Prove equivalence under idempotence, symmetry and associativity of disjunction.
DESCRIPTION
DISJUNCTS_AC takes a pair of terms (t1, t2) and proves
|- t1 = t2 if t1 and t2 are equivalent up to idempotence, symmetry and
associativity of disjunction. That is, if t1 and t2 are two (different)
arbitrarily-nested disjunctions of the same set of terms, then
DISJUNCTS_AC (t1,t2) returns |- t1 = t2. Otherwise, it fails.
FAILURE
Fails if t1 and t2 are not equivalent, as described above.
EXAMPLE
- DISJUNCTS_AC (Term `(P \/ Q) \/ R`, Term `R \/ (Q \/ R) \/ P`);
> val it = |- (P \/ Q) \/ R = R \/ (Q \/ R) \/ P : thm
USES
Used to reorder a disjunction. First sort the disjuncts in a term
t1 into the desired order (e.g., lexicographic order, for
normalization) to get a new term t2, then call
DISJUNCTS_AC(t1,t2).