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The constructive second-order proofs that we study are associated with inductive definitions on classes of finite structures, where each structure represents a database state. To an inductive definition of a predicate P on a class K corresponds a uniform proof of P i.e a function which for each structure U defines a proof of P in Udblp:conf/ijcai/Rougemont87 fatcat:ohknvjiuu5abhidwfy6pcrq4pe