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<span class="kw">let </span><font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c4">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel11.html#D9" onmouseover="rs('waybel11/D9')" onmouseout="rh()">WAYBEL11:def 9</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="c3">i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">j</font> or <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="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c3">i</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <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="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c4">j</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:40_1_1"/><span class="lab"><font color="Green" title="E18">A1</font></span>: 
<font color="Maroon" title="c3">i</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c4">j</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"> <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="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c3">i</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <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="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c4">j</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c5">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="E3:40_1_1"/><span class="lab"><font color="Green" title="E19">A2</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="c5">f</font>
 <span class="kw">and </span><br/><a NAME="E4:40_1_1"/><span class="lab"><font color="Green" title="E20">A3</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="c5">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="E5:40_1_1"/><span class="lab"><font color="Green" title="E21">A4</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="#E3:40_1_1"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="waybel32.html#D3" target="_self" onmouseover="rs('waybel32/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">i9</font> = <font color="Maroon" title="c3">i</font>, <font color="Maroon" title="c7">j9</font> = <font color="Maroon" title="c4">j</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> ;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font>) <span class="kw">-&gt; </span>   <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">R</font> = <font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c1">R</font>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>1</sub></font>[  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font>] <span class="kw">means </span><font color="Maroon" title="c1">R</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j9</font>;<br/>
<span class="kw">defpred </span><font color="Maroon">S<sub>2</sub></font>[  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font>] <span class="kw">means </span><font color="Maroon" title="c1">R</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">i9</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c8">J</font> = <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span> ;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">I</font> = <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span> ;<br/>
<a NAME="E7:40_1_1"/><span class="lab"><font color="Green" title="E22">A5</font></span>: 
<span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span>  is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="domain_1.html#S8" onmouseover="rs('domain_1/S8')" onmouseout="rh()">DOMAIN_1:sch 8</a>();<br/></span>
<span class="kw">consider </span><font color="Maroon" title="c10">j0</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="E9:40_1_1"/><span class="lab"><font color="Green" title="E23">A6</font></span>: 
<font color="Maroon" title="c10">j0</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j9</font>
 <span class="kw">and </span><br/><a NAME="E10:40_1_1"/>
<font color="Maroon" title="c10">j0</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_6.html#D3" onmouseover="rs('yellow_6/D3')" onmouseout="rh()">YELLOW_6:def 3</a></span>;<br/>
<a NAME="E11:40_1_1"/>
<font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c10">j0</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:40_1_1"><span class="lab"><font color="Green" title="E23">A6</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c11">J9</font> = <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span>  as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:40_1_1"><span class="lab"><font color="Green" title="E22">A5</font></span></a></span>;<br/>
<a NAME="E13:40_1_1"/><span class="lab"><font color="Green" title="E24">A7</font></span>: 
<span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span>  is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font>
 
<span class="kw">from</span> <span class="lab"><a class="ref" href="domain_1.html#S8" onmouseover="rs('domain_1/S8')" onmouseout="rh()">DOMAIN_1:sch 8</a>();<br/></span>
<span class="kw">consider </span><font color="Maroon" title="c12">j1</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="E15:40_1_1"/><span class="lab"><font color="Green" title="E25">A8</font></span>: 
<font color="Maroon" title="c12">j1</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">i9</font>
 <span class="kw">and </span><br/><a NAME="E16:40_1_1"/>
<font color="Maroon" title="c12">j1</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c6">i9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_6.html#D3" onmouseover="rs('yellow_6/D3')" onmouseout="rh()">YELLOW_6:def 3</a></span>;<br/>
<a NAME="E17:40_1_1"/>
<font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c12">j1</font> <a href="tarski.html#R2" title="TARSKI:pred.2">in</a> <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E15:40_1_1"><span class="lab"><font color="Green" title="E25">A8</font></span></a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c13">I9</font> = <span class="p1"> { <span class="default"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span>  as   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">R</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:40_1_1"><span class="lab"><font color="Green" title="E24">A7</font></span></a></span>;<br/>
