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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked="dfib"><NAME>Marked_dfib</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>dfib</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>dfib(s(s(x)),y)</LHS><RHS>dfib(s(x),dfib(x,y))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>dfib(s(s(x)),y)</LHS><RHS>dfib(s(x),dfib(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_dfib(s(s(x)),y)</LHS><RHS>Marked_dfib(s(x),dfib(x,y))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_dfib(s(s(x)),y)</LHS><RHS>Marked_dfib(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/><NODE ref="1"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>dfib(s(s(x)),y)</LHS><RHS>dfib(s(x),dfib(x,y))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_dfib(s(s(x)),y)</LHS><RHS>Marked_dfib(s(x),dfib(x,y))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_dfib(s(s(x)),y)</LHS><RHS>Marked_dfib(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_dfib</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_dfib(s(s(x)),y)</LHS><RHS>Marked_dfib(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_dfib(s(s(x)),y)</LHS><RHS>Marked_dfib(s(x),dfib(x,y))</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>dfib(s(s(x)),y)</LHS><RHS>dfib(s(x),dfib(x,y))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
