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<b>let </b><font color="Maroon">R</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> , <font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">f</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">R</font>,<font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/>





<b>assume </b><b>that </b><br/><a NAME="E1:91"/><i><font color="Green">E44</font></i>: 
for <font color="Olive">X</font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font> holds  <font color="Maroon">f</font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Olive">X</font>
 <b>and </b><br/><a NAME="E2:91"/><i><font color="Green">E45</font></i>: 
for <font color="Olive">X</font> being <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> holds  <font color="Maroon">g</font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Olive">X</font>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel34.html#D15" target="_self">WAYBEL34:def 15</a><br/>

<b>let </b><font color="Maroon">X</font> be  <a href="finset_1.html#V1">finite</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">R</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel34.html#D15" target="_self">WAYBEL34:def 15</a><br/>

<a NAME="E3:91"/>
( <font color="Maroon">f</font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Maroon">X</font> &amp; <font color="Maroon">g</font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Maroon">f</font> <a href="relset_1.html#K10">.:</a> <font color="Maroon">X</font> )
 
<b>by </b><i>, </i>;<br/>
<b>hence </b><a NAME="E4:91"/>
<font color="Maroon">g</font> <a href="partfun1.html#K1">*</a> <font color="Maroon">f</font> <a href="waybel_0.html#R4">preserves_sup_of</a> <font color="Maroon">X</font>
 <b>by </b><i/>;<br/>


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