\newcommand{\thetaUp}{\vartheta^\uparrow}
\newcommand{\thetaD}{\vartheta^\downarrow}
\newcommand{\ThetaUp}{\Theta^\uparrow}
\newcommand{\ThetaD}{\Theta^\downarrow}
\newcommand{\ATs}{({\cal A, T}, s)}
\newcommand{\ATt}{({\cal A, T}, t)}
\newcommand{\ASs}{({\cal A, S}, s)}
\newcommand{\BTt}{({\cal B, T}, t)}
\newcommand{\Aa}{(\cal A, \overline a)}
\newcommand{\As}{(\cal A, s)}
\newcommand{\Bt}{(\cal B, t)}
\newcommand{\Ra}{\cal A(\overline a)}
\newcommand{\dom}{{\it dom}}
\newcommand{\node}{{\it node}}
\renewcommand{\root}{{\it root}}
\newcommand{\leaf}{{\it leaf}}
\newcommand{\child}{{\it child}}
\newcommand{\bag}{{\it bag}}
\newcommand{\adj}{{\it adj}}
\renewcommand{\AA}{{\cal A}}
\newcommand{\BB}{{\cal B}}
\newcommand{\GG}{{\cal G}}
\newcommand{\PP}{{\cal P}}
\newcommand{\RR}{{\cal R}}
\newcommand{\LL}{{\cal L}}
\newcommand{\OO}{{\cal O}}
\newcommand{\EE}{{\cal E}}
\newcommand{\TT}{{\cal T}}
\renewcommand{\SS}{{\cal S}}
\newcommand{\RAi}{R_i^\AA}
\newcommand{\RAai}{R_i^{\AA[\bar{a}]}}
\newcommand{\RAaj}{R_j^{\AA[\bar{a}]}}
\newcommand{\RBi}{R_i^\BB}
\newcommand{\RAk}{R_k^\AA}
\newcommand{\RAone}{R_1^\AA}
\newcommand{\RAK}{R_K^\AA}
\newcommand{\ra}{\rightarrow}
\newcommand{\la}{\leftarrow}
\newcommand{\La}{\Leftarrow}
\newcommand{\LR}{\Leftrightarrow}
\newcommand{\domA}{{\it dom}({\cal A})}
\newcommand{\domB}{{\it dom}({\cal B})}
\newcommand{\domG}{{\it dom}({\cal G})}
\newcommand{\tw}{{\it tw}
}
% Indukovane podstruktury
\newcommand{\II}{{\cal I}}
\newcommand{\IASs}{(\AA[\SS_s],\bar{a})}
\newcommand{\IASss}{(\AA[\SS_{s'}],\bar{a}')}
\newcommand{\IBTt}{(\BB[\TT_t],\bar{b})}
\newcommand{\IBTtt}{(\BB[\TT_{t'}],\bar{b}')}
\newcommand{\IASsone}{(\AA[\SS_{s_1}],\bar{a})}
\newcommand{\IASstwo}{(\AA[\SS_{s_2}],\bar{a})}
\newcommand{\IBTtone}{(\BB[\TT_{t_1}],\bar{b})}
\newcommand{\IBTttwo}{(\BB[\TT_{t_2}],\bar{b})}

\newcommand{\IATt}{(\AA[\TT_t],\bar{a})}
\newcommand{\IATtbag}{(\AA[\TT_t],t.bag)}
\newcommand{\IATtt}{(\AA[\TT_{t'}],\bar{a'})}
\newcommand{\IATtone}{(\AA[\TT_{t_1}],\bar{a})}
\newcommand{\IATttwo}{(\AA[\TT_{t_2}],\bar{a})}

\newcommand{\FOk}{{\rm FO[{\it k}]}}
\newcommand{\FOi}{{\rm FO[{\it i}]}}
\newcommand{\MSOk}{{\rm MSO[{\it k}]}}
\newcommand{\MSO}[1]{\text{MSO}[#1]}
\newcommand{\MSOi}{{\rm MSO[{\it i}]}}
\newcommand{\MSOiplus}{{\rm MSO[{\it i+1}]}}
\newcommand{\FOkeq}{\equiv^{FO}_k}
\newcommand{\MSOkeq}{\equiv^{MSO}_k}
\newcommand{\MSOkpluseq}{\equiv^{MSO}_{k+1}}
\newcommand{\MSOipluseq}{\equiv^{MSO}_{i+1}}
\newcommand{\MSOieq}{\equiv^{MSO}_i}
\newcommand{\EFGABk}{{\rm EFG}(\AA, \BB, k)}
\newcommand{\EFGAB}[1]{{\rm EFG}(\AA, \BB, #1)}
\newcommand{\EFGABr}{{\rm EFG}(\AA, \BB, r)}
\newcommand{\EFGABi}{{\rm EFG}(\AA, \BB, i)}
\newcommand{\EFGABiplus}{{\rm EFG}(\AA, \BB, i+1)}
\newcommand{\EFGABkplus}{{\rm EFG}(\AA, \BB, k+1)}
%\renewcommand{\bar}{\overline} % je to dobrej nápad?

\newcommand{\algnull}{{\tt null}}
\newcommand{\typ}{{\sf type}}
\newcommand{\ff}{f(|\varphi|, w)}