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<b>let </b><font color="Maroon" title="c4">S</font>, <font color="Maroon" title="c5">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="borsuk_2.html#V1" title="BORSUK_2:attr.1">arcwise_connected</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c6">s1</font>, <font color="Maroon" title="c7">s2</font>, <font color="Maroon" title="c8">s3</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c4">S</font>;<br/><b>let </b><font color="Maroon" title="c9">t1</font>, <font color="Maroon" title="c10">t2</font>, <font color="Maroon" title="c11">t3</font> be   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <font color="Maroon" title="c5">T</font>;<br/><b>let </b><font color="Maroon" title="c12">l1</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>;<br/><b>let </b><font color="Maroon" title="c13">l2</font> be    <a href="borsuk_2.html#M1" title="BORSUK_2:mode.1">Path</a> of <span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>;<br/>









<a NAME="E1:38"/>
( <span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c6">s1</font>,<font color="Maroon" title="c9">t1</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c7">s2</font>,<font color="Maroon" title="c10">t2</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">[</a><span class="default"><font color="Maroon" title="c8">s3</font>,<font color="Maroon" title="c11">t3</font></span><a href="borsuk_1.html#K7" title="BORSUK_1:func.7">]</a></span> <a href="borsuk_6.html#R1" title="BORSUK_6:pred.1">are_connected</a>  )
 
<b>by </b><i><a class="ref" href="borsuk_2.html#D3" title="BORSUK_2:def.3">BORSUK_2:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:38"/>
 <a href="topalg_4.html#K9" title="TOPALG_4:func.9">pr2</a> <span class="p1">(<span class="default"><font color="Maroon" title="c12">l1</font> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <font color="Maroon" title="c13">l2</font></span>)</span> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K9" title="TOPALG_4:func.9">pr2</a> <font color="Maroon" title="c12">l1</font></span>)</span> <a href="borsuk_2.html#K1" title="BORSUK_2:func.1">+</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K9" title="TOPALG_4:func.9">pr2</a> <font color="Maroon" title="c13">l2</font></span>)</span>
 <b>by </b><i><a class="ref" href="topalg_4.html#T25" target="_self" title="TOPALG_4:th.25">Th25</a></i>;<br/>


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