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<b>let </b><font color="Maroon" title="c7">T</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="c8">a</font>, <font color="Maroon" title="c9">b</font>, <font color="Maroon" title="c10">c</font>, <font color="Maroon" title="c11">d</font>, <font color="Maroon" title="c12">e</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c7">T</font>;<br/><b>let </b><font color="Maroon" title="c13">f</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font>;<br/><b>let </b><font color="Maroon" title="c14">g</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font>;<br/><b>let </b><font color="Maroon" title="c15">h</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">d</font>;<br/><b>let </b><font color="Maroon" title="c16">i</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">e</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:64"/><i><font color="Green" title="E42">A1</font></i>: 
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E2:64"/><i><font color="Green" title="E43">A2</font></i>: 
<font color="Maroon" title="c9">b</font>,<font color="Maroon" title="c10">c</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E3:64"/><i><font color="Green" title="E44">A3</font></i>: 
<font color="Maroon" title="c10">c</font>,<font color="Maroon" title="c11">d</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 <b>and </b><br/><a NAME="E4:64"/><i><font color="Green" title="E45">A4</font></i>: 
<font color="Maroon" title="c11">d</font>,<font color="Maroon" title="c12">e</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 ;<br/>

<a NAME="E5:64"/>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c10">c</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E1:64"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="jordan.html#E2:64"><i><font color="Green" title="E43">A2</font></i></a>, <a class="ref" href="borsuk_6.html#T46" title="BORSUK_6:th.46">BORSUK_6:46</a></i>;<br/>
<a NAME="E6:64"/><b>then </b>
<font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c11">d</font> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a> 
 
<b>by </b><i><a class="txt" href="jordan.html#E3:64"><i><font color="Green" title="E44">A3</font></i></a>, <a class="ref" href="borsuk_6.html#T46" title="BORSUK_6:th.46">BORSUK_6:46</a></i>;<br/>
<b>hence </b> <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">f</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c14">g</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">h</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c16">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c13">f</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c14">g</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c15">h</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c16">i</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E4:64"><i><font color="Green" title="E45">A4</font></i></a>, <a class="ref" href="jordan.html#T37" target="_self" title="JORDAN:th.37">Th37</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c13">f</font></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p3">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c14">g</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c15">h</font></span>)</span></span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c16">i</font></span>)</span>
<b>by </b><i><a class="txt" href="jordan.html#E1:64"><i><font color="Green" title="E42">A1</font></i></a>, <a class="txt" href="jordan.html#E2:64"><i><font color="Green" title="E43">A2</font></i></a>, <a class="txt" href="jordan.html#E3:64"><i><font color="Green" title="E44">A3</font></i></a>, <a class="ref" href="jordan.html#T39" target="_self" title="JORDAN:th.39">Th39</a></i>
;<br/><br/>


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