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<b>let </b><font color="Maroon">T</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">a</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>, <font color="Maroon">b</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>, <font color="Maroon">c</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>, <font color="Maroon">d</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>, <font color="Maroon">e</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">f</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">a</font>,<font color="Maroon">b</font>;<br/><b>let </b><font color="Maroon">g</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">b</font>,<font color="Maroon">c</font>;<br/><b>let </b><font color="Maroon">h</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c</font>,<font color="Maroon">d</font>;<br/><b>let </b><font color="Maroon">i</font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">d</font>,<font color="Maroon">e</font>;<br/>











<b>assume </b><b>that </b><br/><a NAME="E1:64"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">a</font>,<font color="Maroon">b</font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E2:64"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">b</font>,<font color="Maroon">c</font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E3:64"/><i><font color="Green">E74</font></i>: 
<font color="Maroon">c</font>,<font color="Maroon">d</font> <a href="borsuk_6.html#R1">are_connected</a> 
 <b>and </b><br/><a NAME="E4:64"/><i><font color="Green">E78</font></i>: 
<font color="Maroon">d</font>,<font color="Maroon">e</font> <a href="borsuk_6.html#R1">are_connected</a> 
 ;<br/>

<a NAME="E5:64"/>
<font color="Maroon">a</font>,<font color="Maroon">c</font> <a href="borsuk_6.html#R1">are_connected</a> 
 
<b>by </b><i>, , <a class="ref" href="borsuk_6.html#T46">BORSUK_6:46</a></i>;<br/>
<a NAME="E6:64"/><b>then </b>
<font color="Maroon">a</font>,<font color="Maroon">d</font> <a href="borsuk_6.html#R1">are_connected</a> 
 
<b>by </b><i>, <a class="ref" href="borsuk_6.html#T46">BORSUK_6:46</a></i>;<br/>
<b>hence </b> <a href="relset_1.html#K5">rng</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">g</font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">h</font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">i</font></span>)</span> = 
<span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon">f</font> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">g</font></span>)</span> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, </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">rng</a> <font color="Maroon">f</font></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p3">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">g</font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p2">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">h</font></span>)</span></span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5">rng</a> <font color="Maroon">i</font></span>)</span>
<b>by </b><i>, , , </i>
;<br/><br/>


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