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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font> be   <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="borsuk_2.html#M1">Path</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font>;<br/>







<b>assume </b><a NAME="E1:70"/><i><font color="Green">E44</font></i>: 
<font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>3</sub></font> <a href="borsuk_6.html#R1">are_connected</a> 
 ;<br/>

<b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="group_6.html#NM2">Homomorphism</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>3</sub></font></span>)</span>,<span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>;<br/>

<b>assume </b><a NAME="E2:70"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="funct_2.html#R2">=</a>  <a href="topalg_1.html#K4" target="_self">pi_1-iso</a> <font color="Maroon">c<sub>4</sub></font>
 ;<br/>

<a NAME="E3:70"/><i><font color="Green">E46</font></i>: 
<font color="Maroon">c<sub>5</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="topalg_1.html#E1:70"><i><font color="Green">E44</font></i></a>, <a class="txt" href="topalg_1.html#E2:70"><i><font color="Green">E45</font></i></a>, <a class="ref" href="topalg_1.html#T52" target="_self">Th52</a></i>;<br/>
<a NAME="E4:70"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="funct_2.html#V2">onto</a>
 
<b>by </b><i><a class="txt" href="topalg_1.html#E1:70"><i><font color="Green">E44</font></i></a>, <a class="txt" href="topalg_1.html#E2:70"><i><font color="Green">E45</font></i></a>, <a class="ref" href="topalg_1.html#T53" target="_self">Th53</a></i>;<br/>
<a NAME="E5:70"/><b>then </b>
 <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="topalg_1.html#NK4" target="_self">pi_1</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D3">FUNCT_2:def 3</a></i>;<br/>
<b>hence </b><a NAME="E6:70"/>
<font color="Maroon">c<sub>5</sub></font> <a href="group_6.html#NR3" target="_self">is_isomorphism</a> 
 <b>by </b><i><a class="txt" href="topalg_1.html#E3:70"><i><font color="Green">E46</font></i></a>, <a class="ref" href="group_6.html#T70">GROUP_6:70</a></i>;<br/>


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