. Shyp, as (t 1 , t 2 ) ? ? p , the conditions (i) and (ii) hold for the premise. By induction, the result follows

}. , ?. ?. , C. ?. , and ?. ??, For any (s 1 , s 2 ) ? ? p , the condition (i) gives us that there exists C 0 ? (? ? N {(s 1 ? s 2 )}) such that C 0, ? ? t 1 ), (? ? t 2 )} ? C) ? S, we have C 0 ? C ?? . Moreover, consider (t 1 , t 2 ). As ? ? N {(t 1 ? t 2 )} S, there exists C 0 ? S such that C 0 ? C ?? . Thus the condition (i) holds for the premise. Moreover, the condition (ii) holds straightforwardly for premise. By induction, the result follows. (Sdone): the result follows by the conditions (i) and (ii

?. Ms-c-s, Lemma 10.1.27 (Finiteness) Let C be a constraint-set and ?

?. Ms-c-s, Let C be a well-ordered normalized constraint-set and ? Then for all normalized constraint-set C ? ? S, C ? is well-ordered, Lemma 10.1.28

?. , S. , C. ??-?c-?-?-s-?.-?, and C. , nor C 2 ? C 1 . Moreover, we say S ? S ? if for all substitution ? such that

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