Konvexe Geometrie/Gitterpunktsatz/Abschätzungskette/detail

${}\operatorname {Vol} ({\mathfrak {N}})\geq \operatorname {Vol} (X\cup Y\cup B)=\operatorname {Vol} (\bigcup _{i\in I}{\tilde {T_{i}}})+\operatorname {Vol} (B)>\sum _{i\in I}\operatorname {Vol} ({\tilde {T}}_{i})=\sum _{i\in I}\operatorname {Vol} (T_{i})=\operatorname {Vol} (T)\geq 2^{n}\operatorname {Vol} ({\mathfrak {M}})=\operatorname {Vol} ({\mathfrak {N}})\,.$