 reserve n,i,k,m for Nat;
 reserve p for Prime;

theorem P1NotPrime:
  for p being Prime st p > 2 holds
    p+1 is not Prime
  proof
    let p be Prime;
    assume
S1: p > 2; then
    p+1 > 2+1 by XREAL_1:8; then
S3: p+1 > 2 by XXREAL_0:2;
    p is odd by S1,PEPIN:17;
    hence thesis by S3,PEPIN:17;
  end;
