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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="0" unmarked="zprimes"><NAME>Marked_zprimes</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>nats</NAME></SYMBOL><SYMBOL arity="1" unmarked="nats"><NAME>Marked_nats</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>zprimes</NAME></SYMBOL><SYMBOL arity="3" unmarked="filter"><NAME>Marked_filter</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>filter</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>sieve</NAME></SYMBOL><SYMBOL arity="1" unmarked="sieve"><NAME>Marked_sieve</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>cons</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>N</VAR><VAR>M</VAR><VAR>X</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>filter(cons(X),0,M)</LHS><RHS>cons(0)</RHS></RULE><RULE><LHS>filter(cons(X),s(N),M)</LHS><RHS>cons(X)</RHS></RULE><RULE><LHS>sieve(cons(0))</LHS><RHS>cons(0)</RHS></RULE><RULE><LHS>sieve(cons(s(N)))</LHS><RHS>cons(s(N))</RHS></RULE><RULE><LHS>nats(N)</LHS><RHS>cons(N)</RHS></RULE><RULE><LHS>zprimes</LHS><RHS>sieve(nats(s(s(0))))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>filter(cons(X),0,M)</LHS><RHS>cons(0)</RHS></RULE><RULE><LHS>filter(cons(X),s(N),M)</LHS><RHS>cons(X)</RHS></RULE><RULE><LHS>sieve(cons(0))</LHS><RHS>cons(0)</RHS></RULE><RULE><LHS>sieve(cons(s(N)))</LHS><RHS>cons(s(N))</RHS></RULE><RULE><LHS>nats(N)</LHS><RHS>cons(N)</RHS></RULE><RULE><LHS>zprimes</LHS><RHS>sieve(nats(s(s(0))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_zprimes</LHS><RHS>Marked_sieve(nats(s(s(0))))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_zprimes</LHS><RHS>Marked_nats(s(s(0)))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="1"/></NONSCC><NONSCC num="1"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY></PROOF>
