<?xml version="1.0"?>
<div class="add">

<b>set </b><font color="Maroon">c<sub>4</sub></font> = the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> <a href="toler_1.html#K1">|_2</a> <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as    <a href="relset_1.html#M2">Relation</a> of the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font>,the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font> ;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:64_1_1_1"/>
(  not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> or <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_1_1_1"><b>suppose </b></a><a NAME="E1:64_1_1_1_1"/>
not <font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>1</sub></font> as  non <a href="struct_0.html#V3">empty</a>  <a href="struct_0.html#L1">1-sorted</a>  ;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> = the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font>;<br/><b>reconsider </b><font color="Maroon">c<sub>8</sub></font> = the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K2">|</a> <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> as   <a href="funct_2.html#NM1">Function</a> of the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>6</sub></font> <b>by </b><i><a class="ref" href="funct_2.html#T38">FUNCT_2:38</a></i>;<br/><b>set </b><font color="Maroon">c<sub>9</sub></font> =  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> #);<br/><a NAME="E4:64_1_1_1_1"/><i><font color="Green">E35</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><a NAME="E5:64_1_1_1_1"/><b>then </b>
 <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> #) is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>10</sub></font> =  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>8</sub></font> #) as  <a href="waybel_0.html#V6">strict</a>  <a href="yellow_6.html#M1" target="_self">SubNetStr</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="yellow_6.html#D8" target="_self">Def8</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>10</sub></font>
;<br/><b>thus </b><a NAME="E7:64_1_1_1_1"/>
( <font color="Maroon">c<sub>10</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="yellow_6.html#E4:64_1_1_1_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="64_1_1_1_2"><b>suppose </b></a><a NAME="E1:64_1_1_1_2"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a>
 ;<br/><div class="add"><a NAME="E2:64_1_1_1_2"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="struct_0.html#D1">STRUCT_0:def 1</a></i>;<br/><a NAME="E3:64_1_1_1_2"/><b>then </b>
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="partfun1.html#T64">PARTFUN1:64</a></i>;<br/><a NAME="E4:64_1_1_1_2"/><b>then </b><i><font color="Green">E35</font></i>: 
the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="xboole_0.html#K1">{}</a> 
 <b>by </b><i><a class="ref" href="relat_1.html#T172">RELAT_1:172</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="xboole_0.html#K1">{}</a>  as   <a href="funct_2.html#NM1">Function</a> of the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</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#T55">FUNCT_2:55</a>, <a class="ref" href="relat_1.html#T60">RELAT_1:60</a></i>;<br/><b>set </b><font color="Maroon">c<sub>7</sub></font> =  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> #);<br/><a NAME="E6:64_1_1_1_2"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="tarski.html#R1">c=</a> the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="xboole_1.html#T17">XBOOLE_1:17</a></i>;<br/><a NAME="E7:64_1_1_1_2"/><b>then </b><i><font color="Green">E37</font></i>: 
 <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> #) is    <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a></i>;<br/><a NAME="E8:64_1_1_1_2"/>
the <a href="waybel_0.html#U1">mapping</a> of <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> #) <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="partfun1.html#K2">|</a> the <a href="struct_0.html#U1">carrier</a> of <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> #)
 <b>by </b><i><a class="txt" href="yellow_6.html#E4:64_1_1_1_2"><i><font color="Green">E35</font></i></a>, <a class="ref" href="relat_1.html#T110">RELAT_1:110</a></i>;<br/><b>then reconsider </b><font color="Maroon">c<sub>8</sub></font> =  <a href="waybel_0.html#G1">NetStr</a>(# <span class="p1">(<span class="default">the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font></span>)</span>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font> #) as  <a href="waybel_0.html#V6">strict</a>  <a href="yellow_6.html#M1" target="_self">SubNetStr</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="yellow_6.html#E7:64_1_1_1_2"><i><font color="Green">E37</font></i></a>, <a class="ref" href="yellow_6.html#D8" target="_self">Def8</a></i>;<br/><b>take </b>
<font color="Maroon">c<sub>8</sub></font>
;<br/><b>thus </b><a NAME="E10:64_1_1_1_2"/>
( <font color="Maroon">c<sub>8</sub></font> is  <a href="yellow_0.html#V4">full</a>  <a href="yellow_0.html#M1">SubRelStr</a> of <font color="Maroon">c<sub>2</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R1">=</a> the <a href="waybel_0.html#U1">mapping</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K11">"</a> <font color="Maroon">c<sub>3</sub></font> )
 <b>by </b><i><a class="txt" href="yellow_6.html#E6:64_1_1_1_2"><i><font color="Green">E36</font></i></a>, <a class="ref" href="yellow_0.html#D13">YELLOW_0:def 13</a>, <a class="ref" href="yellow_0.html#D14">YELLOW_0:def 14</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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