Prove equivalence under idempotence, symmetry and associativity of conjunction.
DESCRIPTION
CONJUNCTS_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 conjunction. That is, if t1 and t2 are two (different)
arbitrarily-nested conjunctions of the same set of terms, then
CONJUNCTS_AC (t1,t2) returns |- t1 = t2. Otherwise, it fails.
FAILURE
Fails if t1 and t2 are not equivalent, as described above.
EXAMPLE
- CONJUNCTS_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 conjunction. First sort the conjuncts in a term
t1 into the desired order (e.g., lexicographic order, for
normalization) to get a new term t2, then call
CONJUNCTS_AC(t1,t2).