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Sk :S Pi}' On a Yi+l = Yi+adfYi, i.e.: Yi+l Yi + ad f(Yi-l EB sp{ad~YIe ,
1 :Sk :S Pi} La somme n'étant pas forcément directe, on en déduit que dimYi+l :S dimYi + Pi, i.e, Pi+l :S Pi· La démonstration est similaire pour les indices ri ,
(respectivement Qi+! = Qi) pour un entier i donné, alors pour tout k 2' : i, on a ,
D'après la Proposition B.2, Pie= 0 pour tout k 2' :: i + 1. La conclusion s'en suit ,
C Qi+l Démonstration: Montrons d'abord que si Ll est un distribution quelconque, adfK C Ll + adfLl 0, 11; E Ll, l:S;i:S;v+l} Montrons par récurrence sur v que adfadv, ... ad v?V ,
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