
theorem FirstAPPrime:
  for f being increasing Arithmetic_Progression st
    for i being Nat holds f.i is Prime holds
      f.1 > 2
  proof
    let f be increasing Arithmetic_Progression;
    assume
A1: for i being Nat holds f.i is Prime;
A2: f.1 > f.0 by SEQM_3:1;
    f.0 is Prime by A1; then
B2: f.0 > 1 by INT_2:def 4;
    reconsider f0 = f.0 as Prime by A1;
    f0 >= 1 + 1 by B2,NAT_1:13;
    hence thesis by A2,XXREAL_0:2;
  end;
