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<b>thus </b><a NAME="E1:19"/>
for <font color="Olive" title="b1">G</font> being <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a> holds <br/> (  <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Olive" title="b1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Olive" title="b1">G</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/>

<a NAME="E1:19_1"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</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"><font color="Olive" title="b1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 
<b>by </b><i><a class="ref" href="group_6.html#D2" target="_self" title="GROUP_6:def.2">Def2</a></i>;<br/>
<b>hence </b><a NAME="E2:19_1"/>
(  <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp; <font color="Maroon" title="c1">G</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> )
 <b>by </b><i><a class="ref" href="card_1.html#T79" title="CARD_1:th.79">CARD_1:79</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon" title="c1">G</font> be  <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> <a href="group_1.html#NM1" title="GROUP_1:NM.1">Group</a>;<br/>

<b>assume </b><a NAME="E2:19"/>
 <a href="group_1.html#K8" title="GROUP_1:func.8">ord</a> <font color="Maroon" title="c1">G</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1
 ;<br/>

<b>hence </b><a NAME="E3:19"/>
 ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</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"><font color="Olive" title="b1">x</font></span><a href="tarski.html#K1" title="TARSKI:func.1">}</a></span>
 <b>by </b><i><a class="ref" href="card_2.html#T60" title="CARD_2:th.60">CARD_2:60</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="group_6.html#D2" target="_self" title="GROUP_6:def.2">GROUP_6:def 2</a><br/>


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