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<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>; <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   <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Olive" title="b1">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c1">G</font></span><br/><b>let </b><font color="Maroon" title="c2">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">  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c2">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c1">G</font></span><br/>



<a NAME="E1:73"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">H</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">G</font>
 
<b>by </b><i><a class="ref" href="group_2.html#D5" target="_self" title="GROUP_2:def.5">Def5</a></i>;<br/>
<b>hence </b><a NAME="E2:73"/>
 <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c2">H</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="group_1.html#K7" title="GROUP_1:func.7">card</a> <font color="Maroon" title="c1">G</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T44" title="NAT_1:th.44">NAT_1:44</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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