\DOC POP_ASSUM
\TYPE {POP_ASSUM : thm_tactic -> tactic}
\SYNOPSIS
Applies tactic generated from the first element of a goal's assumption
list.
\KEYWORDS
theorem-tactic, assumption.
\DESCRIBE
When applied to a theorem-tactic and a goal, {POP_ASSUM} applies
the theorem-tactic to the {ASSUME}d first element of the assumption list,
and applies the resulting tactic to the goal without the first
assumption in its assumption list:
{
POP_ASSUM f ({A1,...,An} ?- t) = f (A1 |- A1) ({A2,...,An} ?- t)
}
\FAILURE
Fails if the assumption list of the goal is empty, or the theorem-tactic
fails when applied to the popped assumption, or if the resulting tactic
fails when applied to the goal (with depleted assumption list).
\COMMENTS
It is possible simply to use the theorem {ASSUME A1} as required rather
than
use {POP_ASSUM}; this will also maintain {A1} in the assumption list,
which is generally useful. In addition, this approach can equally well be
applied to assumptions other than the first.
There are admittedly times when {POP_ASSUM} is convenient, but it is most
unwise to use it if there is more than one assumption in the assumption
list, since this introduces a dependency on the ordering, which is
vulnerable
to changes in the HOL system.
Another point to consider is that if the relevant assumption has been
obtained
by {DISCH_TAC}, it is often cleaner to use {DISCH_THEN} with a theoremtactic.
For example, instead of:
{
DISCH_TAC THEN POP_ASSUM (\th. SUBST1_TAC (SYM th))
}
one might use
{
DISCH_THEN (SUBST1_TAC o SYM)
}
\EXAMPLE
The goal:
{
{4 = SUC x} ?- x = 3
}
can be solved by:
{
POP_ASSUM
(fn th => REWRITE_TAC[REWRITE_RULE[num_CONV (Term`4`, INV_SUC_EQ]
th]])
}
\USES
Making more delicate use of an assumption than rewriting or resolution
using it.
\SEEALSO
Tactical.ASSUM_LIST, Tactical.EVERY_ASSUM, Tactic.IMP_RES_TAC,
Tactical.POP_ASSUM_LIST, Rewrite.REWRITE_TAC.
\ENDDOC