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A Logiweb sequent is a triple 
where 
is a finite set of premisses, 
is a finite set of side conditions, and 
is a result which holds if the given premisses and side conditions hold. is a term and and are finite sets of terms. Finite sets of terms are represented as lists without repetitions. Finite sets of terms can contain zero, one, or more terms.
A sequent represents the statement that if all terms in the set are provable and all side conditions in evaluate to 
then is provable. In other words, the sequent
represents that the statement
In particular, the sequent 
represents the statement that is provable.
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