Unformatted text preview: + 1 , x ) = a G 1 ( y, x, a H ( y, x ) A 2 ) , G 2 ( y, x, a H ( y, x ) A 1 ) A . . . by deFnition H ( y + 1 , x ) = a G 1 ( y, x, H 2 ( y, x )) , G 2 ( y, x, H 1 ( y, x )) A . . . by hypothesis H ( y + 1 , x ) = a H 1 ( y + 1 , x ) , H 2 ( y + 1 , x ) A . . . deFnition of H 1 and H 2 . Now, H 1 ( y, x ) = a H ( y, x ) A 1 so H 1 is primitive recursive, and H 2 ( y, x ) = a H ( y, x ) A 2 so H 2 is primitive recursive. 1...
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 Spring '08
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 Recursion, Primitive recursive function, H1

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