Generalized rules for quantifiers and the completeness of the intuitionistic operators &, ν, ⊃, λ, ∀, ε

In this paper, we develop a proof-theoretic framework for the treatment of arbitrary quantifiers binding m variables in n formulas. In particular, we motivate a schema for introduction and elimination rules for such quantifiers based on a concept of ‘derivation’ that allows rules as assumptions which may be discharged. With respect to this schema, the system of the standard operators of intuitionistic quantifier logic turns out to be complete.