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<b>thus </b><a NAME="E1:46_1_1"/>
 <a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V12">lower</a>
 <div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D19">WAYBEL_0:def 19</a><br/>

<b>assume </b><a NAME="E1:46_1_1_1"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R3">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> )
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_1_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:46_1_1_1_1"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:46_1_1_1_1"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E1:46_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="abcmiz_0.html#D13" target="_self">Def13</a></i>;<br/><a NAME="E3:46_1_1_1_1"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>3</sub></font> &amp;  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E1:46_1_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="abcmiz_0.html#T10" target="_self">Th10</a>, <a class="ref" href="abcmiz_0.html#T13" target="_self">Th13</a></i>;<br/><b>hence </b><a NAME="E4:46_1_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="abcmiz_0.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:46_1_1_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="ref" href="abcmiz_0.html#D13" target="_self">Def13</a></i>;<br/>


</div><b>end;</b></div>

<b>let </b><font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D1">WAYBEL_0:def 1</a><br/>

<b>assume </b><a NAME="E2:46_1_1"/><i><font color="Green">E21</font></i>: 
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">c<sub>2</sub></font> )
 ;<br/>

<div><i><font color="Green">E22</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="46_1_1_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>5</sub></font> be   <a href="abcmiz_0.html#NM2">adjective</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:46_1_1_2"/>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><a NAME="E2:46_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">c<sub>5</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E2:46_1_1"><i><font color="Green">E21</font></i></a>, <a class="ref" href="abcmiz_0.html#D13" target="_self">Def13</a></i>;<br/><a NAME="E3:46_1_1_2"/><b>then </b>
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>3</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="ref" href="abcmiz_0.html#T13" target="_self">Th13</a></i>;<br/><a NAME="E4:46_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="finsub_1.html#K3">/\</a> <span class="p1">(<span class="default"><a href="abcmiz_0.html#K2" target="_self">adjs</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="xboole_0.html#D3">XBOOLE_0:def 3</a></i>;<br/><a NAME="E5:46_1_1_2"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K2" target="_self">adjs</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="abcmiz_0.html#D11" target="_self">Def11</a></i>;<br/><b>hence </b><a NAME="E6:46_1_1_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K3" target="_self">types</a> <font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="ref" href="abcmiz_0.html#T13" target="_self">Th13</a></i>;<br/></div><b>end;</b></div>
<b>take </b>
<font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font>
;<br/>

<b>thus </b><a NAME="E4:46_1_1"/>
( <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="abcmiz_0.html#K4" target="_self">types</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> <a href="orders_2.html#R1">&lt;=</a> <font color="Maroon">c<sub>3</sub></font> <a href="lattice3.html#K13">"\/"</a> <font color="Maroon">c<sub>4</sub></font> )
 <b>by </b><i><a class="txt" href="abcmiz_0.html#E3:46_1_1"><i><font color="Green">E22</font></i></a>, <a class="ref" href="abcmiz_0.html#D13" target="_self">Def13</a>, <a class="ref" href="yellow_0.html#T22">YELLOW_0:22</a></i>;<br/>


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