Vladimir Timashov wrote:

 > I have some problem with proving in HOL4.

 > I have some subgoal:

 >     -- 1 <= i - 1
 >     ------------------------------------
 >       0.  ...
 >       1.  1 <= i
 >       2.  ...
 >       3.  ...
 >       4.  ...
 >       5.  ...
 >      : goalstack

 > So it seems to be trivial but I can't find the way to prove it in
 > HOL.  Could anybody help me with this please? What tactic should I
 > use? Or may be I should inform HOL in some way to use assumption #1?

Which theory are you working in?

In particular, I don't know what constant you're trying to write with
the symbol --.

In HOL4, the unary negation is written with ~ (the tilde character),
mimicking what is done in SML.

If you were trying to prove

   ``1 <= i ==> ~1 <= i - 1``

the appropriate tactic would depend on whether you were in the
integers or reals.

For the reals, I'd recommend:

   SRW_TAC [realSimps.REAL_ARITH_ss][]

For the integers:

   intLib.ARITH_TAC

There should be an analogue of REAL_ARITH_ss for the integers, but I
haven't written it yet.

Michael.


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