<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="0" unmarked=""><NAME>apply</NAME></SYMBOL><SYMBOL arity="2" unmarked="app"><NAME>Marked_app</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>app</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>x</VAR><VAR>f</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>app(app(apply,f),x)</LHS><RHS>app(f,x)</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(apply,f),x)</LHS><RHS>app(f,x)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(apply,f),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><SCC num="0"><NODE ref="0"/></SCC></CCLIST></DAG></CRITERION><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(apply,f),x)</LHS><RHS>app(f,x)</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(apply,f),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_app</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_app(app(apply,f),x)</LHS><RHS>Marked_app(f,x)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>app(app(apply,f),x)</LHS><RHS>app(f,x)</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
