<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">UA</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">f</font> being  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>  st <font color="Olive" title="b1">f</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font> holds <br/><font color="Olive" title="b1">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font></span><br/><b>let </b><font color="Maroon" title="c2">f</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">f</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font> implies <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font> )</span><br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green" title="E5">A1</font></i>: 
<font color="Maroon" title="c2">f</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font></span><br/>

<a NAME="E2:6"/><b>then </b><i><font color="Green" title="E6">A2</font></i>: 
<font color="Maroon" title="c2">f</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="alg_1.html#T8" title="ALG_1:th.8">ALG_1:8</a></i>;<br/>
<a NAME="E3:6"/>
<font color="Maroon" title="c2">f</font> <a href="alg_1.html#R3" title="ALG_1:pred.3">is_epimorphism</a> <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>
 
<b>by </b><i><a class="txt" href="#E1:6"><i><font color="Green" title="E5">A1</font></i></a>, <a class="ref" href="alg_1.html#D4" title="ALG_1:def.4">ALG_1:def 4</a></i>;<br/>
<a NAME="E4:6"/><b>then </b>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c2">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">UA</font>
 
<b>by </b><i><a class="ref" href="alg_1.html#D3" title="ALG_1:def.3">ALG_1:def 3</a></i>;<br/>
<b>hence </b><a NAME="E5:6"/>
<font color="Maroon" title="c2">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  is   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">UA</font>,<font color="Maroon" title="c1">UA</font>
 <b>by </b><i><a class="txt" href="#E2:6"><i><font color="Green" title="E6">A2</font></i></a>, <a class="ref" href="funct_2.html#T31" title="FUNCT_2:th.31">FUNCT_2:31</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
