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 Th10:
  m < n implies <=6n+1(m) c< <=6n+1(n)
  proof
    assume
A1: m < n;
    hence <=6n+1(m) c= <=6n+1(n) by Th9;
    6*m < 6*n by A1,XREAL_1:68;
    then 6*m+1 < 6*n+1 by XREAL_1:8;
    then not 6*n+1 in <=6n+1(m) by Th7;
    hence thesis;
  end;
