INT_ARITH_TAC : tactic

SYNOPSIS

Attempt to prove goal using basic algebra and linear arithmetic over the integers.

DESCRIPTION

The tactic INT_ARITH_TAC is the tactic form of INT_ARITH. Roughly speaking, it will automatically prove any formulas over the reals that are effectively universally quantified and can be proved valid by algebraic normalization and linear equational and inequality reasoning. See REAL_ARITH for more information about the algorithm used and its scope.

FAILURE CONDITIONS

Fails if the goal is not in the subset solvable by these means, or is not valid.

EXAMPLE

Here is a goal that holds by virtue of pure algebraic normalization:

  # prioritize_int();;
  val it : unit = ()

  # g `(x1 pow 2 + x2 pow 2 + x3 pow 2 + x4 pow 2) *
       (y1 pow 2 + y2 pow 2 + y3 pow 2 + y4 pow 2) =
       (x1 * y1 - x2 * y2 - x3 * y3 - x4 * y4) pow 2  +
       (x1 * y2 + x2 * y1 + x3 * y4 - x4 * y3) pow 2  +
       (x1 * y3 - x2 * y4 + x3 * y1 + x4 * y2) pow 2  +
       (x1 * y4 + x2 * y3 - x3 * y2 + x4 * y1) pow 2`;;

and here is one that holds by linear inequality reasoning:

  # g `!x y:int. abs(x + y) < abs(x) + abs(y) + &1`;;

so either goal is solved simply by:

  # e INT_ARITH_TAC;;
  val it : goalstack = No subgoals