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 Th12:
  for n being non zero Nat holds 2 in <=6n+1(n) /\ SetPrimes
  proof
    let n be non zero Nat;
    0+1 <= n by NAT_1:13;
    then 6*1 <= 6*n by XREAL_1:64;
    then 6+1 <= 6*n+1 by XREAL_1:6;
    then 2 <= 6*n+1 by XXREAL_0:2;
    then
A1: 2 in <=6n+1(n);
    2 in SetPrimes by XPRIMES1:2,NEWTON:def 6;
    hence thesis by A1,XBOOLE_0:def 4;
  end;
