
theorem
  for n being odd Nat holds n div 2 = (n-1)/2
proof
  let n be odd Nat;
  consider k being Integer such that A1: n = 2*k+1 by ABIAN:1;
A2: (n-1)/2 = k by A1;
  (n-1)+1 = n; then
  n-1 <= n by INT_1:6; then
A3: k <= n/2 by A2,XREAL_1:72;
  (n/2) - (1/2) > (n/2) - 1 by XREAL_1:10;
  hence thesis by A1,A3,INT_1:def 6;
end;
