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<b>let </b><font color="Maroon">L</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="xboole_0.html#V1">empty</a> <a href="waybel23.html#V1" target="_self">meet-closed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L</font>;<br/><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M2">Element</a> of <font color="Maroon">S</font>;<br/>





<a NAME="E1:31"/><i><font color="Green">E31</font></i>: 
 <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">S</font> is  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V4">full</a> <a href="yellow_0.html#V5">meet-inheriting</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">L</font>
 
<b>by </b><i/>;<br/>
<a NAME="E2:31"/><i><font color="Green">E33</font></i>: 
( <font color="Maroon">x</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">S</font></span>)</span> &amp; <font color="Maroon">y</font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">S</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>
<b>assume </b><a NAME="E3:31"/><i><font color="Green">E35</font></i>: 
 <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font>
 ;<br/>

<a NAME="E4:31"/><b>then </b>
 <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">S</font></span>)</span>
 
<b>by </b><i>, , <a class="ref" href="yellow_0.html#D16">YELLOW_0:def 16</a></i>;<br/>
<b>hence </b><a NAME="E5:31"/>
(  <a href="yellow_0.html#R2">ex_inf_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>, <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">S</font> &amp;  <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<span class="p1">(<span class="default"><a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">S</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="yellow_0.html#K2">"/\"</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">y</font></span><a href="domain_1.html#K7">}</a></span>,<font color="Maroon">L</font> )
 <b>by </b><i>, , <a class="ref" href="yellow_0.html#T66">YELLOW_0:66</a></i>;<br/>


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