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

<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="waybel_0.html#V24">up-complete</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#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="waybel_0.html#V24">up-complete</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">X</font> be   <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>;<br/>



<b>assume </b><a NAME="E1:64"/><i><font color="Green">E18</font></i>: 
for <font color="Olive">D</font> being non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>  st  <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Olive">D</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> holds <br/> ex <font color="Olive">y</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span> st <br/>( <font color="Olive">y</font> <a href="hidden.html#R2">in</a> <font color="Olive">D</font> &amp; ( for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Olive">D</font> &amp; <font color="Olive">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Olive">y</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D3">WAYBEL11:def 3</a><br/>

<a NAME="E2:64"/><i><font color="Green">E20</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a> <span class="p1"><a href="zfmisc_1.html#K2">[:</a><span class="default">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></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#D2">YELLOW_3:def 2</a></i>;<br/>
<div><b>hereby </b> <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D3">WAYBEL11:def 3</a>
<div class="add"><b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font>;<br/><b>assume </b><a NAME="E1:64_1"/>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="yellow_3.html#K4">proj1</a> <font color="Maroon">X</font>
 ;<br/><b>then consider </b><font color="Maroon">t</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E3:64_1"/><i><font color="Green">E21</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">t</font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="funct_5.html#D1">FUNCT_5:def 1</a></i>;<br/><b>reconsider </b><font color="Maroon">t</font> = <font color="Maroon">t</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font> <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>reconsider </b><font color="Maroon">t'</font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">t</font></span><a href="domain_1.html#K6">}</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font> <b>by </b><i><a class="ref" href="waybel_0.html#T5">WAYBEL_0:5</a></i>;<br/><a NAME="E6:64_1"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span>,<span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>
 <b>by </b><i><a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/><b>then </b> <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span> = 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="yellow_3.html#T46">YELLOW_3:46</a></i>
<br/>.= 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
<br/>.= 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">t'</font></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
<br/>.= 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span>,<font color="Maroon">t</font></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="yellow_0.html#T39">YELLOW_0:39</a></i>
;<br/><b>then consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span><b> such that </b><br/><a NAME="E9:64_1"/><i><font color="Green">E23</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span>
 <b>and </b><br/><a NAME="E10:64_1"/><i><font color="Green">E31</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span> &amp; <font color="Olive">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/><b>take </b><font color="Maroon">z</font> = <font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a> ;<br/><a NAME="E11:64_1"/><i><font color="Green">E32</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a> </span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 <b>by </b><i>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/><b>hence </b><a NAME="E12:64_1"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>by </b><i><a class="txt" href="yellow10.html#E10:64_1"><i><font color="Green">E31</font></i></a>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/><b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font>;<br/><b>assume </b><a NAME="E13:64_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 ;<br/><a NAME="E14:64_1"/><b>then </b><i><font color="Green">E36</font></i>: 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">t</font></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">D</font>,<font color="Maroon">t'</font></span><a href="yellow_3.html#K10">:]</a></span>
 <b>by </b><i><a class="ref" href="zfmisc_1.html#T129">ZFMISC_1:129</a></i>;<br/><b>assume </b><a NAME="E15:64_1"/><i><font color="Green">E45</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">z</font>
 ;<br/><a NAME="E16:64_1"/><i><font color="Green">E54</font></i>: 
<font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="txt" href="yellow10.html#E10:64_1"><i><font color="Green">E31</font></i></a>, , <a class="ref" href="zfmisc_1.html#T129">ZFMISC_1:129</a></i>;<br/><a NAME="E17:64_1"/>
<font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a> 
 ;<br/><a NAME="E18:64_1"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">t</font></span><a href="yellow_3.html#K7">]</a></span> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font>
 <b>by </b><i>, , <a class="txt" href="yellow10.html#E14:64_1"><i><font color="Green">E36</font></i></a>, <a class="ref" href="yellow_3.html#T11">YELLOW_3:11</a></i>;<br/><a NAME="E19:64_1"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">x</font>,<font color="Maroon">t</font></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="txt" href="yellow10.html#E11:64_1"><i><font color="Green">E32</font></i></a>, <a class="ref" href="yellow10.html#T13" target="_self">Th13</a></i>;<br/><b>hence </b><a NAME="E20:64_1"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="yellow_3.html#K4">proj1</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="funct_5.html#T4">FUNCT_5:4</a></i>;<br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon">D</font> be  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">T</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel11.html#D3">WAYBEL11:def 3</a><br/>

<b>assume </b><a NAME="E4:64"/>
 <a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font> <a href="hidden.html#R2">in</a>  <a href="yellow_3.html#K5">proj2</a> <font color="Maroon">X</font>
 ;<br/>

