Tactical.USE_SG

STRUCTURE

SYNOPSIS

Allows the user to use one subgoal to prove another

DESCRIPTION

In USE_SG_THEN ttac nu np, of the current goal list, subgoal number nu can be used in proving subgoal number np. Subgoal number nu is used as a lemma by ttac to simplify subgoal number np. That is, if subgoal number nu is A ?- u, subgoal number np is A1 ?- t1, and

    A1 ?- t1
   ==========  ttac (u |- u)
    A2 ?- t2

then the list-tactic USE_SG_THEN ttac nu np gives this same result (new subgoal(s)) for subgoal np.

This list-tactic will be invalid unless A is a subset of A1.

Note that in the interactive system, subgoals are printed in reverse order of their numbering.

FAILURE

USE_SG_THEN will fail ttac (u |- u) fails on subgoal number np, or if indices np or nu are out of range. Note that the subgoals in the current subgoal list are numbered starting from 1.

USES

Where two subgoals are similar and not easy to prove, one can be used to help prove the other.

EXAMPLE

Here subgoal 1 is assumed, so as to help in proving subgoal 2.

r \/ s
------------------------------------
  0.  p
  1.  q


r
------------------------------------
  0.  p
  1.  q

2 subgoals
:
   proof

> elt (USE_SG_THEN ASSUME_TAC 1 2) ;
OK..
2 subgoals:
val it =

r \/ s
------------------------------------
  0.  p
  1.  q
  2.  r


r
------------------------------------
  0.  p
  1.  q

2 subgoals
:
   proof

Here is an example where the assumptions differ. Subgoal 2 is used to solve subgoal 1, but the assumption p' of subgoal 2 remains to be proved. Without VALIDATE_LT, the list-tactic would be invalid.

r
------------------------------------
  0.  p'
  1.  q


r
------------------------------------
  0.  p
  1.  q

2 subgoals
:
   proof

> elt (VALIDATE_LT (USE_SG_THEN ACCEPT_TAC 2 1)) ;
OK..
2 subgoals:
val it =

r
------------------------------------
  0.  p'
  1.  q


p'
------------------------------------
  0.  p
  1.  q

2 subgoals
:
   proof

COMMENTS

Some users may expect the generated tactic to be ttac (A |- u), rather than ttac (u |- u).