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<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">a</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b3">H</font> being   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Olive" title="b3">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b3">H</font> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Olive" title="b2">A</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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"> for <font color="Olive" title="b1">A</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">G</font><br/> for <font color="Olive" title="b2">H</font> being   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Olive" title="b2">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">H</font> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Olive" title="b1">A</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c3">A</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</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"> for <font color="Olive" title="b1">H</font> being   <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c1">G</font> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Olive" title="b1">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">H</font> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c3">A</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c4">H</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c3">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c3">A</font></span>)</span></span><br/>







<b>thus </b><span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_2.html#K12" title="GROUP_2:func.12">*</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c3">A</font> = 
<span class="p1">(<span class="default"><span class="p2"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c2">a</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span> <a href="group_2.html#K10" title="GROUP_2:func.10">*</a> <font color="Maroon" title="c4">H</font></span>)</span> <a href="group_2.html#K2" title="GROUP_2:func.2">*</a> <font color="Maroon" title="c3">A</font>

<br/>.= 
<font color="Maroon" title="c2">a</font> <a href="group_2.html#K3" title="GROUP_2:func.3">*</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">H</font> <a href="group_2.html#K11" title="GROUP_2:func.11">*</a> <font color="Maroon" title="c3">A</font></span>)</span>
<b>by </b><i><a class="ref" href="group_2.html#T117" title="GROUP_2:th.117">GROUP_2:117</a></i>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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