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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be   <a href="unialg_1.html#NM2">Universal_Algebra</a>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>







<b>assume </b><a NAME="E1:15"/><i><font color="Green">E16</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="alg_1.html#R4" target="_self">is_isomorphism</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></font> <a href="funct_1.html#K2">"</a>  )
 ;<br/>

<a NAME="E2:15"/><b>then </b><i><font color="Green">E17</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="alg_1.html#T8" target="_self">Th8</a></i>;<br/>
<a NAME="E3:15"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="funct_1.html#V2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="alg_1.html#E1:15"><i><font color="Green">E16</font></i></a>, <a class="ref" href="funct_1.html#T62">FUNCT_1:62</a></i>;<br/>
<i><font color="Green">E19</font></i>:  <a href="relset_1.html#K5">rng</a> <font color="Maroon">c<sub>4</sub></font> = 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">c<sub>3</sub></font>
<b>by </b><i><a class="txt" href="alg_1.html#E1:15"><i><font color="Green">E16</font></i></a>, <a class="txt" href="alg_1.html#E2:15"><i><font color="Green">E17</font></i></a>, <a class="ref" href="funct_1.html#T55">FUNCT_1:55</a></i>
<br/>.= 
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>
;<br/>
<a NAME="E5:15"/>
<font color="Maroon">c<sub>4</sub></font> <a href="alg_1.html#R1" target="_self">is_homomorphism</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="alg_1.html#E1:15"><i><font color="Green">E16</font></i></a>, <a class="ref" href="alg_1.html#T10" target="_self">Th10</a></i>;<br/>
<b>hence </b><a NAME="E6:15"/>
<font color="Maroon">c<sub>4</sub></font> <a href="alg_1.html#R4" target="_self">is_isomorphism</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="txt" href="alg_1.html#E3:15"><i><font color="Green">E18</font></i></a>, <a class="txt" href="alg_1.html#E4:15"><i><font color="Green">E19</font></i></a>, <a class="ref" href="alg_1.html#T8" target="_self">Th8</a></i>;<br/>


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