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<b>let </b><font color="Maroon">S1</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">S2</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">T1</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">T2</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">R1</font> be    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">S1</font>,<font color="Maroon">S2</font>;<br/><b>let </b><font color="Maroon">R2</font> be    <a href="yellow_9.html#M3">Refinement</a> of <font color="Maroon">T1</font>,<font color="Maroon">T2</font>;<br/>











<b>assume </b><a NAME="E1:62"/><i><font color="Green">E34</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S2</font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T2</font> )
 ;<br/>

<b>consider </b><font color="Maroon">R</font> being  <a href="pre_topc.html#V1">strict</a>  <a href="yellow_9.html#M3">Refinement</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span>;<br/>
<a NAME="E3:62"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">R1</font>,<font color="Maroon">R2</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1"><b>proof </b></a><div class="add">

<a NAME="E1:62_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">R1</font>,<font color="Maroon">R2</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">R</font> &amp; the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">R1</font>,<font color="Maroon">R2</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <font color="Maroon">R</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E2:62_1"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">R1</font>,<font color="Maroon">R2</font></span><a href="borsuk_1.html#K5">:]</a></span> <a href="hidden.html#R1">=</a> <font color="Maroon">R</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:62"/>
<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">R1</font>,<font color="Maroon">R2</font></span><a href="borsuk_1.html#K5">:]</a></span> is    <a href="yellow_9.html#M3">Refinement</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S1</font>,<font color="Maroon">T1</font></span><a href="borsuk_1.html#K5">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S2</font>,<font color="Maroon">T2</font></span><a href="borsuk_1.html#K5">:]</a></span>
 ;<br/>


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