\DOC ARITH_TAC

\TYPE {ARITH_TAC : tactic}

\SYNOPSIS
Tactic for proving arithmetic goals needing basic rearrangement and linear
inequality reasoning only.

\DESCRIBE
{ARITH_TAC} will automatically prove goals that require basic algebraic
normalization and inequality reasoning over the natural numbers. For nonlinear
equational reasoning use {NUM_RING} and derivatives.

\FAILURE
Fails if the automated methods do not suffice.

\EXAMPLE
{
  # g `1 <= x /\ x <= 3 ==> x = 1 \/ x = 2 \/ x = 3`;;
  Warning: Free variables in goal: x
  val it : goalstack = 1 subgoal (1 total)

  `1 <= x /\ x <= 3 ==> x = 1 \/ x = 2 \/ x = 3`

  # e ARITH_TAC;;
  val it : goalstack = No subgoals
}

\USES
Solving basic arithmetic goals.

\SEEALSO
ARITH_RULE, ASM_ARITH_TAC, INT_ARITH_TAC, NUM_RING, REAL_ARITH_TAC.

\ENDDOC