reserve A for QC-alphabet;
reserve sq for FinSequence,
  x,y,z for bound_QC-variable of A,
  p,q,p1,p2,q1 for Element of QC-WFF(A);
reserve s,t for bound_QC-variable of A;
reserve F,G,H,H1 for Element of QC-WFF(A);
reserve x,y,z for bound_QC-variable of A,
  k,n,m for Nat,
  P for ( QC-pred_symbol of k, A),
  V for QC-variable_list of k, A;

theorem Th42:
  not H is_immediate_constituent_of P!V
proof
  assume
A1: not thesis;
A2: P!V is atomic;
  then
A3: (@(P!V).1)`1 <> 3 by QC_LANG1:19;
A4: (@(P!V).1)`1 <> 2 by A2,QC_LANG1:19;
A5: not ex H1 being Element of QC-WFF(A) st P!V = H '&' H1 or P!V = H1 '&' H
            by A4,QC_LANG1:18,def 20;
  'not' H is negative;
  then
A6: (@('not' H).1)`1 = 1 by QC_LANG1:18;
  (@(P!V).1)`1 <> 1 by A2,QC_LANG1:19;
  then consider z such that
A7: P!V = All(z,H) by A1,A6,A5;
  All(z,H) is universal;
  hence contradiction by A3,A7,QC_LANG1:18;
end;
