HOL: Reference

DISCH_THEN

Thm_cont.DISCH_THEN : (thm_tactic -> tactic)

Undischarges an antecedent of an implication and passes it to a theorem-tactic.

DISCH_THEN removes the antecedent and then creates a theorem by ASSUMEing it. This new theorem is passed to the theorem-tactic given as DISCH_THEN's argument. The consequent tactic is then applied. Thus:

   DISCH_THEN f (asl, t1 ==> t2) = f(ASSUME t1) (asl,t2)

For example, if

    A ?- t
   ========  f (ASSUME u)
    B ?- v

then

    A ?- u ==> t
   ==============  DISCH_THEN f
       B ?- v

Note that DISCH_THEN treats ~u as u ==> F.

Failure

DISCH_THEN will fail for goals which are not implications or negations.

Example

The following shows how DISCH_THEN can be used to preprocess an antecedent before adding it to the assumptions.

    A ?- (x = y) ==> t
   ====================  DISCH_THEN (ASSUME_TAC o SYM)
     A u {y = x} ?- t

In many cases, it is possible to use an antecedent and then throw it away:

    A ?- (x = y) ==> t x
   ======================  DISCH_THEN (\th. PURE_REWRITE_TAC [th])
          A ?- t y

See also

Thm.DISCH, Drule.DISCH_ALL, Tactic.DISCH_TAC, Drule.NEG_DISCH, Tactic.FILTER_DISCH_TAC, Tactic.FILTER_DISCH_THEN, Tactic.STRIP_TAC, Drule.UNDISCH, Drule.UNDISCH_ALL, Tactic.UNDISCH_TAC