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<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="orders_2.html#V3" title="ORDERS_2:attr.3">transitive</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>  <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">T</font>;<br/><b>let </b><font color="Maroon" title="c3">X</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c2">S</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:55_1"/><i><font color="Green" title="E40">A1</font></i>: 
<font color="Maroon" title="c2">S</font> <a href="yellow16.html#R6" title="YELLOW16:pred.6">inherits_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font>
 <b>and </b><br/><a NAME="E2:55_1"/><i><font color="Green" title="E41">A2</font></i>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font>
 ;<br/><a NAME="E3:55_1"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="yellow16.html#E1:55_1"><i><font color="Green" title="E40">A1</font></i></a>, <a class="txt" href="yellow16.html#E2:55_1"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="yellow16.html#D7" target="_self" title="YELLOW16:def.7">Def7</a></i>;<br/><b>hence </b><a NAME="E4:55_1"/>
(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> )
 <b>by </b><i><a class="txt" href="yellow16.html#E2:55_1"><i><font color="Green" title="E41">A2</font></i></a>, <a class="ref" href="yellow_0.html#T64" title="YELLOW_0:th.64">YELLOW_0:64</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:55"/><i><font color="Green" title="E40">A3</font></i>: 
(  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> implies (  <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c2">S</font> &amp;  <a href="yellow_0.html#NK4" title="YELLOW_0:NK.4">inf</a> <font color="Maroon" title="c3">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> ) )
 ;<br/>

<b>assume </b><a NAME="E3:55"/>
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D7" target="_self" title="YELLOW16:def.7">YELLOW16:def 7</a><br/>

<b>hence </b><a NAME="E4:55"/>
 <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> <font color="Maroon" title="c3">X</font>,<font color="Maroon" title="c1">T</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S</font>
 <b>by </b><i><a class="txt" href="yellow16.html#E2:55"><i><font color="Green" title="E40">A3</font></i></a></i>;<br/>


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