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 Th26:
  |- f^<*p*>^<*q*> & |- f^<*'not' p*>^<*q*> implies |- f^<*q*>
proof
  set f1 = f^<*p*>^<*q*>;
  set f2 = f^<*'not' p*>^<*q*>;
  assume
A1: |- f1 & |- f2;
A2: Ant(f2) = f^<*'not' p*> by CALCUL_1:5;
A3: Ant(f1) = f^<*p*> by CALCUL_1:5;
  then Suc(Ant(f1)) = p by CALCUL_1:5;
  then
A4: 'not' Suc(Ant(f1)) = Suc(Ant(f2)) by A2,CALCUL_1:5;
A5: 1 < len f1 & 1 < len f2 by CALCUL_1:9;
A6: Suc(f1) = q by CALCUL_1:5;
  then
A7: Suc(f1) = Suc(f2) by CALCUL_1:5;
A8: Ant(Ant(f1)) = f by A3,CALCUL_1:5;
  then Ant(Ant(f1)) = Ant(Ant(f2)) by A2,CALCUL_1:5;
  hence thesis by A1,A8,A4,A6,A5,A7,CALCUL_1:37;
end;
