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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</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"> ( <font color="Maroon" title="c1">L</font> is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a>  iff <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E1:62"/>
( <font color="Maroon" title="c1">L</font> is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a>  implies <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</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"> ( <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a>  implies <font color="Maroon" title="c1">L</font> is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a>  )</span><div><a class="txt" onmouseover="tooltip.show('hs2',this)" onmouseout="tooltip.hide()" onclick="hs2(this)" href="javascript:()" title="62_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">assume </span><a NAME="E1:62_1"/><span class="lab"><font color="Green" title="E35">A1</font></span>: 
<font color="Maroon" title="c1">L</font> is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</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"> <font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a> </span><br/>

<span class="kw">hence </span><a NAME="E2:62_1"/>
<font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> 
 ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_5.html#D3" onmouseover="rs('waybel_5/D3')" onmouseout="rh()">WAYBEL_5: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">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive">b<sub>3</sub></font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> holds   <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Olive">b<sub>3</sub></font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">J</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive">b<sub>2</sub></font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c2">J</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> holds   <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Olive">b<sub>2</sub></font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Olive">b<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">K</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V8</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c2">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">  for <font color="Olive">b<sub>1</sub></font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">J</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> holds   <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Olive">b<sub>1</sub></font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="waybel_5.html#NM2" title="WAYBEL_5:NM.2">DoubleIndexedSet</a> of <font color="Maroon" title="c3">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></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">  <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Maroon" title="c4">F</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Maroon" title="c4">F</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c4">F</font> as   <a href="waybel_5.html#NM2" title="WAYBEL_5:NM.2">DoubleIndexedSet</a> of <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c1">L</font> ;<br/>
<span class="kw">thus </span> <a href="yellow_2.html#NK7" title="YELLOW_2:NK.7">Inf</a>  = 
 <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#NK6" title="WAYBEL_5:NK.6">Sups</a> </span>)</span>,<font color="Maroon" title="c1">L</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62_1"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="yellow_7.html#T49" target="_self" onmouseover="rs('yellow_7/T49')" onmouseout="rh()">Th49</a></span>
<br/>.= 
 <a href="yellow_2.html#NK6" title="YELLOW_2:NK.6">Sup</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62_1"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="yellow_7.html#T50" target="_self" onmouseover="rs('yellow_7/T50')" onmouseout="rh()">Th50</a></span>
<br/>.= 
 <a href="yellow_2.html#NK7" title="YELLOW_2:NK.7">Inf</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62_1"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="yellow_7.html#T48" target="_self" onmouseover="rs('yellow_7/T48')" onmouseout="rh()">Th48</a></span>
<br/>.= 
 <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#NK9" title="WAYBEL_5:NK.9">Infs</a> </span>)</span>,<font color="Maroon" title="c1">L</font>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62_1"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="yellow_7.html#T50" target="_self" onmouseover="rs('yellow_7/T50')" onmouseout="rh()">Th50</a></span>
<br/>.= 
 <a href="yellow_2.html#NK6" title="YELLOW_2:NK.6">Sup</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:62_1"><span class="lab"><font color="Green" title="E35">A1</font></span></a>, <a class="ref" href="yellow_7.html#T49" target="_self" onmouseover="rs('yellow_7/T49')" onmouseout="rh()">Th49</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">assume </span><a NAME="E2:62"/><span class="lab"><font color="Green" title="E35">A2</font></span>: 
<font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a>  is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</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"> <font color="Maroon" title="c1">L</font> is  <a href="waybel_5.html#V1" title="WAYBEL_5:attr.1">completely-distributive</a> </span><br/>

