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<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">T</font> being  <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a><br/> for <font color="Olive" title="b2">g</font> being  <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Olive" title="b1">T</font>  st  <a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Olive" title="b2">g</font> is  <a href="waybel34.html#V1" title="WAYBEL34:attr.1">waybelow-preserving</a>  holds <br/><font color="Olive" title="b2">g</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">T</font> be   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="waybel_0.html#NM8" title="WAYBEL_0:NM.8">LATTICE</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">g</font> being  <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>  st  <a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Olive" title="b1">g</font> is  <a href="waybel34.html#V1" title="WAYBEL34:attr.1">waybelow-preserving</a>  holds <br/><font color="Olive" title="b1">g</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c3">g</font> be   <a href="waybel_0.html#V17" title="WAYBEL_0:attr.17">infs-preserving</a>  <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font> is  <a href="waybel34.html#V1" title="WAYBEL34:attr.1">waybelow-preserving</a>  implies <font color="Maroon" title="c3">g</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a>  )</span><br/>





<span class="kw">assume </span><a NAME="E1:43"/><span class="lab"><font color="Green" title="E29">A1</font></span>: 
for <font color="Olive" title="b1">t</font>, <font color="Olive" title="b2">t9</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">T</font>  st <font color="Olive" title="b1">t</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Olive" title="b2">t9</font> holds <br/><span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">t</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">t9</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="waybel34.html#D8" target="_self" title="WAYBEL34:def.8">WAYBEL34:def 8</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">g</font> is  <a href="waybel_0.html#V22" title="WAYBEL_0:attr.22">directed-sups-preserving</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c4">D</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="waybel_0.html#D37" title="WAYBEL_0:def.37">WAYBEL_0:def 37</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="c4">D</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  or  not <font color="Maroon" title="c4">D</font> is  <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>  or <font color="Maroon" title="c3">g</font> <a href="waybel_0.html#R4" title="WAYBEL_0:pred.4">preserves_sup_of</a> <font color="Maroon" title="c4">D</font> )</span><br/>

<span class="kw">assume </span><a NAME="E2:43"/><span class="lab"><font color="Green" title="E30">A2</font></span>: 
( not <font color="Maroon" title="c4">D</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  &amp; <font color="Maroon" title="c4">D</font> is  <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</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">g</font> <a href="waybel_0.html#R4" title="WAYBEL_0:pred.4">preserves_sup_of</a> <font color="Maroon" title="c4">D</font></span><br/>

<span class="kw">assume </span><a NAME="E3:43"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c4">D</font>,<font color="Maroon" title="c1">S</font>
 ; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="waybel_0.html#D31" title="WAYBEL_0:def.31">WAYBEL_0:def 31</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font>,<font color="Maroon" title="c2">T</font> &amp;  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c4">D</font>,<font color="Maroon" title="c1">S</font></span>)</span> )</span><br/>

<span class="kw">thus </span><a NAME="E4:43"/>
 <a href="yellow_0.html#R1" title="YELLOW_0:pred.1">ex_sup_of</a> <font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font>,<font color="Maroon" title="c2">T</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#T17" title="YELLOW_0:th.17">YELLOW_0:17</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c4">D</font>,<font color="Maroon" title="c1">S</font></span>)</span></span><br/>

<a NAME="E5:43"/><span class="lab"><font color="Green" title="E31">A3</font></span>: 
 <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel17.html#T15" title="WAYBEL17:th.15">WAYBEL17:15</a></span>;<br/>
<a NAME="E6:43"/><span class="lab"><font color="Green" title="E32">A4</font></span>: 
<font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_3.html#D5" title="WAYBEL_3:def.5">WAYBEL_3:def 5</a></span>;<br/>
<a NAME="E7:43"/>
 <a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="lattice3.html#R2" title="LATTICE3:pred.2">is_&lt;=_than</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="43_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c5">t</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">T</font>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="lattice3.html#D9" title="LATTICE3:def.9">LATTICE3:def 9</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="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> or <font color="Maroon" title="c5">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E1:43_1"/>
<font color="Maroon" title="c5">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="waybel_3.html#K1" title="WAYBEL_3:func.1">waybelow</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span>
 ; <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="c5">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span></span><br/>

