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I would like to thank my advisor for his valuable comments and suggestions. His extensive experience with proof systems and logic helped me a lot. Finally I want to thank my family for their support. Prohlašuji, že jsem svou diplomovou práci napsal samostatne ̌ a výhradně s použit́ım citovaných pramen̊u. Souhlaśım se zap̊ujčováńım práce. I hereby declare that I have created this master thesis on my own and listed all used references. I agree with lending of this thesis