METIS : thm list -> term -> thm
Attempt to prove a term by first-order proof search using Metis algorithm.
A call METIS[theorems] `tm` will attempt to prove tm using pure first-order
reasoning, taking theorems as the starting-point. It will usually either
prove it completely or run for an infeasibly long time, but it may sometimes
Although METIS is capable of some fairly non-obvious pieces of first-order
reasoning, and will handle equality adequately, it does purely logical
reasoning. It will exploit no special properties of the constants in the goal,
other than equality and logical primitives. Any properties that are needed must
be supplied explicitly in the theorem list, e.g. LE_REFL to tell it that <=
on natural numbers is reflexive, or REAL_ADD_SYM to tell it that addition on
real numbers is symmetric.
Sometimes the similar MESON rule is faster, especially on simpler problems.
- FAILURE CONDITIONS
Fails if the term is unprovable within the search bounds.
A typical application is to prove some elementary logical lemma for use inside
a tactic proof:
# METIS[num_CASES] `(!n. P n) <=> P 0 /\ (!n. P (SUC n))`;;
Generating simple logical lemmas as part of a large proof.
- SEE ALSO
ASM_METIS_TAC, MESON, METIS_TAC.