\def\Cs{\mbox{$\mathcal{C}$}}
\def\CO{\mbox{$\cal{C}$}}
\def\cs{\mbox{$\cal{c}$} }
\def\Es{\mbox{$\cal{E}$} }
\def\Fs{\mbox{$\mathcal{F}$} }
\def\Ws{\mbox{$\mathcal{W}$} }
\def\FCs{\mbox{$\mathcal{FCS}$}}
\def\RFCs{\mbox{$\mathcal{FCS}_r$}}
\def\ds{\displaystyle\strut}
\def\DFCs{\mbox{$\mathcal{FCS_\delta}$}}
\def\FWs{{\cal{FW}}}
\def\Fws{{\cal{FW}}}
\def\CC{{\cal{CC}}}
\def\CE{\mbox{$\mathcal{CE}$}}
\def\workspace{\mbox{$\cal{W}$}}
\def\vor{{\EuScript F}}
\def\rvor{{\EuScript{RF}}}
\def\eqi{{\EuScript S}}
\def\sur{{\EuScript{SS}}}
\def\grad{\nabla}
\def\bdy{\partial}
\def\af{\operatorname{Af}}
\def\Af{\operatorname{Af}}
\def\Co{\operatorname{Co}}
\def\dim{\operatorname{dim}}
\def\codim{\operatorname{codim}}
\def\argmin{\operatorname{argmin}}
\def\rank{\operatorname{rank}}
\def\Null{\operatorname{Null}}
\def\Im{\operatorname{Im}}
\def\cl{\operatorname{cl}}
\def\nbhd{\operatorname{nbhd}}
\def\interior{\operatorname{int}}
\def\co{\operatorname{Co}}
\def\conto{{\big|_{\vor_{ij}}}}
\def\hpi1m1cs{\mbox{$\pi_{1, \dots, m-1}|_{\mathcal{FCS}}$}}
\def\hfcs{\mbox{$h|_{\partial\mathcal{FCS}}$}}
\def\hpi1fcs{\mbox{$\pi_{1}|_{\mathcal{FCS}}$}}
\def\hpi2fcs{\mbox{$\pi_{2}|_{\mathcal{FCS}}$}}
\def\hpi2N{\mbox{$\pi_{2}|_{\mathcal{N}}$}}
\def\hpi12fcs{\mbox{$\pi_{12}|_{\mathcal{FCS}}$}}
\def\hfSpi1{\mbox{$h|_{\partial\mathcal{\Sigma(\pi_1)}}$}}
\def\hfSpi12{\mbox{$h|_{\partial\mathcal{\Sigma(\pi_{12})}}$}}
\def\hfSpi1m1{\mbox{$h|_{\partial\mathcal{\Sigma(\pi_{1,\dots,m-1})}}$}}
