REWRITE_RULE : (thm list -> thm -> thm)
Rewrites a theorem including built-in tautologies in the list of rewrites.
Rewriting a theorem using REWRITE_RULE utilizes as rewrites two sets of theorems: the tautologies in the ML list implicit_rewrites and the ones supplied by the user. The rule searches top-down and recursively for subterms which match the left-hand side of any of the possible rewrites, until none of the transformations are applicable. There is no ordering specified among the set of rewrites.

Variants of this rule allow changes in the set of equations used: PURE_REWRITE_RULE and others in its family do not rewrite with the theorems in implicit_rewrites. Rules such as ASM_REWRITE_RULE add the assumptions of the object theorem (or a specified subset of these assumptions) to the set of possible rewrites.

The top-down recursive search for matches may not be desirable, as this may increase the number of inferences being made or may result in divergence. In this case other rewriting tools such as ONCE_REWRITE_RULE and GEN_REWRITE_RULE can be used, or the set of theorems given may be reduced.

See GEN_REWRITE_RULE for the general strategy for simplifying theorems in HOL using equational theorems.

Does not fail, but may diverge if the sequence of rewrites is non-terminating.
Used to manipulate theorems by rewriting them with other theorems. While resulting in high degree of automation, REWRITE_RULE can spawn a large number of inference steps. Thus, variants such as PURE_REWRITE_RULE, or other rules such as SUBST, may be used instead to improve efficiency.
HOL  Kananaskis-14