
theorem Th1:
  for n being non zero Nat holds n-1 is Nat & 1 <= n
proof
  let n be non zero Nat;
A1: 0+1 <= n by NAT_1:13;
  then 0+1-1 <= n-1 by XREAL_1:9;
  then n-1 in NAT by INT_1:3;
  hence n-1 is Nat;
  thus thesis by A1;
end;
