On the Many Sorted Closure Operator and the Many Sorted Closure System
نویسنده
چکیده
For simplicity, we adopt the following rules: i, x, I denote sets, A, M denote many sorted sets indexed by I, f denotes a function, and F denotes a many sorted function indexed by I. The scheme MSSUBSET deals with a set A , a non-empty many sorted set B indexed by A , a many sorted set C indexed by A , and a unary predicate P , and states that: If for every many sorted set X indexed by A holds X ∈ B iff X ∈ C and P [X ], then B ⊆ C for all values of the parameters. One can prove the following two propositions:
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