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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>let </b><font color="Maroon" title="c3">h</font> be   <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>;<br/><b>let </b><font color="Maroon" title="c4">h1</font> be   <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>;<br/>







<b>assume </b><a NAME="E1:14"/><i><font color="Green" title="E16">A1</font></i>: 
( <font color="Maroon" title="c3">h</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> &amp; <font color="Maroon" title="c4">h1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">h</font> <a href="funct_1.html#K2" title="FUNCT_1:func.2">"</a>  )
 ;<br/>

<a NAME="E2:14"/><b>then </b><i><font color="Green" title="E17">A2</font></i>: 
<font color="Maroon" title="c3">h</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" target="_self" title="ALG_1:th.8">Th8</a></i>;<br/>
<a NAME="E3:14"/><b>then </b><i><font color="Green" title="E18">A3</font></i>: 
<font color="Maroon" title="c4">h1</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="txt" href="alg_1.html#E1:14"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="funct_1.html#T62" title="FUNCT_1:th.62">FUNCT_1:62</a></i>;<br/>
<i><font color="Green" title="E19">A4</font></i>:  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">h1</font> = 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">h</font>
<b>by </b><i><a class="txt" href="alg_1.html#E1:14"><i><font color="Green" title="E16">A1</font></i></a>, <a class="txt" href="alg_1.html#E2:14"><i><font color="Green" title="E17">A2</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/>
<a NAME="E5:14"/>
<font color="Maroon" title="c4">h1</font> <a href="alg_1.html#R1" title="ALG_1:pred.1">is_homomorphism</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#E1:14"><i><font color="Green" title="E16">A1</font></i></a>, <a class="ref" href="alg_1.html#T10" target="_self" title="ALG_1:th.10">Th10</a></i>;<br/>
<b>hence </b><a NAME="E6:14"/>
<font color="Maroon" title="c4">h1</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#E3:14"><i><font color="Green" title="E18">A3</font></i></a>, <a class="txt" href="alg_1.html#E4:14"><i><font color="Green" title="E19">A4</font></i></a>, <a class="ref" href="alg_1.html#T8" target="_self" title="ALG_1:th.8">Th8</a></i>;<br/>


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