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<b>let </b><font color="Maroon" title="c1">U1</font>, <font color="Maroon" title="c2">U2</font> be   <a href="unialg_1.html#NM2" title="UNIALG_1:NM.2">Universal_Algebra</a>;<br/>



<b>assume </b><a NAME="E1:17"/>
<font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font> <a href="alg_1.html#R5" title="ALG_1:pred.5">are_isomorphic</a> 
 ;<br/>

<b>then consider </b><font color="Maroon" title="c3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font><b> such that </b><br/><a NAME="E3:17"/><i><font color="Green" title="E17">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>
 <b>by </b><i><a class="ref" href="alg_1.html#D5" target="_self" title="ALG_1:def.5">Def5</a></i>;<br/>
<a NAME="E4:17"/><i><font color="Green" title="E18">A2</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="alg_1.html#R3" title="ALG_1:pred.3">is_epimorphism</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>
 
<b>by </b><i><a class="txt" href="alg_1.html#E3:17"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="alg_1.html#D4" target="_self" title="ALG_1:def.4">Def4</a></i>;<br/>
<a NAME="E5:17"/>
<font color="Maroon" title="c3">f</font> <a href="alg_1.html#R2" title="ALG_1:pred.2">is_monomorphism</a> <font color="Maroon" title="c1">U1</font>,<font color="Maroon" title="c2">U2</font>
 
<b>by </b><i><a class="txt" href="alg_1.html#E3:17"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="alg_1.html#D4" target="_self" title="ALG_1:def.4">Def4</a></i>;<br/>
<a NAME="E6:17"/><b>then </b><i><font color="Green" title="E19">A3</font></i>: 
<font color="Maroon" title="c3">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#D2" target="_self" title="ALG_1:def.2">Def2</a></i>;<br/>
<b>then </b><i><font color="Green" title="E20">A4</font></i>:  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> = 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font>
<b>by </b><i><a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">U2</font>
<b>by </b><i><a class="txt" href="alg_1.html#E4:17"><i><font color="Green" title="E18">A2</font></i></a>, <a class="ref" href="alg_1.html#D3" target="_self" title="ALG_1:def.3">Def3</a></i>
;<br/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a> </span>)</span> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
<b>by </b><i><a class="txt" href="alg_1.html#E6:17"><i><font color="Green" title="E19">A3</font></i></a>, <a class="ref" href="funct_1.html#T55" title="FUNCT_1:th.55">FUNCT_1:55</a></i>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">U1</font>
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>
;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">g</font> = <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c1">U1</font> <b>by </b><i><a class="txt" href="alg_1.html#E7:17"><i><font color="Green" title="E20">A4</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c4">g</font>
; <i><font color="Red">:: according to </font></i><a class="ref" href="alg_1.html#D5" target="_self" title="ALG_1:def.5">ALG_1:def 5</a><br/>

<b>thus </b><a NAME="E10:17"/>
<font color="Maroon" title="c4">g</font> <a href="alg_1.html#R4" title="ALG_1:pred.4">is_isomorphism</a> <font color="Maroon" title="c2">U2</font>,<font color="Maroon" title="c1">U1</font>
 <b>by </b><i><a class="txt" href="alg_1.html#E3:17"><i><font color="Green" title="E17">A1</font></i></a>, <a class="ref" href="alg_1.html#T11" target="_self" title="ALG_1:th.11">Th11</a></i>;<br/>


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