  A numeral system is a sequence of an infinite different closed normal
$\lambda$-terms which has closed $\lambda$-terms for successor and zero test. A
numeral system is said adequate iff it has a closed $\lambda$-term for
predecessor. A storage operator for a numeral system is a closed $\lambda$-term
which simulate "call-by-value" in the context of a "call-by-name" strategy. E.
Tronci conjectured the following result : a numeral system is adequate if it
has a storage operator. This paper gives a negative answer to this conjecture
for the numeral systems typable in the J.-Y. Girard type system F. The E.
Tronci's conjecture remains open in pure $\lambda$-calculus.
