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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="borsuk_2.html#V1">arcwise_connected</a> <a href="pre_topc.html#NM1">TopSpace</a>, <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="borsuk_2.html#V1">arcwise_connected</a> <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">s1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Maroon">s2</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>, <font color="Maroon">s3</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">t1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>, <font color="Maroon">t2</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>, <font color="Maroon">t3</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">l1</font> be    <a href="borsuk_2.html#M1">Path</a> of <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s1</font>,<font color="Maroon">t1</font></span><a href="borsuk_1.html#K7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s2</font>,<font color="Maroon">t2</font></span><a href="borsuk_1.html#K7">]</a></span>;<br/><b>let </b><font color="Maroon">l2</font> be    <a href="borsuk_2.html#M1">Path</a> of <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s2</font>,<font color="Maroon">t2</font></span><a href="borsuk_1.html#K7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s3</font>,<font color="Maroon">t3</font></span><a href="borsuk_1.html#K7">]</a></span>;<br/>









<a NAME="E1:36"/>
( <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s1</font>,<font color="Maroon">t1</font></span><a href="borsuk_1.html#K7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s2</font>,<font color="Maroon">t2</font></span><a href="borsuk_1.html#K7">]</a></span> <a href="borsuk_6.html#R1">are_connected</a>  &amp; <span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s2</font>,<font color="Maroon">t2</font></span><a href="borsuk_1.html#K7">]</a></span>,<span class="p1"><a href="borsuk_1.html#K7">[</a><span class="default"><font color="Maroon">s3</font>,<font color="Maroon">t3</font></span><a href="borsuk_1.html#K7">]</a></span> <a href="borsuk_6.html#R1">are_connected</a>  )
 
<b>by </b><i><a class="ref" href="borsuk_2.html#D3">BORSUK_2:def 3</a></i>;<br/>
<b>hence </b><a NAME="E2:36"/>
 <a href="topalg_4.html#K8" target="_self">pr1</a> <span class="p1">(<span class="default"><font color="Maroon">l1</font> <a href="borsuk_2.html#K1">+</a> <font color="Maroon">l2</font></span>)</span> <a href="funct_2.html#R2">=</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K8" target="_self">pr1</a> <font color="Maroon">l1</font></span>)</span> <a href="borsuk_2.html#K1">+</a> <span class="p1">(<span class="default"><a href="topalg_4.html#K8" target="_self">pr1</a> <font color="Maroon">l2</font></span>)</span>
 <b>by </b><i/>;<br/>


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