<a NAME="E2:43_1"/><span class="kw">then </span>
<font color="Maroon" title="c5">t</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_3.html#T7" title="WAYBEL_3:th.7">WAYBEL_3:7</a></span>;<br/>
<a NAME="E3:43_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E33">A5</font></span>: 
<span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">t</font> <a href="waybel_3.html#NR2" title="WAYBEL_3:NR.2">&lt;&lt;</a> <span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E29">A1</font></span></a></span>;<br/>
<a NAME="E4:43_1"/><span class="lab"><font color="Green" title="E34">A6</font></span>: 
<span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c3">g</font>,<span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span> is  <a href="waybel_1.html#V3" title="WAYBEL_1:attr.3">Galois</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel34.html#D1" target="_self" title="WAYBEL34:def.1">Def1</a></span>;<br/>
<a NAME="E5:43_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E35">A7</font></span>: 
<span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">g</font> <a href="yellow_2.html#R1" title="YELLOW_2:pred.1">&lt;=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_1.html#T19" title="WAYBEL_1:th.19">WAYBEL_1:19</a></span>;<br/>
<a NAME="E6:43_1"/>
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></span>;<br/>
<a NAME="E7:43_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43_1"><span class="lab"><font color="Green" title="E35">A7</font></span></a>, <a class="ref" href="yellow_2.html#T10" title="YELLOW_2:th.10">YELLOW_2:10</a></span>;<br/>
<a NAME="E8:43_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>;<br/>
<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c6">x</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">S</font><span class="kw"> such that </span><br/><a NAME="E10:43_1"/><span class="lab"><font color="Green" title="E36">A8</font></span>: 
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">D</font>
 <span class="kw">and </span><br/><a NAME="E11:43_1"/><span class="lab"><font color="Green" title="E37">A9</font></span>: 
<span class="p1">(<span class="default"><a href="waybel34.html#K1" title="WAYBEL34:func.1">LowerAdj</a> <font color="Maroon" title="c3">g</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:43"><span class="lab"><font color="Green" title="E30">A2</font></span></a>, <a class="txt" href="#E3:43_1"><span class="lab"><font color="Green" title="E33">A5</font></span></a>, <a class="ref" href="waybel_3.html#D1" title="WAYBEL_3:def.1">WAYBEL_3:def 1</a></span>;<br/>
<a NAME="E12:43_1"/><span class="lab"><font color="Green" title="E38">A10</font></span>: 
<font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E10:43_1"><span class="lab"><font color="Green" title="E36">A8</font></span></a>, <a class="ref" href="funct_2.html#T43" title="FUNCT_2:th.43">FUNCT_2:43</a></span>;<br/>
<a NAME="E13:43_1"/><span class="lab"><font color="Green" title="E39">A11</font></span>: 
<font color="Maroon" title="c5">t</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:43_1"><span class="lab"><font color="Green" title="E34">A6</font></span></a>, <a class="txt" href="#E11:43_1"><span class="lab"><font color="Green" title="E37">A9</font></span></a>, <a class="ref" href="waybel_1.html#T9" title="WAYBEL_1:th.9">WAYBEL_1:9</a></span>;<br/>
<a NAME="E14:43_1"/>
<font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">x</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:43_1"><span class="lab"><font color="Green" title="E38">A10</font></span></a>, <a class="ref" href="yellow_2.html#T24" title="YELLOW_2:th.24">YELLOW_2:24</a></span>;<br/>
<span class="kw">hence </span><a NAME="E15:43_1"/>
<font color="Maroon" title="c5">t</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:43_1"><span class="lab"><font color="Green" title="E39">A11</font></span></a>, <a class="ref" href="orders_2.html#T26" title="ORDERS_2:th.26">ORDERS_2:26</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/>


</div><span class="kw">end;</span></div>
<a NAME="E8:43"/><span class="kw">then </span>
<font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <font color="Maroon" title="c4">D</font></span>)</span> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a>  <a href="yellow_0.html#NK3" title="YELLOW_0:NK.3">sup</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:43"><span class="lab"><font color="Green" title="E32">A4</font></span></a>, <a class="ref" href="yellow_0.html#T32" title="YELLOW_0:th.32">YELLOW_0:32</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:43"/>
 <a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">g</font> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c4">D</font></span>)</span>,<font color="Maroon" title="c2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">g</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="yellow_0.html#K1" title="YELLOW_0:func.1">"\/"</a> <font color="Maroon" title="c4">D</font>,<font color="Maroon" title="c1">S</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:43"><span class="lab"><font color="Green" title="E31">A3</font></span></a>, <a class="ref" href="orders_2.html#T25" title="ORDERS_2:th.25">ORDERS_2:25</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/>


</div>
