STRUCT_CASES_TAC

Tactic.STRUCT_CASES_TAC : thm_tactic

Performs very general structural case analysis.

When it is applied to a theorem of the form:

   th = A' |- ?y11...y1m. (x=t1) /\ (B11 /\ ... /\ B1k) \/ ... \/
                ?yn1...ynp. (x=tn) /\ (Bn1 /\ ... /\ Bnp)

in which there may be no existential quantifiers where a ‘vector’ of them is shown above, STRUCT_CASES_TAC th splits a goal A ?- s into n subgoals as follows:

                             A ?- s
   ===============================================================
    A u {B11,...,B1k} ?- s[t1/x] ... A u {Bn1,...,Bnp} ?- s[tn/x]

that is, performs a case split over the possible constructions (the ti) of a term, providing as assumptions the given constraints, having split conjoined constraints into separate assumptions. Note that unless A' is a subset of A, this is an invalid tactic.

Failure

Fails unless the theorem has the above form, namely a conjunction of (possibly multiply existentially quantified) terms which assert the equality of the same variable x and the given terms.

Example

Suppose we have the goal:

  ?- ~(l:(*)list = []) ==> (LENGTH l) > 0

then we can get rid of the universal quantifier from the inbuilt list theorem list_CASES:

   list_CASES = !l. (l = []) \/ (?t h. l = CONS h t)

and then use STRUCT_CASES_TAC. This amounts to applying the following tactic:

   STRUCT_CASES_TAC (SPEC_ALL list_CASES)

which results in the following two subgoals:

   ?- ~(CONS h t = []) ==> (LENGTH(CONS h t)) > 0

   ?- ~([] = []) ==> (LENGTH[]) > 0

Note that this is a rather simple case, since there are no constraints, and therefore the resulting subgoals have no assumptions.

Generating a case split from the axioms specifying a structure.

See also

Tactic.ASM_CASES_TAC, Tactic.BOOL_CASES_TAC, Tactic.COND_CASES_TAC, Tactic.DISJ_CASES_TAC