`FREEZE_THEN : thm_tactical`
STRUCTURE
SYNOPSIS
‘Freezes’ a theorem to prevent instantiation of its free variables.
DESCRIPTION
FREEZE_THEN expects a tactic-generating function f:thm->tactic and a theorem (A1 |- w) as arguments. The tactic-generating function f is applied to the theorem (w |- w). If this tactic generates the subgoal:
```    A0 ?- t
=========  f (w |- w)
A ?- t1
```
then applying FREEZE_THEN f (A1 |- w) to the goal (A0 ?- t) produces the subgoal:
```             A0 ?- t
===================  FREEZE_THEN f (A1 |- w)
A - {w}, A1 ?- t1
```
Since the term w is a hypothesis of the argument to the function f, none of the free variables present in w may be instantiated or generalized. The hypothesis is discharged by PROVE_HYP upon the completion of the proof of the subgoal.
FAILURE
Failures may arise from the tactic-generating function. An invalid tactic arises if the hypotheses of the theorem are not alpha-convertible to assumptions of the goal.
EXAMPLE
Given the goal ([ ``b < c``, ``a < b`` ], ``SUC a <= c``), and the specialized variant of the theorem LESS_TRANS:
```   th = |- !p. a < b /\ b < p ==> a < p
```
IMP_RES_TAC th will generate several unneeded assumptions:
```   {b < c, a < b, a < c, !p. c < p ==> b < p, !a'. a' < a ==> a' < b}
?- SUC a <= c
```
which can be avoided by first ‘freezing’ the theorem, using the tactic
```   FREEZE_THEN IMP_RES_TAC th
```
This prevents the variables a and b from being instantiated.
```   {b < c, a < b, a < c} ?- SUC a <= c
```

USES
Used in serious proof hacking to limit the matches achievable by resolution and rewriting.
SEEALSO