reserve a,b,p,k,l,m,n,s,h,i,j,t,i1,i2 for natural Number;

theorem
  n mod k < k - 1 implies (n+1) mod k = (n mod k) + 1
proof
  assume n mod k < k - 1;
  then
A1: (n mod k) + 1 < k by XREAL_1:20;
  (n+1) mod k = ((n mod k)+1) mod k by Th22;
  hence thesis by A1,Th24;
end;
