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F. ?. Let and F. So, Hence, there exist ? 1 , ? 2 and A such that ? 1 ? M : A ? F and ? 2 ? N : A and ? = ? 1 ? ? 2 . So ? ? ? 1 , and ? 1 ? ?. Hence, A ? F ? M ? . We also have A ? N ? . So we have F ? M ? @N ? . Conversely, let F ? M ? @N ? . There exists A such that A ? F ? M ? and A ? N ? . So there exists ? ? ? such that ? ? M : A ? F and there exists ? ? ? such that

F. Let, . M. ?x, and . @u, There exists A ? u such that A ? F ? ?x.M ? . So there exists ? ? ? such that ? ? ?x.M : A ? F . Hence, there exists U such that

F. So-we-have, F. Conversely, and . ?u, There exists ? ? (?, x ? u) such that then there exist ? 1 ? ? and A ? u such that ? = ? 1 , x : A (using Lemma 10.1) So we have ? 1 ? ?x.M : A ? F , and then A ? F ? ?x.M ? . Hence, we have F ? ?x.M ? @u, then for all y ? Dom(?), y = x (using Lemma 10.1). So ? ? ? and ?, x : ? ? M : F . Since u is a value

. Proof, By induction on the derivation of G S M : A. Let ? be a valuation