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<b>let </b><font color="Maroon" title="c1">XX</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">X</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="pre_topc.html#M1" title="PRE_TOPC:mode.1">SubSpace</a> of <font color="Maroon" title="c1">XX</font>;<br/><b>let </b><font color="Maroon" title="c3">D</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="eqrel_1.html#M1" title="EQREL_1:mode.1">a_partition</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X</font>;<br/><b>let </b><font color="Maroon" title="c4">W</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c1">XX</font>;<br/>







<a NAME="E1:83"/><i><font color="Green" title="E62">A1</font></i>: 
<font color="Maroon" title="c3">D</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="borsuk_1.html#K16" title="BORSUK_1:func.16">TrivExt</a> <font color="Maroon" title="c3">D</font>
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<b>assume </b><a NAME="E2:83"/><i><font color="Green" title="E63">A2</font></i>: 
<font color="Maroon" title="c4">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">X</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c5">p</font> = <font color="Maroon" title="c4">W</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c2">X</font> ;<br/>
<a NAME="E4:83"/>
<span class="p1">(<span class="default"><a href="borsuk_1.html#K2" title="BORSUK_1:func.2">proj</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">D</font>
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c6">A</font> = <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" title="BORSUK_1:func.15">Proj</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">W</font> as    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="borsuk_1.html#K16" title="BORSUK_1:func.16">TrivExt</a> <font color="Maroon" title="c3">D</font> <b>by </b><i><a class="txt" href="borsuk_1.html#E1:83"><i><font color="Green" title="E62">A1</font></i></a></i>;<br/>
<a NAME="E6:83"/>
<font color="Maroon" title="c4">W</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">A</font>
 
<b>by </b><i><a class="txt" href="borsuk_1.html#E2:83"><i><font color="Green" title="E63">A2</font></i></a>, <a class="ref" href="borsuk_1.html#D1" target="_self" title="BORSUK_1:def.1">Def1</a></i>;<br/>
<b>hence </b><a NAME="E7:83"/>
<span class="p1">(<span class="default"><a href="borsuk_1.html#K15" title="BORSUK_1:func.15">Proj</a> <span class="p2">(<span class="default"><a href="borsuk_1.html#K16" title="BORSUK_1:func.16">TrivExt</a> <font color="Maroon" title="c3">D</font></span>)</span></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">W</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="borsuk_1.html#K15" title="BORSUK_1:func.15">Proj</a> <font color="Maroon" title="c3">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">W</font>
 <b>by </b><i><a class="ref" href="borsuk_1.html#T29" target="_self" title="BORSUK_1:th.29">Th29</a></i>;<br/>


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