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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="b"><NAME>Marked_b</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>c</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>v</NAME></SYMBOL><SYMBOL arity="1" unmarked="c"><NAME>Marked_c</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>u</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>a</NAME></SYMBOL><SYMBOL arity="1" unmarked="d"><NAME>Marked_d</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>d</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>b</NAME></SYMBOL><SYMBOL arity="1" unmarked="v"><NAME>Marked_v</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>e</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>d(x)</LHS><RHS>e(u(x))</RHS></RULE><RULE><LHS>d(u(x))</LHS><RHS>c(x)</RHS></RULE><RULE><LHS>c(u(x))</LHS><RHS>b(x)</RHS></RULE><RULE><LHS>v(e(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>b(u(x))</LHS><RHS>a(e(x))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>d(x)</LHS><RHS>e(u(x))</RHS></RULE><RULE><LHS>d(u(x))</LHS><RHS>c(x)</RHS></RULE><RULE><LHS>c(u(x))</LHS><RHS>b(x)</RHS></RULE><RULE><LHS>v(e(x))</LHS><RHS>x</RHS></RULE><RULE><LHS>b(u(x))</LHS><RHS>a(e(x))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_d(u(x))</LHS><RHS>Marked_c(x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_c(u(x))</LHS><RHS>Marked_b(x)</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><EDGE end="0" start="1"/></DAG></CRITERION></PROPERTY></PROPERTY></PROOF>
