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<b>set </b><font color="Maroon" title="c2">f</font> =  <a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font>;<br/>
<b>let </b><font color="Maroon" title="c3">x</font>, <font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1"><a href="yellow_3.html#K3" title="YELLOW_3:func.3">[:</a><span class="default"><font color="Maroon" title="c1">L</font>,<font color="Maroon" title="c1">L</font></span><a href="yellow_3.html#K3" title="YELLOW_3:func.3">:]</a></span>; <i><font color="Red">:: according to </font></i><a class="ref" href="orders_3.html#D5" title="ORDERS_3:def.5">ORDERS_3:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">y</font> or for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> or <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> ) )</span><br/>

<b>assume </b><a NAME="E1:46_1_1"/>
<font color="Maroon" title="c3">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">y</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font>  holds <br/>(  not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> or  not <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> or <font color="Olive">b<sub>1</sub></font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Olive">b<sub>2</sub></font> )</span><br/>

<a NAME="E2:46_1_1"/><b>then </b><i><font color="Green" title="E29">A1</font></i>: 
( <font color="Maroon" title="c3">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a>  &amp; <font color="Maroon" title="c3">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a>  )
 
<b>by </b><i><a class="ref" href="yellow_3.html#T12" title="YELLOW_3:th.12">YELLOW_3:12</a></i>;<br/>
<b>let </b><font color="Maroon" title="c5">a</font>, <font color="Maroon" title="c6">b</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">x</font> or  not <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">y</font> or <font color="Maroon" title="c5">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">b</font> )</span><br/>

<b>assume </b><a NAME="E3:46_1_1"/><i><font color="Green" title="E30">A2</font></i>: 
( <font color="Maroon" title="c5">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> &amp; <font color="Maroon" title="c6">b</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">b</font></span><br/>

<a NAME="E4:46_1_1"/>
( <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span> &amp; <span class="p1">(<span class="default"><a href="waybel_2.html#K4" title="WAYBEL_2:func.4">inf_op</a> <font color="Maroon" title="c1">L</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="yellow_3.html#K8" title="YELLOW_3:func.8">`1</a> </span>)</span> <a href="lattice3.html#K12" title="LATTICE3:func.12">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">y</font> <a href="yellow_3.html#K9" title="YELLOW_3:func.9">`2</a> </span>)</span> )
 
<b>by </b><i><a class="ref" href="waybel_2.html#T31" target="_self" title="WAYBEL_2:th.31">Th31</a></i>;<br/>
<b>hence </b><a NAME="E5:46_1_1"/>
<font color="Maroon" title="c5">a</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c6">b</font>
 <b>by </b><i><a class="txt" href="#E2:46_1_1"><i><font color="Green" title="E29">A1</font></i></a>, <a class="txt" href="#E3:46_1_1"><i><font color="Green" title="E30">A2</font></i></a>, <a class="ref" href="yellow_3.html#T2" title="YELLOW_3:th.2">YELLOW_3:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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