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 Th34:
  for m,n being non zero Nat st 6*m+1 is prime & 6*n+1 is prime &
  LP<=6n+1(m) = LP<=6n+1(n) holds m = n
  proof
    let m,n be non zero Nat such that
A1: 6*m+1 is prime & 6*n+1 is prime & LP<=6n+1(m) = LP<=6n+1(n);
    assume m <> n;
    then m < n or n < m by XXREAL_0:1;
    hence thesis by A1,Th33;
  end;
