reserve Al for QC-alphabet;
reserve b,c,d for set,
  X,Y for Subset of CQC-WFF(Al),
  i,j,k,m,n for Nat,
  p,p1,q,r,s,s1 for Element of CQC-WFF(Al),
  x,x1,x2,y,y1 for bound_QC-variable of Al,
  A for non empty set,
  J for interpretation of Al, A,
  v for Element of Valuations_in(Al,A),
  f1,f2 for FinSequence of CQC-WFF(Al),
  CX,CY,CZ for Consistent Subset of CQC-WFF(Al),
  JH for Henkin_interpretation of CX,
  a for Element of A,
  t,u for QC-symbol of Al;

theorem
  QuantNbr(Ex(x,p)) = QuantNbr(p)+1
proof
  QuantNbr(Ex(x,p)) = QuantNbr('not' All(x,'not' p)) by QC_LANG2:def 5
    .= QuantNbr(All(x,'not' p)) by CQC_SIM1:16
    .= QuantNbr('not' p) + 1 by CQC_SIM1:18;
  hence thesis by CQC_SIM1:16;
end;
