That is, all the expressions we obtain from a given sequent have the same associated partial order.
It is a set of vectors of pairs, each pair consisting of a sequent and (possibly) a reducibility candidate.
However, in this case there is only one sort of sequent and, consequently, it is possible to have nested contexts.
A sequent is a pair (, a) consisting of an environment and a pseudoterm.
The operational semantics of this class of languages is given via a sequent-calculi presentation of the corresponding fragment of linear logic.
We associate with every sequent a quintuple of natural numbers.
The correspondence between sequent calculus derivations and natural deduction derivations is, however, not a one-one map, which causes some syntactic technicalities.
Such a sequent is not an axiom unless a formula in that matches the facts in exists.
