reserve Al for QC-alphabet;
reserve a,b,c,d for object,
  i,j,k,m,n for Nat,
  p,q,r for Element of CQC-WFF(Al),
  x,y,y0 for bound_QC-variable of Al,
  X for Subset of CQC-WFF(Al),
  A for non empty set,
  J for interpretation of Al,A,
  v,w for Element of Valuations_in(Al,A),
  Sub for CQC_Substitution of Al,
  f,f1,g,h,h1 for FinSequence of CQC-WFF(Al);
reserve fin,fin1 for FinSequence;
reserve PR,PR1 for FinSequence of [:set_of_CQC-WFF-seq(Al),Proof_Step_Kinds:];
reserve a for Element of A;

theorem Th30:
  Ant(f^<*VERUM(Al)*>) |= Suc(f^<*VERUM(Al)*>)
proof
  let A,J,v such that
  J,v |= Ant(f^<*VERUM(Al)*>);
  Suc(f^<*VERUM(Al)*>) = VERUM(Al) by Th5;
  hence thesis by VALUAT_1:32;
end;
