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;
reserve P for Permutation of dom f;

theorem Th24:
  |- f^<*p*> & |- f^<*p*>^<*q*> implies |- f^<*q*>
proof
A1: 1 <= len (f^<*p*>) by CALCUL_1:10;
  assume |- f^<*p*> & |- f^<*p*>^<*q*>;
  then |- Ant(f^<*p*>)^<*q*> by A1,CALCUL_1:45;
  hence thesis by CALCUL_1:5;
end;
