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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>





<a NAME="E1:16"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a>  <a href="tsep_2.html#R2" target="_self">constitute_a_decomposition</a>  &amp; <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="tsep_2.html#R2" target="_self">constitute_a_decomposition</a>  )
 
<b>by </b><i><a class="ref" href="tsep_2.html#T6" target="_self">Th6</a></i>;<br/>
<b>hence </b><a NAME="E2:16"/>
( <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="tsep_1.html#R2">are_weakly_separated</a>  iff <font color="Maroon">c<sub>2</sub></font> <a href="subset_1.html#K3">`</a> ,<font color="Maroon">c<sub>3</sub></font> <a href="subset_1.html#K3">`</a>  <a href="tsep_1.html#R2">are_weakly_separated</a>  )
 <b>by </b><i><a class="ref" href="tsep_2.html#T16" target="_self">Th16</a></i>;<br/>


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