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<b>consider </b><font color="Maroon">c<sub>2</sub></font> being  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="hidden.html#M1">set</a> ] means <font color="Maroon">a<sub>1</sub></font> is  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>
<a NAME="E2:24_1_1"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">c<sub>2</sub></font>]
 
;<br/>
<a NAME="E3:24_1_1"/>
<font color="Maroon">c<sub>2</sub></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">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="funct_2.html#T12">FUNCT_2:12</a></i>;<br/>
<a NAME="E4:24_1_1"/><b>then </b><i><font color="Green">E11</font></i>: 
<font color="Maroon">c<sub>2</sub></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_1.html#K7">MonMaps</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#D6">YELLOW_1:def 6</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>3</sub></font> being  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V1">strict</a> <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of  <a href="yellow_1.html#K7">MonMaps</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E6:24_1_1"/><i><font color="Green">E12</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K7">MonMaps</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span> holds <br/>( <font color="Olive">b<sub>1</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font> iff <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">b<sub>1</sub></font>] )
 <b>from </b><i><a class="ref" href="waybel10.html#S1" target="_self">WAYBEL10:sch 1</a>(<a class="txt" href="waybel10.html#E2:24_1_1"><i><font color="Green">E10</font></i></a>, <a class="txt" href="waybel10.html#E4:24_1_1"><i><font color="Green">E11</font></i></a>);<br/></i>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font>
;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:24_1_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/><a NAME="E2:24_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_1.html#K7">MonMaps</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/><b>hence </b><a NAME="E3:24_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="waybel_1.html#V7">closure</a>
 <b>by </b><i><a class="txt" href="waybel10.html#E6:24_1_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="waybel10.html#E1:24_1_1_1"><i><font color="Green">E13</font></i></a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E8:24_1_1"/><i><font color="Green">E13</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="waybel_1.html#V7">closure</a>
 ;<br/>

<a NAME="E9:24_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is  <a href="waybel_1.html#V7">closure</a> <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
;<br/>
<a NAME="E10:24_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> is <a href="orders_3.html#V5">monotone</a> &amp; <font color="Maroon">c<sub>4</sub></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">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> )
 
<b>by </b><i><a class="ref" href="funct_2.html#T12">FUNCT_2:12</a></i>;<br/>
<a NAME="E11:24_1_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></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_1.html#K7">MonMaps</a> <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="yellow_1.html#D6">YELLOW_1:def 6</a></i>;<br/>
<b>hence </b><a NAME="E12:24_1_1"/>
<font color="Maroon">c<sub>4</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>3</sub></font>
 <b>by </b><i><a class="txt" href="waybel10.html#E6:24_1_1"><i><font color="Green">E12</font></i></a>, <a class="txt" href="waybel10.html#E8:24_1_1"><i><font color="Green">E13</font></i></a></i>;<br/>


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