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Moreover: the reduction rules of the are easy theorems of To show this, we need another remarkable fact concerning namely, that the use of definite articles is available in it: (where is a new variable, not occurring in Here (which is a valid term of by clauses 6 and 2 in the definition of intuitively denotes the intersection of all such that In particular: if there exists a unique such that then denotes that Indeed, it can easily be proved6 that It should again be emphasized, however, that is always meaningful, and denotes if there is no set which satisfies and the intersection of all the sets which satisfy in case there is more than one such set7.
The current usage of these files in our system is described in the next section. 6 Emacs Parsing, Presentation and Browsing of the Generated Mizar Abstracts As already mentioned, the Emacs parser of the text/mmlquery format is just a customization of the unified Emacs mechanism for formatted files, which is also used for the text/enriched format. This customization is quite simple and takes only about 200 lines of the Emacs Lisp code. The parser uses the annotations from a given GAB and produces internal information necessary for presentation and browsing.
We say that is a prefixtree (simply, a prefix) of if can be obtained from t by pruning subtrees (replaced by a special “empty” tree this is equivalent to the following definition Definition 4. The set by the following rules: if of prefixes of a tree (a first order term) for any tree and for is defined then Example 6. Consider the goal The set of prefixes (neglecting variables) is In particular, we cannot have a prefix containing S but not nor a prefix containing 0 but not S. Any matching goal must satisfy the same condition, thus imposing to have equality in MainConclusion, the set of exactly constraint for is shown in the following table: Efficient Retrieval of Mathematical Statements 7 27 Mixing Exactly Constraint and Atleast Constraints When, even restricting to prefixes, the total number of exactly constraints is too big to allow a feasible computation, we may always employ exactly constraints up to a given number of occurrences, and then requiring atleast constraints for all possible subsets of constants.