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 Th43:
  F is_immediate_constituent_of 'not' H iff F = H
proof
  thus F is_immediate_constituent_of 'not' H implies F = H
  proof
    'not' H is negative;
    then
A1: (@('not' H).1)`1 = 1 by QC_LANG1:18;
A2: not ex H1 st 'not' H = F '&' H1 or 'not' H = H1 '&' F
       by A1,QC_LANG1:18,def 20;
A3: not ex x st 'not' H = All(x,F) by A1,QC_LANG1:18,def 21;
    assume 'not' H = 'not' F or ( ex H1 st 'not' H = F '&' H1 or 'not' H = H1
    '&' F ) or ex x st 'not' H = All(x,F);
    hence thesis by A2,A3,FINSEQ_1:33;
  end;
  thus thesis;
end;
