We show that when certain statements are provable in subsystems of constructive analysis using intuitionistic predicate calculus, related sequential statements are provable in weak classical subsystems. In particular, if a \Pi^1_2 sentence of a certain form is provable using E-HAω along with the axiom of choice and an independence of premise principle, the sequential form of the statement is provable in the classical system RCA. We obtain this and similar results using applications of modified realizability and the Dialectica interpretation. These results allow us to use techniques of classical reverse mathematics to demonstrate the unprovability of several mathematical principles in subsystems of constructive analysis.
J. L. Hirst and C. Mummert, Reverse mathematics and uniformity in proofs without excluded middle, Notre Dame Journal of Formal Logic 52 (2011), no. 2, 149-162. https://doi.org/10.1215/00294527-1306163