<a NAME="E19:40_1_1"/><span class="lab"><font color="Green" title="E26">A9</font></span>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c11">J9</font>,<font color="Maroon" title="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T76" onmouseover="rs('waybel_0/T76')" onmouseout="rh()">WAYBEL_0:76</a></span>;<br/>
<a NAME="E20:40_1_1"/><span class="lab"><font color="Green" title="E27">A10</font></span>: 
 <a href="yellow_0.html#R2" title="YELLOW_0:pred.2">ex_inf_of</a> <font color="Maroon" title="c13">I9</font>,<font color="Maroon" title="c1">R</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_0.html#T76" onmouseover="rs('waybel_0/T76')" onmouseout="rh()">WAYBEL_0:76</a></span>;<br/>
<a NAME="E21:40_1_1"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
<font color="Maroon" title="c11">J9</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <font color="Maroon" title="c13">I9</font>
 
<div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="40_1_1_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c14">a</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="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">J9</font> or <font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">I9</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:40_1_1_1"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
<font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c11">J9</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"> <font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">I9</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">x</font> = <font color="Maroon" title="c14">a</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font> ;<br/>
<span class="kw">consider </span><font color="Maroon" title="c16">k</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="E4:40_1_1_1"/><span class="lab"><font color="Green" title="E30">A13</font></span>: 
<font color="Maroon" title="c15">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">N</font> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c16">k</font>
 <span class="kw">and </span><br/><a NAME="E5:40_1_1_1"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
<font color="Maroon" title="c16">k</font> <a href="orders_2.html#NR2" title="ORDERS_2:NR.2">&gt;=</a> <font color="Maroon" title="c7">j9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40_1_1_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a></span>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c17">k9</font> = <font color="Maroon" title="c16">k</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> ;<br/>
<a NAME="E7:40_1_1_1"/>
<font color="Maroon" title="c6">i9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">j9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:40_1_1"><span class="lab"><font color="Green" title="E18">A1</font></span></a>, <a class="txt" href="#E5:40_1_1"><span class="lab"><font color="Green" title="E21">A4</font></span></a>, <a class="ref" href="yellow_0.html#T1" onmouseover="rs('yellow_0/T1')" onmouseout="rh()">YELLOW_0:1</a></span>;<br/>
<a NAME="E8:40_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">i9</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c17">k9</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:40_1_1_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a>, <a class="ref" href="yellow_0.html#D2" onmouseover="rs('yellow_0/D2')" onmouseout="rh()">YELLOW_0:def 2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:40_1_1_1"/>
<font color="Maroon" title="c14">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c13">I9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:40_1_1_1"><span class="lab"><font color="Green" title="E30">A13</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>
<a NAME="E22:40_1_1"/><span class="lab"><font color="Green" title="E29">A15</font></span>: 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">i9</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"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>2</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span> ,<font color="Maroon" title="c1">R</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:40_1_1"><span class="lab"><font color="Green" title="E20">A3</font></span></a></span>;<br/>
<a NAME="E23:40_1_1"/><span class="lab"><font color="Green" title="E30">A16</font></span>: 
<font color="Maroon" title="c5">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c7">j9</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"> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">k</font>) 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="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">k</font>] </span> } </span> ,<font color="Maroon" title="c1">R</font>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:40_1_1"><span class="lab"><font color="Green" title="E20">A3</font></span></a></span>;<br/>
<a NAME="E24:40_1_1"/>
 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="c5">f</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:40_1_1"><span class="lab"><font color="Green" title="E19">A2</font></span></a>, <a class="ref" href="waybel32.html#D3" target="_self" onmouseover="rs('waybel32/D3')" onmouseout="rh()">Def3</a></span>;<br/>
<span class="kw">hence </span><a NAME="E25:40_1_1"/>
<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="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c3">i</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <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="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c4">j</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E19:40_1_1"><span class="lab"><font color="Green" title="E26">A9</font></span></a>, <a class="txt" href="#E20:40_1_1"><span class="lab"><font color="Green" title="E27">A10</font></span></a>, <a class="txt" href="#E21:40_1_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E22:40_1_1"><span class="lab"><font color="Green" title="E29">A15</font></span></a>, <a class="txt" href="#E23:40_1_1"><span class="lab"><font color="Green" title="E30">A16</font></span></a>, <a class="ref" href="yellow_0.html#T35" onmouseover="rs('yellow_0/T35')" onmouseout="rh()">YELLOW_0:35</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>
