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

<b>let </b><font color="Maroon" title="c1">G</font> be   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</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">H1</font>, <font color="Olive" title="b2">H2</font> being   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>  st <font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> holds <br/>the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Olive" title="b1">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Olive" title="b2">H2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">H1</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Olive" title="b2">H2</font></span><br/><b>let </b><font color="Maroon" title="c2">H1</font>, <font color="Maroon" title="c3">H2</font> be    <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> implies the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c3">H2</font> )</span><br/>





<b>assume </b><a NAME="E1:62"/>
<font color="Maroon" title="c1">G</font> is  <a href="group_1.html#V5" title="GROUP_1:attr.5">commutative</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c3">H2</font></span><br/>

<a NAME="E2:62"/><b>then </b>
<font color="Maroon" title="c2">H1</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c3">H2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">H2</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c2">H1</font>
 
<b>by </b><i><a class="ref" href="group_2.html#T29" title="GROUP_2:th.29">GROUP_2:29</a></i>;<br/>
<b>hence </b><a NAME="E3:62"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">H1</font> <a href="group_4.html#K8" title="GROUP_4:func.8">"\/"</a> <font color="Maroon" title="c3">H2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">H1</font> <a href="group_4.html#K7" title="GROUP_4:func.7">*</a> <font color="Maroon" title="c3">H2</font>
 <b>by </b><i><a class="ref" href="group_4.html#T69" target="_self" title="GROUP_4:th.69">Th69</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>
