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<b>let </b><font color="Maroon" title="c1">X</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">X0</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font>;<br/><b>let </b><font color="Maroon" title="c3">Y0</font> be    <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K8" title="TMAP_1:func.8">modified_with_respect_to</a> <font color="Maroon" title="c2">X0</font>;<br/>





<b>assume </b><a NAME="E1:117"/><i><font color="Green" title="E90">A1</font></i>: 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">Y0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">Y</font> = <font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K8" title="TMAP_1:func.8">modified_with_respect_to</a> <font color="Maroon" title="c2">X0</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c5">A</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X0</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">X</font> <b>by </b><i><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<a NAME="E3:117"/><i><font color="Green" title="E91">A2</font></i>: 
<font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K8" title="TMAP_1:func.8">modified_with_respect_to</a> <font color="Maroon" title="c2">X0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K6" title="TMAP_1:func.6">modified_with_respect_to</a> <font color="Maroon" title="c5">A</font>
 
<b>by </b><i><a class="ref" href="tmap_1.html#D10" target="_self" title="TMAP_1:def.10">Def10</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">B</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">Y0</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K8" title="TMAP_1:func.8">modified_with_respect_to</a> <font color="Maroon" title="c2">X0</font></span>)</span> <b>by </b><i><a class="ref" href="tsep_1.html#T1" title="TSEP_1:th.1">TSEP_1:1</a></i>;<br/>
<a NAME="E5:117"/>
<font color="Maroon" title="c6">B</font> is <a href="pre_topc.html#V3" title="PRE_TOPC:attr.3">open</a>
 
<b>by </b><i><a class="txt" href="tmap_1.html#E1:117"><i><font color="Green" title="E90">A1</font></i></a>, <a class="txt" href="tmap_1.html#E3:117"><i><font color="Green" title="E91">A2</font></i></a>, <a class="ref" href="tmap_1.html#T105" target="_self" title="TMAP_1:th.105">Th105</a></i>;<br/>
<b>hence </b><a NAME="E6:117"/>
<font color="Maroon" title="c3">Y0</font> is  <a href="tsep_1.html#V1" title="TSEP_1:attr.1">open</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">X</font> <a href="tmap_1.html#K8" title="TMAP_1:func.8">modified_with_respect_to</a> <font color="Maroon" title="c2">X0</font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T16" title="TSEP_1:th.16">TSEP_1:16</a></i>;<br/>


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