Abstract
Lattice theory with the meet and join operations is formulated as a system of rules of inference. The order of application of these rules can be permuted so that a subterm property follows: If an atomic formula is derivable from given atomic formulas by the rules, it has a derivation all terms of which are terms in the given formulas or the conclusion. A direct decision method for universal formulas in lattice theory with the meet and join operations follows.
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