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 Th45:
  F is_immediate_constituent_of G '&' H iff F = G or F = H
proof
  thus F is_immediate_constituent_of G '&' H implies F = G or F = H
  proof
    G '&' H is conjunctive;
    then
A1: (@(G '&' H).1)`1 = 2 by QC_LANG1:18;
A2: G '&' H <> 'not' F by A1,QC_LANG1:18,def 19;
A3: not ex x st G '&' H = All(x,F) by A1,QC_LANG1:18,def 21;
    assume G '&' H = 'not' F or (ex H1 st G '&' H = F '&' H1 or G '&' H = H1
    '&' F) or ex x st G '&' H = All(x,F);
    hence thesis by A2,A3,Th2;
  end;
  assume F = G or F = H;
  hence thesis;
end;
