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We show that the uniform validity is equivalent to the non-uniform validity for Blass' semantics of [1]. We present a shorter proof (than that of [2]) of the completeness of the positive fragment of intuitionistic logic for this semantics, computability logic semantics, and the abstract resource semantics. 1. A. Blass, “A game semantics for linear logic”, Ann. Pure Appl. Logic, 56:1-3 (1992), 183–220. 2. G. Japaridze “The intuitionistic fragment of computability logic at the propositional level”, Ann. Pure Appl. Logic, 147:3 (2007), 187–227.