reserve A for QC-alphabet;
reserve i,j,k,l,m,n for Nat;
reserve a,b,e for set;
reserve t,u,v,w,z for QC-symbol of A;
reserve p,q,r,s for Element of CQC-WFF(A);
reserve x for Element of bound_QC-variables(A);
reserve ll for CQC-variable_list of k,A;
reserve P for QC-pred_symbol of k,A;
reserve f,h for Element of Funcs(bound_QC-variables(A),bound_QC-variables(A)),
  K,L for Element of Fin bound_QC-variables(A);

theorem Th26:
  SepVar(P!ll) = P!ll
proof
A1: dom ll = dom ll;
  rng ll c= bound_QC-variables(A) by RELAT_1:def 19;
  then reconsider lf = ll as PartFunc of NAT,bound_QC-variables(A) by A1,
RELSET_1:4;
A2: id bound_QC-variables(A)*lf = ll by PARTFUN1:7;
  thus SepVar (P!ll) =ATOMIC(P,ll).(index (P!ll),(id bound_QC-variables(A)))
by Def7
    .= P!ll by A2,Def5;
end;
