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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>;<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>;<br/>





<a NAME="E1:47"/>
(  <a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s1</font>, <a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s2</font> <a href="group_6.html#R2">are_isomorphic</a>  &amp;  <a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t1</font>, <a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t2</font> <a href="group_6.html#R2">are_isomorphic</a>  )
 
<b>by </b><i><a class="ref" href="topalg_3.html#T35">TOPALG_3:35</a></i>;<br/>
<a NAME="E2:47"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="group_7.html#K2">product</a> <span class="p1"><a href="group_7.html#K15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s1</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t1</font></span>)</span></span><a href="group_7.html#K15">*&gt;</a></span>, <a href="group_7.html#K2">product</a> <span class="p1"><a href="group_7.html#K15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s2</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t2</font></span>)</span></span><a href="group_7.html#K15">*&gt;</a></span> <a href="group_6.html#R2">are_isomorphic</a> 
 
<b>by </b><i/>;<br/>
<a NAME="E3:47"/>
 <a href="topalg_1.html#NK4" target="_self">pi_1</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K5">:]</a></span>,<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>, <a href="group_7.html#K2">product</a> <span class="p1"><a href="group_7.html#K15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s1</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t1</font></span>)</span></span><a href="group_7.html#K15">*&gt;</a></span> <a href="group_6.html#R2">are_isomorphic</a> 
 
<b>by </b><i><a class="txt" href="topalg_4.html#E1"><i><font color="Green">Lemma31</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:47"/>
 <a href="topalg_1.html#NK4" target="_self">pi_1</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="borsuk_1.html#K5">:]</a></span>,<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>, <a href="group_7.html#K2">product</a> <span class="p1"><a href="group_7.html#K15">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">S</font>,<font color="Maroon">s2</font></span>)</span>,<span class="p2">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">T</font>,<font color="Maroon">t2</font></span>)</span></span><a href="group_7.html#K15">*&gt;</a></span> <a href="group_6.html#R2">are_isomorphic</a> 
 <b>by </b><i><a class="txt" href="topalg_4.html#E2"><i><font color="Green">Lemma32</font></i></a>, <a class="ref" href="group_6.html#T78">GROUP_6:78</a></i>;<br/>


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