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<div class="add">

<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">T1</font>, <font color="Maroon" title="c4">T2</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="c5">R1</font> be    <a href="yellow_9.html#M3" title="YELLOW_9:mode.3">Refinement</a> of <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c2">S2</font>;<br/><b>let </b><font color="Maroon" title="c6">R2</font> be    <a href="yellow_9.html#M3" title="YELLOW_9:mode.3">Refinement</a> of <font color="Maroon" title="c3">T1</font>,<font color="Maroon" title="c4">T2</font>;<br/>











<b>assume </b><a NAME="E1:62"/><i><font color="Green" title="E27">A1</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</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">S2</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">T1</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="c4">T2</font> )
 ;<br/>

<b>consider </b><font color="Maroon" title="c7">R</font> being  <a href="pre_topc.html#V1" title="PRE_TOPC:attr.1">strict</a>  <a href="yellow_9.html#M3" title="YELLOW_9:mode.3">Refinement</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">T1</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c4">T2</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>;<br/>
<a NAME="E3:62"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">R1</font>,<font color="Maroon" title="c6">R2</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">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" title="STRUCT_0:sel.1">carrier</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">R1</font>,<font color="Maroon" title="c6">R2</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <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="c7">R</font> &amp; the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">R1</font>,<font color="Maroon" title="c6">R2</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c7">R</font> )
 
<b>by </b><i><a class="txt" href="yellow12.html#E1:62"><i><font color="Green" title="E27">A1</font></i></a>, <a class="ref" href="yellow12.html#T49" target="_self" title="YELLOW12:th.49">Th49</a></i>;<br/>
<b>hence </b><a NAME="E2:62_1"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">R1</font>,<font color="Maroon" title="c6">R2</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">R</font>
 ;<br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E4:62"/>
<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c5">R1</font>,<font color="Maroon" title="c6">R2</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span> is    <a href="yellow_9.html#M3" title="YELLOW_9:mode.3">Refinement</a> of <span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">T1</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>,<span class="p1"><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">[:</a><span class="default"><font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c4">T2</font></span><a href="borsuk_1.html#K4" title="BORSUK_1:func.4">:]</a></span>
 ;<br/>


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