ASM_INT_ARITH_TAC : tactic

SYNOPSIS

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

DESCRIPTION

The tactic ASM_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. Unlike plain INT_ARITH_TAC, ASM_INT_ARITH_TAC uses any assumptions that are not universally quantified as additional hypotheses.

FAILURE CONDITIONS

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

EXAMPLE

This example illustrates how ASM_INT_ARITH_TAC uses assumptions while INT_ARITH_TAC does not. Of course, this is for illustration only: plain INT_ARITH_TAC would solve the entire goal before application of STRIP_TAC.

  # g `!x y:int. x <= y /\ &2 * y <= &2 * x + &1 ==> x = y`;;
  val it : goalstack = 1 subgoal (1 total)

  `!x y. x <= y /\ &2 * y <= &2 * x + &1 ==> x = y`

  # e(REPEAT STRIP_TAC);;
  val it : goalstack = 1 subgoal (1 total)

    0 [`x <= y`]
    1 [`&2 * y <= &2 * x + &1`]

  `x = y`

  # e INT_ARITH_TAC;;
  Exception: Failure "linear_ineqs: no contradiction".
  # e ASM_INT_ARITH_TAC;;
  val it : goalstack = No subgoals