`REAL_FIELD : term -> thm`

SYNOPSIS
Prove basic `field' facts over the reals.

DESCRIPTION
Most of the built-in HOL arithmetic decision procedures have limited ability to deal with inversion or division. REAL_FIELD is an enhancement of REAL_RING that has the same underlying method but first performs various case-splits, reducing a goal involving the inverse inv(t) of a term t to the cases where t = 0 where t * inv(t) = &1, repeatedly for all such t. After subsequently splitting the goal into normal form, REAL_RING (for algebraic reasoning) is applied; if this fails then REAL_ARITH is also tried, since this allows some t = 0 cases to be excluded by simple linear reasoning.

FAILURE CONDITIONS
Fails if the term is not provable using the methods described.

EXAMPLE
Here we do some simple algebraic simplification, ruling out the degenerate x = &0 case using the inequality in the antecedent.
```  # REAL_FIELD `!x. &0 < x ==> &1 / x - &1 / (x + &1) = &1 / (x * (x + &1))`;;
...
val it : thm = |- !x. &0 < x ==> &1 / x - &1 / (x + &1) = &1 / (x * (x + &1))
```