formal/hol/Help/ASSUME_TAC.doc

\DOC ASSUME_TAC

\TYPE {ASSUME_TAC : thm_tactic}

\SYNOPSIS
Adds an assumption to a goal.

\KEYWORDS
tactic, assumption.

\DESCRIBE
Given a theorem {th} of the form {A' |- u}, and a goal, {ASSUME_TAC th}
adds {u} to the assumptions of the goal.
{
         A ?- t
    ==============  ASSUME_TAC (A' |- u)
     A u {{u}} ?- t
}
\noindent Note that unless {A'} is a subset of {A}, this tactic is invalid. The
new assumption is unlabelled; for a named assumption use {LABEL_TAC}.

\FAILURE
Never fails.

\EXAMPLE
One can add an external theorem as an assumption if desired, for example so
that {ASM_REWRITE_TAC[]} will automatically apply it. But usually the theorem
is derived from some theorem-tactical, e.g. by discharging the antecedent of an
implication or doing forward inference on another assumption. For example iff
faced with the goal:
{
  # g `0 = x ==> f(2 * x) = f(x * f(x))`;;
}
\noindent one might not want to just do {DISCH_TAC} or {STRIP_TAC} because the
assumption will be {`0 = x`}. One can swap it first then put it on the
assumptions by:
{
  # e(DISCH_THEN(ASSUME_TAC o SYM));;
  val it : goalstack = 1 subgoal (1 total)

   0 [`x = 0`]

  `f (2 * x) = f (x * f x)`
}
\noindent after which the goal can very easily be solved:
{
  # e(ASM_REWRITE_TAC[MULT_CLAUSES]);;
  val it : goalstack = No subgoals
}

\USES
Useful as a parameter to various theorem-tacticals such as {X_CHOOSE_THEN},
{DISCH_THEN} etc. when it is simply desired to add the theorem that has been
deduced to the assumptions rather than used further at once.

\SEEALSO
ACCEPT_TAC, DESTRUCT_TAC, LABEL_TAC, STRIP_ASSUME_TAC.

\ENDDOC