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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   <a href="relat_1.html#NM1" title="RELAT_1:NM.1">Relation</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">R</font> is  <a href="orders_1.html#V3" title="ORDERS_1:attr.3">being_linear-order</a>  implies <font color="Maroon" title="c1">R</font> <a href="orders_1.html#R3" title="ORDERS_1:pred.3">linearly_orders</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:148"/><span class="lab"><font color="Green" title="E28">A1</font></span>: 
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font>
 <span class="kw">and </span><br/><a NAME="E2:148"/><span class="lab"><font color="Green" title="E29">A2</font></span>: 
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font>
 <span class="kw">and </span><br/><a NAME="E3:148"/><span class="lab"><font color="Green" title="E30">A3</font></span>: 
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font>
 <span class="kw">and </span><br/><a NAME="E4:148"/><span class="lab"><font color="Green" title="E31">A4</font></span>: 
<font color="Maroon" title="c1">R</font> <a href="relat_2.html#R6" title="RELAT_2:pred.6">is_connected_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="relat_2.html#D9" title="RELAT_2:def.9">RELAT_2:def 9</a>,<a class="ref" href="relat_2.html#D12" title="RELAT_2:def.12">RELAT_2:def 12</a>,<a class="ref" href="relat_2.html#D14" title="RELAT_2:def.14">RELAT_2:def 14</a>,<a class="ref" href="relat_2.html#D16" title="RELAT_2:def.16">RELAT_2:def 16</a>,<a class="ref" href="orders_1.html#D5" target="_self" title="ORDERS_1:def.5">ORDERS_1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c1">R</font> <a href="orders_1.html#R3" title="ORDERS_1:pred.3">linearly_orders</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font></span><br/>

<span class="kw">thus </span><a NAME="E5:148"/>
( <font color="Maroon" title="c1">R</font> <a href="relat_2.html#R1" title="RELAT_2:pred.1">is_reflexive_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_2.html#R8" title="RELAT_2:pred.8">is_transitive_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_2.html#R4" title="RELAT_2:pred.4">is_antisymmetric_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> &amp; <font color="Maroon" title="c1">R</font> <a href="relat_2.html#R6" title="RELAT_2:pred.6">is_connected_in</a>  <a href="relat_1.html#K3" title="RELAT_1:func.3">field</a> <font color="Maroon" title="c1">R</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:148"><span class="lab"><font color="Green" title="E28">A1</font></span></a>, <a class="txt" href="#E2:148"><span class="lab"><font color="Green" title="E29">A2</font></span></a>, <a class="txt" href="#E3:148"><span class="lab"><font color="Green" title="E30">A3</font></span></a>, <a class="txt" href="#E4:148"><span class="lab"><font color="Green" title="E31">A4</font></span></a></span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="orders_1.html#D8" target="_self" title="ORDERS_1:def.8">ORDERS_1:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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