reserve X for set, x,y,z for object,
  k,l,n for Nat,
  r for Real;
reserve i,i0,i1,i2,i3,i4,i5,i8,i9,j for Integer;
reserve r1,p,p1,g,g1,g2 for Real,
  Y for Subset of REAL;
reserve r, s for Real;
reserve i for Integer,
  a, b, r, s for Real;

theorem :: moved from CHORD:1
  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 Th3;
    hence n-1 is Nat;
    thus thesis by A1;
end;
