reserve a, b, k, n, m for Nat,
  i for Integer,
  r for Real,
  p for Rational,
  c for Complex,
  x for object,
  f for Function;

theorem Th2:
  i <= r & r < i+1 implies [\ r /] = i
proof
  assume
A1: i <= r;
  assume r < i+1;
  then r - 1 < i+1 - 1 by XREAL_1:14;
  hence thesis by A1,INT_1:def 6;
end;
