reserve a,b,c,k,m,n for Nat;
reserve i,j,x,y for Integer;
reserve p,q for Prime;
reserve r,s for Real;

theorem Th9:
  m <= n implies <=6n+1(m) c= <=6n+1(n)
  proof
    assume
A1: m <= n;
    let x be object;
    assume
A2: x in <=6n+1(m);
    then reconsider x as Element of NAT;
A3: x <= 6*m+1 by A2,Th7;
    6*m <= 6*n by A1,XREAL_1:64;
    then 6*m+1 <= 6*n+1 by XREAL_1:6;
    hence thesis by A3,Th7,XXREAL_0:2;
  end;
