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<div><i><font color="Green">E35</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">g1</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>let </b><font color="Maroon">g2</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>assume </b><a NAME="E1:62_1_1_1"/>
( <font color="Maroon">g1</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> &amp; <font color="Maroon">g2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="domain_1.html#K6">}</a></span> )
 ;<br/><a NAME="E2:62_1_1_1"/><b>then </b>
( <font color="Maroon">g1</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font> &amp; <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font> )
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:62_1_1_1"/><b>then </b>
<font color="Maroon">g1</font> <a href="group_1.html#K1">*</a> <font color="Maroon">g2</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="group_1.html#D5">GROUP_1:def 5</a></i>;<br/><b>hence </b><a NAME="E4:62_1_1_1"/>
<font color="Maroon">g1</font> <a href="group_1.html#K1">*</a> <font color="Maroon">g2</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="62_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">G</font>;<br/><b>assume </b><a NAME="E1:62_1_1_2"/>
<font color="Maroon">g</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 ;<br/><a NAME="E2:62_1_1_2"/><b>then </b>
<font color="Maroon">g</font> <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/><a NAME="E3:62_1_1_2"/><b>then </b>
<font color="Maroon">g</font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R1">=</a>  <a href="group_1.html#K2">1.</a> <font color="Maroon">G</font>
 <b>by </b><i><a class="ref" href="group_1.html#T16">GROUP_1:16</a></i>;<br/><b>hence </b><a NAME="E4:62_1_1_2"/>
<font color="Maroon">g</font> <a href="group_1.html#K3">"</a>  <a href="hidden.html#R2">in</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i><a class="ref" href="tarski.html#D1">TARSKI:def 1</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:62_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being <a href="group_1.html#V1">strict</a>  <a href="group_2.html#M1" target="_self">Subgroup</a> of <font color="Maroon">G</font> st the <a href="struct_0.html#U1">carrier</a> of <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><span class="p2">(<span class="default"><a href="group_1.html#K2">1.</a> <font color="Maroon">G</font></span>)</span></span><a href="domain_1.html#K6">}</a></span>
 <b>by </b><i>, </i>;<br/>


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