<b>then consider </b><font color="Maroon">s</font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E6:64"/><i><font color="Green">E56</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">s</font>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="funct_5.html#D2">FUNCT_5:def 2</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s</font> = <font color="Maroon">s</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> <b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>
<b>reconsider </b><font color="Maroon">s'</font> = <span class="p1"><a href="domain_1.html#K6">{</a><span class="default"><font color="Maroon">s</font></span><a href="domain_1.html#K6">}</a></span> as  non <a href="xboole_0.html#V1">empty</a> <a href="waybel_0.html#V1">directed</a> <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">S</font> <b>by </b><i><a class="ref" href="waybel_0.html#T5">WAYBEL_0:5</a></i>;<br/>
<a NAME="E9:64"/>
 <a href="yellow_0.html#R1">ex_sup_of</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span>,<span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>
 
<b>by </b><i><a class="ref" href="waybel_0.html#T75">WAYBEL_0:75</a></i>;<br/>
<b>then </b> <a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span> = 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K4">proj1</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="yellow_3.html#T46">YELLOW_3:46</a></i>
<br/>.= 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">s'</font></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <span class="p3">(<span class="default"><a href="yellow_3.html#K5">proj2</a> <span class="p4"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span></span>)</span></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
<br/>.= 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">s'</font></span>)</span>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="funct_5.html#T11">FUNCT_5:11</a></i>
<br/>.= 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">s</font>,<span class="p2">(<span class="default"><a href="yellow_0.html#NK3" target="_self">sup</a> <font color="Maroon">D</font></span>)</span></span><a href="yellow_3.html#K7">]</a></span>
<b>by </b><i><a class="ref" href="yellow_0.html#T39">YELLOW_0:39</a></i>
;<br/>
<b>then consider </b><font color="Maroon">y</font> being   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span><b> such that </b><br/><a NAME="E12:64"/><i><font color="Green">E58</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span>
 <b>and </b><br/><a NAME="E13:64"/><i><font color="Green">E59</font></i>: 
for <font color="Olive">x</font> being  <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">S</font>,<font color="Maroon">T</font></span><a href="yellow_3.html#K3">:]</a></span>  st <font color="Olive">x</font> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span> &amp; <font color="Olive">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font> holds <br/><font color="Olive">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 <b>by </b><i>, </i>;<br/>
<b>take </b><font color="Maroon">z</font> = <font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a> ;<br/>

<a NAME="E14:64"/><i><font color="Green">E60</font></i>: 
<font color="Maroon">y</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">y</font> <a href="yellow_3.html#K9">`2</a> </span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
<b>by </b><i>, <a class="ref" href="mcart_1.html#T23">MCART_1:23</a></i>;<br/>
<b>hence </b><a NAME="E15:64"/>
<font color="Maroon">z</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 <b>by </b><i>, <a class="ref" href="zfmisc_1.html#T106">ZFMISC_1:106</a></i>;<br/>

<b>let </b><font color="Maroon">x</font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">T</font>;<br/>

<b>assume </b><a NAME="E16:64"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a> <font color="Maroon">D</font>
 ;<br/>

<a NAME="E17:64"/><b>then </b><i><font color="Green">E68</font></i>: 
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">x</font></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <span class="p1"><a href="yellow_3.html#K10">[:</a><span class="default"><font color="Maroon">s'</font>,<font color="Maroon">D</font></span><a href="yellow_3.html#K10">:]</a></span>
 
<b>by </b><i><a class="ref" href="zfmisc_1.html#T128">ZFMISC_1:128</a></i>;<br/>
<b>assume </b><a NAME="E18:64"/><i><font color="Green">E69</font></i>: 
<font color="Maroon">x</font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">z</font>
 ;<br/>

<a NAME="E19:64"/><i><font color="Green">E70</font></i>: 
<font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a>  <a href="hidden.html#R1">=</a> <font color="Maroon">s</font>
 
<b>by </b><i>, , <a class="ref" href="zfmisc_1.html#T128">ZFMISC_1:128</a></i>;<br/>
<a NAME="E20:64"/>
<font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a>  <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">y</font> <a href="yellow_3.html#K8">`1</a> 
 
;<br/>
<a NAME="E21:64"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">x</font></span><a href="yellow_3.html#K7">]</a></span> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">y</font>
 
<b>by </b><i>, , , <a class="ref" href="yellow_3.html#T11">YELLOW_3:11</a></i>;<br/>
<a NAME="E22:64"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">s</font>,<font color="Maroon">x</font></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a> <font color="Maroon">X</font>
 
<b>by </b><i>, <a class="ref" href="yellow10.html#T13" target="_self">Th13</a></i>;<br/>
<b>hence </b><a NAME="E23:64"/>
<font color="Maroon">x</font> <a href="hidden.html#R2">in</a>  <a href="yellow_3.html#K5">proj2</a> <font color="Maroon">X</font>
 <b>by </b><i><a class="ref" href="funct_5.html#T4">FUNCT_5:4</a></i>;<br/>


</div>
