Geodesic
A growth of length of $\mathrm L$-derivationtrans formed into natural deduction
Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VIII, Tome 88 (1979), pp. 192-196 
S. V. Solov'ev. A growth of length of $\mathrm L$-derivationtrans formed into natural deduction. Zapiski Nauchnykh Seminarov POMI, Studies in constructive mathematics and mathematical logic. Part VIII, Tome 88 (1979), pp. 192-196. http://geodesic.mathdoc.fr/item/ZNSL_1979_88_a14/
@article{ZNSL_1979_88_a14,
     author = {S. V. Solov'ev},
     title = {A~growth of length of $\mathrm L$-derivationtrans formed into natural deduction},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {192--196},
     year = {1979},
     volume = {88},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_88_a14/}
}
TY  - JOUR
AU  - S. V. Solov'ev
TI  - A growth of length of $\mathrm L$-derivationtrans formed into natural deduction
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1979
SP  - 192
EP  - 196
VL  - 88
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1979_88_a14/
LA  - ru
ID  - ZNSL_1979_88_a14
ER  - 
%0 Journal Article
%A S. V. Solov'ev
%T A growth of length of $\mathrm L$-derivationtrans formed into natural deduction
%J Zapiski Nauchnykh Seminarov POMI
%D 1979
%P 192-196
%V 88
%U http://geodesic.mathdoc.fr/item/ZNSL_1979_88_a14/
%G ru
%F ZNSL_1979_88_a14

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $\varphi$ be a standard transformation [5] of Gentzen's $\mathrm L$-derivation $\alpha$ into natural deduction $\varphi(\alpha)$. We prove that $\operatorname{length}(\varphi(\alpha))\leq2^{2\cdot\operatorname{length}(\alpha)}$ where $\alpha$ is $(\&,\supset)$-Gentzen's intuitionistic $\mathrm L$-derivation. This bound is almost optimal: an increasing sequence of $\mathrm L$-derivations $\alpha_i$ is constructed such that $\operatorname{length}(\varphi(\alpha_i))\leq2^{1/3\operatorname{length}(\alpha_i)}$.