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<b>let </b><font color="Maroon" title="c1">T</font> be    <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a> implies <font color="Maroon" title="c1">T</font> is <a href="orders_4.html#V1" title="ORDERS_4:attr.1">countable</a> )</span><br/>

<b>assume </b><a NAME="E1:4_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="struct_0.html#V8" title="STRUCT_0:attr.8">finite</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">T</font> is <a href="orders_4.html#V1" title="ORDERS_4:attr.1">countable</a></span><br/>

<a NAME="E2:4_1_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>
 
;<br/>
<a NAME="E3:4_1_1"/><b>then </b>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">T</font> is <a href="card_3.html#V4" title="CARD_3:attr.4">countable</a>
 
<b>by </b><i><a class="ref" href="card_4.html#T43" title="CARD_4:th.43">CARD_4:43</a></i>;<br/>
<b>hence </b><a NAME="E4:4_1_1"/>
<font color="Maroon" title="c1">T</font> is <a href="orders_4.html#V1" title="ORDERS_4:attr.1">countable</a>
 <b>by </b><i><a class="ref" href="orders_4.html#D2" title="ORDERS_4:def.2">ORDERS_4:def 2</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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