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<span class="kw">reconsider </span><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c1">X</font> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">L</font></span>)</span> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel24.html#T21" title="WAYBEL24:th.21">WAYBEL24:21</a></span>;<br/>
<span class="kw">take </span>
<font color="Maroon" title="c3">f</font>
; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="yellow_0.html#D4" title="YELLOW_0:def.4">YELLOW_0:def 4</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c3">f</font> <a href="lattice3.html#R1" title="LATTICE3:pred.1">is_&lt;=_than</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span></span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">g</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="lattice3.html#D8" title="LATTICE3:def.8">LATTICE3:def 8</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> or <font color="Maroon" title="c3">f</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">g</font> )</span><br/>

<a NAME="E2:20_1_1"/><span class="lab"><font color="Green" title="E10">A1</font></span>: 
 <a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font> is   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">L</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel24.html#D3" title="WAYBEL24:def.3">WAYBEL24:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">a</font> = <font color="Maroon" title="c4">g</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">L</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T59" title="YELLOW_0:th.59">YELLOW_0:59</a></span>;<br/>
<a NAME="E4:20_1_1"/><span class="lab"><font color="Green" title="E11">A2</font></span>: 
 <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">X</font></span>)</span>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">X</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#G1" title="PRE_TOPC:aggr.1">TopStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font>,the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <font color="Maroon" title="c1">X</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel25.html#D2" title="WAYBEL25:def.2">WAYBEL25:def 2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><a href="waybel25.html#K1" title="WAYBEL25:func.1">Omega</a> <font color="Maroon" title="c1">X</font></span>)</span> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">L</font></span>)</span> = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font> <a href="funcop_1.html#K8" title="FUNCOP_1:func.8">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">L</font></span>)</span>

<br/>.= 
<font color="Maroon" title="c1">X</font> <a href="struct_0.html#K6" title="STRUCT_0:func.6">--&gt;</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <font color="Maroon" title="c2">L</font></span>)</span>

;<br/>
<a NAME="E6:20_1_1"/><span class="kw">then </span>
( <font color="Maroon" title="c5">a</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a>  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">L</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span> &amp;  <a href="yellow_0.html#K3" title="YELLOW_0:func.3">Bottom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">L</font> <a href="yellow_1.html#K6" title="YELLOW_1:func.6">|^</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">X</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:20_1_1"><span class="lab"><font color="Green" title="E11">A2</font></span></a>, <a class="ref" href="waybel24.html#T33" title="WAYBEL24:th.33">WAYBEL24:33</a>, <a class="ref" href="yellow_0.html#T44" title="YELLOW_0:th.44">YELLOW_0:44</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:20_1_1"/>
(  not <font color="Maroon" title="c4">g</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel24.html#K3" title="WAYBEL24:func.3">ContMaps</a> <font color="Maroon" title="c1">X</font>,<font color="Maroon" title="c2">L</font></span>)</span> or <font color="Maroon" title="c3">f</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">g</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:20_1_1"><span class="lab"><font color="Green" title="E10">A1</font></span></a>, <a class="ref" href="yellow_0.html#T61" title="YELLOW_0:th.61">YELLOW_0:61</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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