SYNOPSIS

Add an assumption with a named label to a goal.

DESCRIPTION

Given a theorem th, the tactic LABEL_TAC "name" th will add th as a new hypothesis, just as ASSUME_TAC does, but will also give it name as a label. The name will show up when the goal is printed, and can be used to refer to the theorem in tactics like USE_THEN and REMOVE_THEN.

FAILURE CONDITIONS

Never fails, though may be invalid if the theorem has assumptions that are not a subset of those in the goal, up to alpha-equivalence.

EXAMPLE

Suppose we want to prove that a binary relation <<= that is antisymmetric and has a strong wellfoundedness property is also total and transitive, and hence a wellorder:

  # g `(!x y. x <<= y /\ y <<= x ==> x = y) /\
       (!s. ~(s = {}) ==> ?a:A. a IN s /\ !x. x IN s ==> a <<= x)
       ==> (!x y. x <<= y \/ y <<= x) /\
           (!x y z. x <<= y /\ y <<= z ==> x <<= z)`;;

We might start by putting the two hypotheses on the assumption list with intuitive names:

  # e(DISCH_THEN(CONJUNCTS_THEN2 (LABEL_TAC "antisym") (LABEL_TAC "wo")));;
  val it : goalstack = 1 subgoal (1 total)

   0 [`!x y. x <<= y /\ y <<= x ==> x = y`] (antisym)
   1 [`!s. ~(s = {}) ==> (?a. a IN s /\ (!x. x IN s ==> a <<= x))`] (wo)

  `(!x y. x <<= y \/ y <<= x) /\ (!x y z. x <<= y /\ y <<= z ==> x <<= z)`

Now we break down the goal a bit

  # e(REPEAT STRIP_TAC);;
  val it : goalstack = 2 subgoals (2 total)

   0 [`!x y. x <<= y /\ y <<= x ==> x = y`] (antisym)
   1 [`!s. ~(s = {}) ==> (?a. a IN s /\ (!x. x IN s ==> a <<= x))`] (wo)
   2 [`x <<= y`]
   3 [`y <<= z`]

  `x <<= z`

   0 [`!x y. x <<= y /\ y <<= x ==> x = y`] (antisym)
   1 [`!s. ~(s = {}) ==> (?a. a IN s /\ (!x. x IN s ==> a <<= x))`] (wo)

  `x <<= y \/ y <<= x`

We want to specialize the wellordering assumption to an appropriate set for each case, and we can identify it using the label wo; the problem is then simple set-theoretic reasoning:

  # e(USE_THEN "wo" (MP_TAC o SPEC `{x:A,y:A}`) THEN SET_TAC[]);;
  ...
  val it : goalstack = 1 subgoal (1 total)

   0 [`!x y. x <<= y /\ y <<= x ==> x = y`] (antisym)
   1 [`!s. ~(s = {}) ==> (?a. a IN s /\ (!x. x IN s ==> a <<= x))`] (wo)
   2 [`x <<= y`]
   3 [`y <<= z`]

  `x <<= z`

Similarly for the other one:

  # e(USE_THEN "wo" (MP_TAC o SPEC `{x:A,y:A,z:A}`) THEN ASM SET_TAC[]);;
  ...
  val it : goalstack = No subgoals

USES

Convenient for referring to an assumption explicitly, just as in mathematics books one sometimes marks a theorem with an asterisk or dagger, then refers to it using that symbol.

COMMENTS

There are other ways of identifying assumptions than by label, but they are not always convenient. For example, explicitly doing ASSUME `asm` is cumbersome if asm is large, and using its number in the assumption list can make proofs very brittle under later changes.