reserve m,k,j,j1,i,i1,i2,n for Nat,
  r,s for Real,
  C for compact non vertical non horizontal Subset of TOP-REAL 2,
  G for Go-board,
  p for Point of TOP-REAL 2;

theorem Th35:
  1 <= i implies [\ (i-2)/2|^(n-'m)+2 /] is Element of NAT
proof
  set i1 = [\ (i-2)/2|^(n-'m)+2 /];
  (i-2)/2|^(n-'m)+2-1 = (i-2)/2|^(n-'m)+(2-1);
  then
A1: (i-2)/2|^(n-'m)+1 < i1 by INT_1:def 6;
  n -' m + 1 >= 0 qua Nat + 1 & n-'m +1 <= 2|^(n-'m) by NEWTON:85,XREAL_1:6;
  then 0 qua Nat + 1 <= 2|^(n-'m) by XXREAL_0:2;
  then
A2: (-1)/1 <= (-1)/2|^(n-'m) by XREAL_1:120;
  assume 1 <= i;
  then 1-2 <= i-2 by XREAL_1:9;
  then (-1)/2|^(n-'m) <= (i-2)/2|^(n-'m) by XREAL_1:72;
  then -1 <= (i-2)/2|^(n-'m) by A2,XXREAL_0:2;
  then -1 + 1 <= (i-2)/2|^(n-'m) + 1 by XREAL_1:6;
  hence thesis by A1,INT_1:3;
end;
