider s = CQC_Subst(ll,Sub) as FinSequence of bound_QC-variables(Al);
A1: s = CQC_Subst(@ll,Sub) by SUBSTUT1:def 5;
  len ll = k by CARD_1:def 7;
  then len @ll = k by SUBSTUT1:def 4;
  then len s = k by A1,SUBSTUT1:def 3;
  then s is CQC-variable_list of k,Al by SUBSTUT1:34;
  hence thesis by A1,SUBSTUT1:def 4;
end;
