reserve X1,x,y,z for set,
  n,m for Nat,
  X for non empty set;
reserve A,B for Event of Borel_Sets,
  D for Subset of REAL;
reserve Q for QM_Str;
reserve A1 for Element of Obs Q;
reserve s for Element of Sts Q;
reserve E for Event of Borel_Sets;
reserve ASeq for SetSequence of Borel_Sets;
reserve Q for Quantum_Mechanics;
reserve s for Element of Sts Q;
reserve x1 for Element of X1;
reserve Inv for Function of X1,X1;
reserve p,q,r,p1,q1 for Element of Prop Q;
reserve B,C for Subset of Prop Q;

theorem
  for B,C st B in Class PropRel Q & C in Class PropRel Q for p,q holds
  'not' p in C & 'not' q in C & p in B implies q in B
proof
  let B,C such that
A1: B in Class PropRel Q & C in Class PropRel Q;
  let p,q;
  'not'('not' p) = p & 'not'('not' q) =q;
  hence thesis by A1,Th11;
end;
