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<span class="kw">let </span><font color="Maroon" title="c1">R</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">N</font> being   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">R</font> holds   <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Olive" title="b1">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Olive" title="b1">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b3">i</font></span>)</span> where <font color="Olive" title="b3">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">N</font> : <font color="Olive" title="b3">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b2">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b2">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">N</font> : verum </span> } </span> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be   <a href="waybel_0.html#NM2" title="WAYBEL_0:NM.2">net</a> of <font color="Maroon" title="c1">R</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span> </span><br/>



<span class="kw">consider </span><font color="Maroon" title="c3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c2">N</font>,<font color="Maroon" title="c1">R</font><span class="kw"> such that </span><br/><a NAME="E2:42"/><span class="lab"><font color="Green" title="E19">A1</font></span>: 
 <a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font> <a href="waybel32.html#K1" title="WAYBEL32:func.1">*'</a> <font color="Maroon" title="c3">f</font>
 <span class="kw">and </span><br/><a NAME="E3:42"/><span class="lab"><font color="Green" title="E20">A2</font></span>: 
 for <font color="Olive" title="b1">i</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> holds  <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">k</font></span>)</span> where <font color="Olive" title="b2">k</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">k</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">i</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel32.html#D4" target="_self" onmouseover="rs('waybel32/D4')" onmouseout="rh()">Def4</a></span>;<br/>
<a NAME="E4:42"/><span class="lab"><font color="Green" title="E21">A3</font></span>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(#  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">N</font>, the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">N</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="waybel32.html#D3" target="_self" onmouseover="rs('waybel32/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<a NAME="E5:42"/><span class="lab"><font color="Green" title="E22">A4</font></span>: 
 the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:42"><span class="lab"><font color="Green" title="E19">A1</font></span></a>, <a class="ref" href="waybel32.html#D3" target="_self" onmouseover="rs('waybel32/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<a NAME="E6:42"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A5</font></span>: 
 the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a></span>;<br/>
<span class="kw">thus </span><a NAME="E7:42"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span> 
  <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="xboole_0.html#D10" onmouseover="rs('xboole_0/D10')" onmouseout="rh()">XBOOLE_0:def 10</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span>  <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span></span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="42_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> or <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:42_1"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span> </span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">u</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> <span class="kw"> such that </span><br/><a NAME="E3:42_1"/><span class="lab"><font color="Green" title="E24">A6</font></span>: 
<font color="Maroon" title="c5">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Maroon" title="c3">f</font>
 <span class="kw">and </span><br/><a NAME="E4:42_1"/><span class="lab"><font color="Green" title="E25">A7</font></span>: 
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">u</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c6">u</font> = <font color="Maroon" title="c5">u</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42_1"><span class="lab"><font color="Green" title="E24">A6</font></span></a></span>;<br/>
<a NAME="E6:42_1"/>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">k</font></span>)</span> where <font color="Olive" title="b1">k</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b1">k</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">u</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E20">A2</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:42_1"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42_1"><span class="lab"><font color="Green" title="E25">A7</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>

<span class="kw">let </span><font color="Maroon" title="c4">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span>  or <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> )</span><br/>

<span class="kw">assume </span><a NAME="E8:42"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p3"> { <span class="default"> <span class="p4">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b2">i</font></span>)</span> where <font color="Olive" title="b2">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b2">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Olive" title="b1">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)</span>)</span> where <font color="Olive" title="b1">j</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : verum </span> } </span> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span></span><br/>

<span class="kw">then </span><span class="kw">consider </span><font color="Maroon" title="c5">j</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font><span class="kw"> such that </span><br/><a NAME="E10:42"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_0.html#K2" title="YELLOW_0:func.2">"/\"</a> (<span class="p1"> { <span class="default"> <span class="p2">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> : <font color="Olive" title="b1">i</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c5">j</font> </span> } </span> ,<font color="Maroon" title="c1">R</font>)
 ;<br/>
<a NAME="E11:42"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:42"><span class="lab"><font color="Green" title="E20">A2</font></span></a>, <a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E10:42"><span class="lab"><font color="Green" title="E24">A8</font></span></a></span>;<br/>
<span class="kw">hence </span><a NAME="E12:42"/>
<font color="Maroon" title="c4">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a>  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel32.html#K2" title="WAYBEL32:func.2">inf_net</a> <font color="Maroon" title="c2">N</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:42"><span class="lab"><font color="Green" title="E21">A3</font></span></a>, <a class="txt" href="#E5:42"><span class="lab"><font color="Green" title="E22">A4</font></span></a>, <a class="txt" href="#E6:42"><span class="lab"><font color="Green" title="E23">A5</font></span></a>, <a class="ref" href="funct_1.html#D3" onmouseover="rs('funct_1/D3')" onmouseout="rh()">FUNCT_1:def 3</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
