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<b>let </b><font color="Maroon" title="c1">G</font>, <font color="Maroon" title="c2">H</font>, <font color="Maroon" title="c3">I</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/><b>let </b><font color="Maroon" title="c4">h</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c1">G</font>,<font color="Maroon" title="c2">H</font>;<br/><b>let </b><font color="Maroon" title="c5">h1</font> be   <a href="group_6.html#NM2" title="GROUP_6:NM.2">Homomorphism</a> of <font color="Maroon" title="c2">H</font>,<font color="Maroon" title="c3">I</font>;<br/>









<b>assume </b><a NAME="E1:85"/><i><font color="Green" title="E64">A1</font></i>: 
( <font color="Maroon" title="c4">h</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a>  &amp; <font color="Maroon" title="c5">h1</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a>  )
 ;<br/>

<a NAME="E2:85"/><b>then </b><i><font color="Green" title="E65">A2</font></i>: 
( <font color="Maroon" title="c4">h</font> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a> &amp; <font color="Maroon" title="c5">h1</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="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a></i>;<br/>
<a NAME="E3:85"/><i><font color="Green" title="E66">A3</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="group_6.html#K8" title="GROUP_6:func.8">*</a> <font color="Maroon" title="c4">h</font></span>)</span> <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="c3">I</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="85_1"><b>proof </b></a><div class="add">

<a NAME="E1:85_1"/><i><font color="Green" title="E67">A4</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">h1</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="c2">H</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="E2:85_1"/>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c4">h</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="c2">H</font>
 
<b>by </b><i><a class="txt" href="group_6.html#E1:85"><i><font color="Green" title="E64">A1</font></i></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a></i>;<br/>
<b>hence </b> <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h1</font> <a href="group_6.html#K8" title="GROUP_6:func.8">*</a> <font color="Maroon" title="c4">h</font></span>)</span> = 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c5">h1</font>
<b>by </b><i><a class="txt" href="group_6.html#E1:85_1"><i><font color="Green" title="E67">A4</font></i></a>, <a class="ref" href="relat_1.html#T47" title="RELAT_1:th.47">RELAT_1:47</a></i>
<br/>.= 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">I</font>
<b>by </b><i><a class="txt" href="group_6.html#E1:85"><i><font color="Green" title="E64">A1</font></i></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a></i>
;<br/><br/>


</div><b>end;</b></div>
<a NAME="E4:85"/>
<font color="Maroon" title="c5">h1</font> <a href="group_6.html#K8" title="GROUP_6:func.8">*</a> <font color="Maroon" title="c4">h</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="group_6.html#E2:85"><i><font color="Green" title="E65">A2</font></i></a>, <a class="ref" href="funct_1.html#T46" title="FUNCT_1:th.46">FUNCT_1:46</a></i>;<br/>
<b>hence </b><a NAME="E5:85"/>
<font color="Maroon" title="c5">h1</font> <a href="group_6.html#K8" title="GROUP_6:func.8">*</a> <font color="Maroon" title="c4">h</font> <a href="group_6.html#NR3" title="GROUP_6:NR.3">is_isomorphism</a> 
 <b>by </b><i><a class="txt" href="group_6.html#E3:85"><i><font color="Green" title="E66">A3</font></i></a>, <a class="ref" href="group_6.html#T70" target="_self" title="GROUP_6:th.70">Th70</a></i>;<br/>


</div>
