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<b>let </b><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">a1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">b1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">c1</font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">T</font>;<br/>







<a NAME="E1:29"/>
( <font color="Maroon">a1</font>,<font color="Maroon">b1</font> <a href="borsuk_6.html#R1">are_connected</a>  &amp; <font color="Maroon">c1</font>,<font color="Maroon">b1</font> <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="E2:29"/>
for <font color="Olive">A</font>, <font color="Olive">B</font> being   <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">a1</font>,<font color="Maroon">b1</font><br/> for <font color="Olive">C</font> being   <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">b1</font>,<font color="Maroon">c1</font>  st <font color="Olive">A</font> <a href="borsuk_2.html#K1">+</a> <font color="Olive">C</font>,<font color="Olive">B</font> <a href="borsuk_2.html#K1">+</a> <font color="Olive">C</font> <a href="borsuk_2.html#R4">are_homotopic</a>  holds <br/><font color="Olive">A</font>,<font color="Olive">B</font> <a href="borsuk_2.html#R4">are_homotopic</a> 
 <b>by </b><i/>;<br/>


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