Soit $E$ un $\mathbb R$-espace vectoriel. Soient $A, B$ et $C$ trois sous-espaces vectoriels de $E$ vérifiant
\[A
\cap C \subset B \qquad
C\subset A+B \qquad \text{et} \qquad B \subset C .
\]
Montrer que: $~~B = C$.
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