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<b>set </b><font color="Maroon">X</font> =  <a href="orders_3.html#K1">MonFuncs</a> <font color="Maroon">S</font>,<font color="Maroon">T</font>;<br/>
<a NAME="E1:59_1_1"/>
 <a href="orders_3.html#K1">MonFuncs</a> <font color="Maroon">S</font>,<font color="Maroon">T</font> <a href="tarski.html#R1">c=</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font>
 
<b>by </b><i><a class="ref" href="orders_3.html#T11">ORDERS_3:11</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">X</font> =  <a href="orders_3.html#K1">MonFuncs</a> <font color="Maroon">S</font>,<font color="Maroon">T</font> as   <a href="struct_0.html#NM2">Subset</a> of <span class="p1">(<span class="default"><font color="Maroon">T</font> <a href="yellow_1.html#K6" target="_self">|^</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font></span>)</span> <b>by </b><i/>;<br/>
<b>take </b><font color="Maroon">SX</font> =  <a href="yellow_0.html#K5">subrelstr</a> <font color="Maroon">X</font>;<br/>

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

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:59_1_1_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">SX</font>
 ;<br/><a NAME="E2:59_1_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/><b>then consider </b><font color="Maroon">f'</font> being   <a href="struct_0.html#NM6">Function</a> of <font color="Maroon">S</font>,<font color="Maroon">T</font><b> such that </b><br/><a NAME="E4:59_1_1_1"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">f'</font> <a href="hidden.html#R1">=</a> <font color="Maroon">f</font> &amp; <font color="Maroon">f'</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">f'</font> is <a href="orders_3.html#V5">monotone</a> )
 <b>by </b><i><a class="ref" href="orders_3.html#D6">ORDERS_3:def 6</a></i>;<br/><b>thus </b><a NAME="E5:59_1_1_1"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">f</font> is <a href="orders_3.html#V5">monotone</a> )
 <b>by </b><i/>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:59_1_1"/>
( <font color="Maroon">f</font> <a href="hidden.html#R2">in</a>  <a href="funct_2.html#K1">Funcs</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">S</font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">T</font> &amp; <font color="Maroon">f</font> is <a href="orders_3.html#V5">monotone</a> )
 ;<br/>

<a NAME="E5:59_1_1"/><b>then </b>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i><a class="ref" href="orders_3.html#D6">ORDERS_3:def 6</a></i>;<br/>
<b>hence </b><a NAME="E6:59_1_1"/>
<font color="Maroon">f</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">SX</font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D15">YELLOW_0:def 15</a></i>;<br/>


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