MATCH_MP_TAC : thm_tactic

SYNOPSIS

Reduces the goal using a supplied implication, with matching.

DESCRIPTION

When applied to a theorem of the form

   A' |- !x1...xn. s ==> t

MATCH_MP_TAC produces a tactic that reduces a goal whose conclusion t' is a substitution and/or type instance of t to the corresponding instance of s. Any variables free in s but not in t will be existentially quantified in the resulting subgoal:

     A ?- t'
  ======================  MATCH_MP_TAC (A' |- !x1...xn. s ==> t)
     A ?- ?z1...zp. s'

where z1, ..., zp are (type instances of) those variables among x1, ..., xn that do not occur free in t. Note that this is not a valid tactic unless A' is a subset of A.

EXAMPLE

The following goal might be solved by case analysis:

  # g `!n:num. n <= n * n`;;

We can ``manually'' perform induction by using the following theorem:

  # num_INDUCTION;;
  val it : thm = |- !P. P 0 /\ (!n. P n ==> P (SUC n)) ==> (!n. P n)

which is useful with MATCH_MP_TAC because of higher-order matching:

  # e(MATCH_MP_TAC num_INDUCTION);;
  val it : goalstack = 1 subgoal (1 total)

  `0 <= 0 * 0 /\ (!n. n <= n * n ==> SUC n <= SUC n * SUC n)`

The goal can be finished with ARITH_TAC.

FAILURE CONDITIONS

Fails unless the theorem is an (optionally universally quantified) implication whose consequent can be instantiated to match the goal.