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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> <a href="waybel_0.html#V24">up-complete</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">T</font> be  non <a href="struct_0.html#V3">empty</a> <a href="yellow_0.html#V1">lower-bounded</a> <a href="waybel_0.html#V24">up-complete</a> <a href="orders_2.html#NM1">Poset</a>;<br/><b>let </b><font color="Maroon">x</font> be   <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>;<br/>





<a NAME="E1:49"/>
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/>
<a NAME="E2:49"/><b>then </b><i><font color="Green">E18</font></i>: 
<font color="Maroon">x</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">x</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</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>thus </b><a NAME="E3:49"/>
 <a href="yellow_3.html#K4">proj1</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font></span>)</span> <a href="tarski.html#R1">c=</a>  <a href="waybel_3.html#K1">waybelow</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>
 <b>by </b><i><a class="txt" href="yellow10.html#E6:49"><i><font color="Green">E21</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a><br/>

<b>let </b><font color="Maroon">a</font> be    <a href="hidden.html#M1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a><br/>

<b>assume </b><a NAME="E4:49"/><i><font color="Green">E20</font></i>: 
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="waybel_3.html#K1">waybelow</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>
 ;<br/>

<b>then reconsider </b><font color="Maroon">a'</font> = <font color="Maroon">a</font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">S</font> ;<br/>
<a NAME="E6:49"/><i><font color="Green">E21</font></i>: 
<font color="Maroon">a'</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a> 
 
<b>by </b><i><a class="ref" href="yellow10.html#T3" target="_self">Th3</a>, <a class="ref" href="waybel_3.html#T7">WAYBEL_3:7</a></i>;<br/>
<a NAME="E7:49"/>
 <a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">T</font> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a> 
 
<b>by </b><i><a class="ref" href="waybel_3.html#T4">WAYBEL_3:4</a></i>;<br/>
<a NAME="E8:49"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">a'</font>,<span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">T</font></span>)</span></span><a href="yellow_3.html#K7">]</a></span> <a href="waybel_3.html#NR2" target="_self">&lt;&lt;</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a> </span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
<b>by </b><i>, </i>;<br/>
<a NAME="E9:49"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><font color="Maroon">a'</font>,<span class="p2">(<span class="default"><a href="yellow_0.html#K3">Bottom</a> <font color="Maroon">T</font></span>)</span></span><a href="yellow_3.html#K7">]</a></span> <a href="hidden.html#R2">in</a>  <a href="waybel_3.html#K1">waybelow</a> <span class="p1"><a href="yellow_3.html#K7">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K8">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">x</font> <a href="yellow_3.html#K9">`2</a> </span>)</span></span><a href="yellow_3.html#K7">]</a></span>
 
;<br/>
<b>hence </b><a NAME="E10:49"/>
<font color="Maroon">a</font> <a href="hidden.html#R2">in</a>  <a href="yellow_3.html#K4">proj1</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1">waybelow</a> <font color="Maroon">x</font></span>)</span>
 <b>by </b><i>, <a class="ref" href="funct_5.html#D1">FUNCT_5:def 1</a></i>;<br/>


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