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<b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V3">transitive</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">T</font>;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/>





<div><b>hereby </b>
<div class="add"><b>assume </b><b>that </b><br/><a NAME="E1:54_1"/><i><font color="Green">E29</font></i>: 
<font color="Maroon">S</font> <a href="yellow16.html#R5" target="_self">inherits_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">T</font>
 <b>and </b><br/><a NAME="E2:54_1"/><i><font color="Green">E32</font></i>: 
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">T</font>
 ;<br/><a NAME="E3:54_1"/>
 <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 <b>by </b><i>, , </i>;<br/><b>hence </b><a NAME="E4:54_1"/>
(  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">S</font> &amp;  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> )
 <b>by </b><i>, <a class="ref" href="yellow_0.html#T65">YELLOW_0:65</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:54"/><i><font color="Green">E47</font></i>: 
(  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> implies (  <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">S</font> &amp;  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">X</font> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> ) )
 ;<br/>

<b>assume </b><a NAME="E3:54"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <font color="Maroon">X</font>,<font color="Maroon">T</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow16.html#D6" target="_self">YELLOW16:def 6</a><br/>

<b>hence </b><a NAME="E4:54"/>
 <a href="yellow_0.html#K1">"\/"</a> <font color="Maroon">X</font>,<font color="Maroon">T</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>
 <b>by </b><i/>;<br/>


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