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Natural deduction systems for the lambda-cube?



Hi list,

I've been working a system of natural deduction that is a sort of a
natural deduction version for the systems in the \lambda-cube, and I
just realized that probably other people could have also attempted to
do that before me, and that I should take a look at their papers...

Anyone knows of any work in that direction?

  Thanks in advance, cheers,
    Eduardo Ochs
    http://angg.twu.net/
    ochs@math.mcgill.ca