`REAL_ARITH_TAC : tactic`

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

DESCRIPTION
The tactic REAL_ARITH_TAC is the tactic form of REAL_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:
```  # g `(x1 pow 2 + x2 pow 2 + x3 pow 2 + x4 pow 2) pow 2 =
((x1 + x2) pow 4 + (x1 + x3) pow 4 + (x1 + x4) pow 4 +
(x2 + x3) pow 4 + (x2 + x4) pow 4 + (x3 + x4) pow 4 +
(x1 - x2) pow 4 + (x1 - x3) pow 4 + (x1 - x4) pow 4 +
(x2 - x3) pow 4 + (x2 - x4) pow 4 + (x3 - x4) pow 4) / &6`;;
```
and here is one that holds by linear inequality reasoning:
```  # g `&26 < x / &2 ==> abs(x / &4 + &1) < abs(x / &3)`;;
```
so either goal is solved simply by:
```  # e REAL_ARITH_TAC;;
val it : goalstack = No subgoals
```