
theorem Th5: :: EvenOdd04:
  for n being odd Nat st 1 <> n
  ex m being odd Nat st m+2 = n
proof
  let n being odd Nat;
A1: 1 <= n by ABIAN:12;
  assume 1 <> n;
  then 2*0+1 < n by A1,XXREAL_0:1;
  then 1+2 <= n by Th4;
  then 1+2-2 <= n-2 by XREAL_1:9;
  then n-2*1 in NAT by INT_1:3;
  then reconsider m = n-2 as odd Nat;
  take m;
  thus thesis;
end;
