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<b>let </b><font color="Maroon">X</font> be    <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">S</font> be   <a href="subset_1.html#NM2">Subset</a> of <font color="Maroon">X</font>;<br/><b>let </b><font color="Maroon">R</font> be   <a href="orders_1.html#NM2">Order</a> of <font color="Maroon">X</font>;<br/>





<b>assume </b><a NAME="E1:3"/>
<font color="Maroon">R</font> <a href="orders_1.html#NR3" target="_self">is_linear-order</a> 
 ;<br/>

<a NAME="E2:3"/><b>then </b><i><font color="Green">E23</font></i>: 
<font color="Maroon">R</font> <a href="orders_1.html#R3">linearly_orders</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T133">ORDERS_1:133</a></i>;<br/>
<a NAME="E3:3"/>
<font color="Maroon">S</font> <a href="tarski.html#R1">c=</a> <font color="Maroon">X</font>
 
;<br/>
<a NAME="E4:3"/><b>then </b>
<font color="Maroon">S</font> <a href="tarski.html#R1">c=</a>  <a href="relat_1.html#K3">field</a> <font color="Maroon">R</font>
 
<b>by </b><i><a class="ref" href="orders_1.html#T100">ORDERS_1:100</a></i>;<br/>
<b>hence </b><a NAME="E5:3"/>
<font color="Maroon">R</font> <a href="orders_1.html#R3">linearly_orders</a> <font color="Maroon">S</font>
 <b>by </b><i>, <a class="ref" href="orders_1.html#T134">ORDERS_1:134</a></i>;<br/>


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