<a NAME="E3:62"/><span class="kw">then </span><span class="lab"><font color="Green" title="E36">A3</font></span>: 
<font color="Maroon" title="c1">L</font> is   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a>  <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_7.html#T17" target="_self" onmouseover="rs('yellow_7/T17')" onmouseout="rh()">Th17</a></span>;<br/>
<span class="kw">thus </span><a NAME="E4:62"/>
<font color="Maroon" title="c1">L</font> is  <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> 
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="yellow_7.html#T17" target="_self" onmouseover="rs('yellow_7/T17')" onmouseout="rh()">Th17</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="waybel_5.html#D3" onmouseover="rs('waybel_5/D3')" onmouseout="rh()">WAYBEL_5: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">  for <font color="Olive">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive">b<sub>2</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive">b<sub>3</sub></font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>1</sub></font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> holds   <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Olive">b<sub>3</sub></font>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>)</span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">J</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">b<sub>1</sub></font> being    <a href="hidden.html#M2" title="HIDDEN:mode.2">set</a> <br/>  for <font color="Olive">b<sub>2</sub></font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c2">J</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> holds   <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Olive">b<sub>2</sub></font>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Olive">b<sub>2</sub></font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c3">K</font> be  <a href="relat_1.html#V2" title="RELAT_1:attr.2">V8</a>() <a href="pboole.html#NM1" title="PBOOLE:NM.1">ManySortedSet</a> of <font color="Maroon" title="c2">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">  for <font color="Olive">b<sub>1</sub></font> being    <a href="pboole.html#M2" title="PBOOLE:mode.2">ManySortedFunction</a> of <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c2">J</font> <a href="funcop_1.html#K7" title="FUNCOP_1:func.7">--&gt;</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> holds   <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Olive">b<sub>1</sub></font>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c4">F</font> be   <a href="waybel_5.html#NM2" title="WAYBEL_5:NM.2">DoubleIndexedSet</a> of <font color="Maroon" title="c3">K</font>,<font color="Maroon" title="c1">L</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="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K4" title="WAYBEL_5:func.4">\//</a> (<font color="Maroon" title="c4">F</font>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#K5" title="WAYBEL_5:func.5">/\\</a> (<span class="p2">(<span class="default"><a href="waybel_5.html#K2" title="WAYBEL_5:func.2">Frege</a> <font color="Maroon" title="c4">F</font></span>)</span>,<font color="Maroon" title="c1">L</font>)</span>)</span>,<font color="Maroon" title="c1">L</font>)</span><br/>





<span class="kw">reconsider </span><font color="Maroon" title="c5">G</font> = <font color="Maroon" title="c4">F</font> as   <a href="waybel_5.html#NM2" title="WAYBEL_5:NM.2">DoubleIndexedSet</a> of <font color="Maroon" title="c3">K</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span> ;<br/>
<span class="kw">thus </span> <a href="yellow_2.html#NK7" title="YELLOW_2:NK.7">Inf</a>  = 
 <a href="yellow_2.html#K4" title="YELLOW_2:func.4">\\/</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#NK6" title="WAYBEL_5:NK.6">Sups</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="yellow_7.html#T49" target="_self" onmouseover="rs('yellow_7/T49')" onmouseout="rh()">Th49</a></span>
<br/>.= 
 <a href="yellow_2.html#NK6" title="YELLOW_2:NK.6">Sup</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="yellow_7.html#T50" target="_self" onmouseover="rs('yellow_7/T50')" onmouseout="rh()">Th50</a></span>
<br/>.= 
 <a href="yellow_2.html#NK7" title="YELLOW_2:NK.7">Inf</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:62"><span class="lab"><font color="Green" title="E35">A2</font></span></a>, <a class="ref" href="yellow_7.html#T48" target="_self" onmouseover="rs('yellow_7/T48')" onmouseout="rh()">Th48</a></span>
<br/>.= 
 <a href="yellow_2.html#K5" title="YELLOW_2:func.5">//\</a> (<span class="p1">(<span class="default"><a href="waybel_5.html#NK9" title="WAYBEL_5:NK.9">Infs</a> </span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c1">L</font> <a href="yellow_7.html#NK1" title="YELLOW_7:NK.1">opp</a></span>)</span>)
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="yellow_7.html#T50" target="_self" onmouseover="rs('yellow_7/T50')" onmouseout="rh()">Th50</a></span>
<br/>.= 
 <a href="yellow_2.html#NK6" title="YELLOW_2:NK.6">Sup</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:62"><span class="lab"><font color="Green" title="E36">A3</font></span></a>, <a class="ref" href="yellow_7.html#T49" target="_self" onmouseover="rs('yellow_7/T49')" onmouseout="rh()">Th49</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/>


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