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<b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">L1</font>,<font color="Maroon">L2</font>;<br/>

<b>assume </b><a NAME="E1:124_2_1"/><i><font color="Green">E30</font></i>: 
for <font color="Olive">X</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L1</font> holds  <font color="Maroon">f</font> <a href="waybel_0.html#R4" target="_self">preserves_sup_of</a> <font color="Olive">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D33" target="_self">WAYBEL_0:def 33</a><br/>

<b>hence </b><a NAME="E2:124_2_1"/>
for <font color="Olive">X</font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">L1</font>  st not <font color="Olive">X</font> is <a href="xboole_0.html#V1">empty</a> &amp; <font color="Olive">X</font> is <a href="waybel_0.html#V1" target="_self">directed</a> holds <br/><font color="Maroon">f</font> <a href="waybel_0.html#R4" target="_self">preserves_sup_of</a> <font color="Olive">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D37" target="_self">WAYBEL_0:def 37</a><br/>

<b>thus </b><a NAME="E3:124_2_1"/>
for <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">L1</font> holds  <font color="Maroon">f</font> <a href="waybel_0.html#R4" target="_self">preserves_sup_of</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><font color="Olive">x</font>,<font color="Olive">y</font></span><a href="domain_1.html#K7">}</a></span>
 <b>by </b><i/>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D35" target="_self">WAYBEL_0:def 35</a><br/>


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