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<b>set </b><font color="Maroon">c<sub>3</sub></font> = <span class="p1"><a href="yellow_3.html#K3" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3" target="_self">:]</a></span>;<br/>
<b>let </b><font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3" target="_self">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="lattice3.html#D10">LATTICE3:def 10</a><br/>

<b>consider </b><font color="Maroon">c<sub>6</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font><b> such that </b><br/><a NAME="E2:35_1_1"/><i><font color="Green">E8</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>and </b><br/><a NAME="E3:35_1_1"/><i><font color="Green">E9</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st <font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="lattice3.html#D10">LATTICE3:def 10</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>7</sub></font> being   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E5:35_1_1"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>7</sub></font> )
 <b>and </b><br/><a NAME="E6:35_1_1"/><i><font color="Green">E11</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> st <font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font> holds <br/><font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Olive">b<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="lattice3.html#D10">LATTICE3:def 10</a></i>;<br/>
<a NAME="E7:35_1_1"/><i><font color="Green">E12</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1"><a href="yellow_3.html#K3" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3" target="_self">:]</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">c<sub>1</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font></span><a href="zfmisc_1.html#K2">:]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#D2" target="_self">Def2</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>8</sub></font>, <font color="Maroon">c<sub>9</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E9:35_1_1"/><i><font color="Green">E13</font></i>: 
( <font color="Maroon">c<sub>8</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>9</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>consider </b><font color="Maroon">c<sub>10</sub></font>, <font color="Maroon">c<sub>11</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E11:35_1_1"/><i><font color="Green">E14</font></i>: 
( <font color="Maroon">c<sub>10</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>11</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="txt" href="yellow_3.html#E7:35_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>take </b><font color="Maroon">c<sub>12</sub></font> = <span class="p1"><a href="yellow_3.html#K7" target="_self">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="yellow_3.html#K7" target="_self">]</a></span>;<br/>

<a NAME="E12:35_1_1"/>
( <span class="p1"><a href="yellow_3.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a> </span>)</span></span><a href="yellow_3.html#K7" target="_self">]</a></span> <a href="orders_2.html#R1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" target="_self">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="yellow_3.html#K7" target="_self">]</a></span> &amp; <span class="p1"><a href="yellow_3.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a> </span>)</span></span><a href="yellow_3.html#K7" target="_self">]</a></span> <a href="orders_2.html#R1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" target="_self">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="yellow_3.html#K7" target="_self">]</a></span> )
 
<b>by </b><i><a class="txt" href="yellow_3.html#E2:35_1_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="yellow_3.html#E5:35_1_1"><i><font color="Green">E10</font></i></a>, <a class="ref" href="yellow_3.html#T11" target="_self">Th11</a></i>;<br/>
<b>hence </b><a NAME="E13:35_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>12</sub></font> )
 <b>by </b><i><a class="txt" href="yellow_3.html#E9:35_1_1"><i><font color="Green">E13</font></i></a>, <a class="txt" href="yellow_3.html#E11:35_1_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="mcart_1.html#T8">MCART_1:8</a></i>;<br/>

<b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <span class="p1"><a href="yellow_3.html#K3" target="_self">[:</a><span class="default"><font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font></span><a href="yellow_3.html#K3" target="_self">:]</a></span>;<br/>

<b>consider </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> being    <a href="hidden.html#M1">set</a> <b> such that </b><br/><a NAME="E15:35_1_1"/><i><font color="Green">E15</font></i>: 
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i><a class="txt" href="yellow_3.html#E7:35_1_1"><i><font color="Green">E12</font></i></a>, <a class="ref" href="zfmisc_1.html#D2">ZFMISC_1:def 2</a></i>;<br/>
<b>assume </b><a NAME="E16:35_1_1"/>
( <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> )
 ;<br/>

<a NAME="E17:35_1_1"/><b>then </b>
( <font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  &amp; <font color="Maroon">c<sub>4</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  &amp; <font color="Maroon">c<sub>5</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  )
 
<b>by </b><i><a class="ref" href="yellow_3.html#T12" target="_self">Th12</a></i>;<br/>
<a NAME="E18:35_1_1"/><b>then </b>
( <font color="Maroon">c<sub>6</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a>  &amp; <font color="Maroon">c<sub>7</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a>  )
 
<b>by </b><i><a class="txt" href="yellow_3.html#E3:35_1_1"><i><font color="Green">E9</font></i></a>, <a class="txt" href="yellow_3.html#E6:35_1_1"><i><font color="Green">E11</font></i></a></i>;<br/>
<a NAME="E19:35_1_1"/><b>then </b>
<span class="p1"><a href="yellow_3.html#K7" target="_self">[</a><span class="default"><font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>7</sub></font></span><a href="yellow_3.html#K7" target="_self">]</a></span> <a href="orders_2.html#R1">&lt;=</a> <span class="p1"><a href="yellow_3.html#K7" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K8" target="_self">`1</a> </span>)</span>,<span class="p2">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="yellow_3.html#K9" target="_self">`2</a> </span>)</span></span><a href="yellow_3.html#K7" target="_self">]</a></span>
 
<b>by </b><i><a class="ref" href="yellow_3.html#T11" target="_self">Th11</a></i>;<br/>
<b>hence </b><a NAME="E20:35_1_1"/>
<font color="Maroon">c<sub>12</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>13</sub></font>
 <b>by </b><i><a class="txt" href="yellow_3.html#E15:35_1_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="mcart_1.html#T8">MCART_1:8</a></i>;<br/>


</div>
