reserve A for QC-alphabet;
reserve k,n,m for Nat;
reserve P for QC-pred_symbol of A;
reserve F for Element of QC-WFF(A);
reserve Q for QC-pred_symbol of A;
reserve F, G for (Element of QC-WFF(A)), s for FinSequence;
reserve p for Element of QC-WFF(A);
reserve F for Element of QC-WFF(A);
reserve p for Element of QC-WFF(A);
reserve j,k for Nat;
reserve k for Nat;
reserve s,t,u,v for QC-symbol of A;

theorem
  for Y1,Y2 being non empty Subset of QC-symbols(A) st Y1 c= Y2 holds
    min Y2 <= min Y1
proof
  let Y1,Y2 be non empty Subset of QC-symbols(A) such that
A1: Y1 c= Y2;
  min Y1 in Y1 by Def35;
  hence min Y2 <= min Y1 by A1,Def35;
end;
