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<a NAME="E1:119_1_1"/>
(  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> &amp;  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="pre_topc.html#D9">PRE_TOPC:def 9</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">c<sub>3</sub></font> =  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> ;<br/>
<a NAME="E3:119_1_1"/>
<font color="Maroon">c<sub>1</sub></font> <a href="tmap_1.html#K8" target="_self">modified_with_respect_to</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>1</sub></font> <a href="tmap_1.html#K6" target="_self">modified_with_respect_to</a> <font color="Maroon">c<sub>3</sub></font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#D10" target="_self">Def10</a></i>;<br/>
<b>hence </b><a NAME="E4:119_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> <a href="tmap_1.html#K8" target="_self">modified_with_respect_to</a> <font color="Maroon">c<sub>2</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/>


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