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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">H</font> be  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c2">G</font>;<br/><b>reconsider </b><font color="Maroon" title="c4">G'</font> = <font color="Maroon" title="c2">G</font> as   <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> ;<br/><b>reconsider </b><font color="Maroon" title="c5">H'</font> = <font color="Maroon" title="c3">H</font> as  <a href="algstr_0.html#V15" title="ALGSTR_0:attr.15">strict</a>  <a href="group_2.html#M1" title="GROUP_2:mode.1">Subgroup</a> of <font color="Maroon" title="c4">G'</font> ;<br/><b>assume </b><a NAME="E3:24_1_1_1"/>
<font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="algstr_0.html#G3" title="ALGSTR_0:aggr.3">multMagma</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Maroon" title="c2">G</font></span>)</span>,the <a href="algstr_0.html#U2" title="ALGSTR_0:sel.2">multF</a> of <span class="p1">(<span class="default"><a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Maroon" title="c2">G</font></span>)</span> #)
 ;<br/><a NAME="E4:24_1_1_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">H</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="tarski.html#K1" title="TARSKI:func.1">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <font color="Maroon" title="c2">G</font></span>)</span></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="group_9.html#D8" target="_self" title="GROUP_9:def.8">Def8</a></i>;<br/><a NAME="E5:24_1_1_1"/><b>then </b>
<font color="Maroon" title="c5">H'</font> <a href="group_2.html#R1" title="GROUP_2:pred.1">=</a>  <a href="group_2.html#K5" title="GROUP_2:func.5">(1).</a> <font color="Maroon" title="c4">G'</font>
 <b>by </b><i><a class="ref" href="group_2.html#D7" title="GROUP_2:def.7">GROUP_2:def 7</a></i>;<br/><b>hence </b><a NAME="E6:24_1_1_1"/>
<font color="Maroon" title="c3">H</font> is <a href="group_3.html#V1" title="GROUP_3:attr.1">normal</a>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:24_1_1"/>
 <a href="group_9.html#K4" title="GROUP_9:func.4">(1).</a> <font color="Maroon" title="c2">G</font> is <a href="group_9.html#V4" title="GROUP_9:attr.4">normal</a>
 <b>by </b><i><a class="ref" href="group_9.html#D10" target="_self" title="GROUP_9:def.10">Def10</a></i>;<br/>


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