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<b>let </b><font color="Maroon" title="c1">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> <a href="orders_1.html#R1" title="ORDERS_1:pred.1">quasi_orders</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> <a href="orders_1.html#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Maroon" title="c1">X</font> )</span><br/>

<i><font color="Green" title="E37">A1</font></i>:  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font></span>)</span> = 
<font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <span class="p1">(<span class="default"><a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <span class="p2">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>
<br/>.= 
<font color="Maroon" title="c1">X</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> <font color="Maroon" title="c1">X</font>
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>
<br/>.= 
<font color="Maroon" title="c1">X</font>

;<br/>
<a NAME="E2:65"/>
(  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> <a href="orders_1.html#NR1" title="ORDERS_1:NR.1">is_quasi-order</a>  &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> <a href="orders_1.html#NR2" title="ORDERS_1:NR.2">is_partial-order</a>  )
 
<b>by </b><i><a class="ref" href="orders_1.html#T120" target="_self" title="ORDERS_1:th.120">Th120</a></i>;<br/>
<b>hence </b><a NAME="E3:65"/>
(  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> <a href="orders_1.html#R1" title="ORDERS_1:pred.1">quasi_orders</a> <font color="Maroon" title="c1">X</font> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c1">X</font> <a href="orders_1.html#R2" title="ORDERS_1:pred.2">partially_orders</a> <font color="Maroon" title="c1">X</font> )
 <b>by </b><i><a class="txt" href="orders_1.html#E1:65"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="orders_1.html#T127" target="_self" title="ORDERS_1:th.127">Th127</a>, <a class="ref" href="orders_1.html#T130" target="_self" title="ORDERS_1:th.130">Th130</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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