reserve Al for QC-alphabet;
reserve p,q,p1,p2,q1 for Element of CQC-WFF(Al),
  k for Element of NAT,
  f,f1,f2,g for FinSequence of CQC-WFF(Al),
  a,b,b1,b2,c,i,n for Nat;

theorem Th1:
  c in seq(a,b) iff 1+a <= c & c <= b+a
proof
A1: c in { m where m is Element of NAT: 1+a <= m & m <= b+a }
    iff ex m being Element of NAT st c = m & 1+a <= m & m <= b+a;
  c is Element of NAT by ORDINAL1:def 12;
  hence thesis by A1;
end;
