reserve Al for QC-alphabet;
reserve i,j,n,k,l for Nat;
reserve a for set;
reserve T,S,X,Y for Subset of CQC-WFF(Al);
reserve p,q,r,t,F,H,G for Element of CQC-WFF(Al);
reserve s for QC-formula of Al;
reserve x,y for bound_QC-variable of Al;
reserve f,g for FinSequence of [:CQC-WFF(Al),Proof_Step_Kinds:];

theorem
  (p => q) => ('not'(q '&' r) => 'not'(p '&' r)) is valid
proof
 (p => q) => ('not'(q '&' r) => 'not'(p '&' r)) in TAUT(Al)
  proof
    TAUT(Al) is being_a_theory by Th11;
    hence thesis;
  end;
  hence thesis;
end;
