Note on Conditional Constructivity

In this note we provide a straightforward translation CpΓ(T) for sets of formulas T and HΓ(∃xA(x)) for existential formulas ∃xA(x) s.t. CpΓ(T) ⊢ HΓ (∃xA(x)) expresses "&existxA(x) is derivable constructively from T iff it is derivable at all".