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<span class="kw">let </span><font color="Maroon" title="c2">D1</font>, <font color="Maroon" title="c3">D2</font> be   <a href="xxreal_0.html#V1" title="XXREAL_0:attr.1">ext-real</a>   <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</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="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c1">K</font> is  <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a>  &amp; ( for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp; ( for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> ) &amp; ( <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1 &amp; <font color="Maroon" title="c3">D2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1 implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> ) &amp; ( ( <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  or  not <font color="Maroon" title="c1">K</font> is  <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a>  ) &amp; not <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  &amp; <font color="Maroon" title="c3">D2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> ) )</span><br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="73_1_2_1"><span class="kw">now </span></a><div class="add"><span class="kw">assume </span><a NAME="E1:73_1_2_1"/><span class="lab"><font color="Green" title="E28">A11</font></span>: 
( not <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c1">K</font> is  <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</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">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S1</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp; ( for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S2</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> )</span><br/><span class="kw">assume </span><a NAME="E2:73_1_2_1"/><span class="lab"><font color="Green" title="E29">A12</font></span>: 
for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">S1</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S1</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp; ( for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S2</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> )</span><br/><span class="kw">given </span><font color="Maroon" title="c4">S1</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font><span class="kw"> such that </span><a NAME="E4:73_1_2_1"/><span class="lab"><font color="Green" title="E30">A13</font></span>: 
( <font color="Maroon" title="c4">S1</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c4">S1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 )
 ; <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">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S2</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> )</span><br/><span class="kw">assume </span><a NAME="E5:73_1_2_1"/><span class="lab"><font color="Green" title="E31">A14</font></span>: 
for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">S2</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S2</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> )</span><br/><span class="kw">given </span><font color="Maroon" title="c5">S2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font><span class="kw"> such that </span><a NAME="E7:73_1_2_1"/><span class="lab"><font color="Green" title="E32">A15</font></span>: 
( <font color="Maroon" title="c5">S2</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Maroon" title="c5">S2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 )
 ; <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="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font></span><br/><a NAME="E8:73_1_2_1"/><span class="lab"><font color="Green" title="E33">A16</font></span>: 
<font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73_1_2_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E2:73_1_2_1"><span class="lab"><font color="Green" title="E29">A12</font></span></a>, <a class="txt" href="#E7:73_1_2_1"><span class="lab"><font color="Green" title="E32">A15</font></span></a></span>;<br/><a NAME="E9:73_1_2_1"/>
<font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:73_1_2_1"><span class="lab"><font color="Green" title="E28">A11</font></span></a>, <a class="txt" href="#E4:73_1_2_1"><span class="lab"><font color="Green" title="E30">A13</font></span></a>, <a class="txt" href="#E5:73_1_2_1"><span class="lab"><font color="Green" title="E31">A14</font></span></a></span>;<br/><span class="kw">hence </span><a NAME="E10:73_1_2_1"/>
<font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:73_1_2_1"><span class="lab"><font color="Green" title="E33">A16</font></span></a>, <a class="ref" href="xxreal_0.html#T1" title="XXREAL_0:th.1">XXREAL_0:1</a>, <a class="ref" href="xxreal_3.html#T11" title="XXREAL_3:th.11">XXREAL_3:11</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>
<span class="kw">hence </span><a NAME="E2:73_1_2"/>
( ( not <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c1">K</font> is  <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a>  &amp; ( for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D1</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp; ( for <font color="Olive" title="b1">S</font> being  <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font>  st <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  holds <br/> <a href="card_1.html#K5" title="CARD_1:func.5">card</a> <font color="Olive" title="b1">S</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) &amp;  ex <font color="Olive" title="b1">S</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">K</font> st <br/>( <font color="Olive" title="b1">S</font> is  <a href="simplex0.html#NV2" title="SIMPLEX0:NV.2">simplex-like</a>  &amp;  <a href="card_1.html#K1" title="CARD_1:func.1">card</a> <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> <a href="xxreal_3.html#K1" title="XXREAL_3:func.1">+</a> 1 ) implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> ) &amp; ( <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1 &amp; <font color="Maroon" title="c3">D2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_3.html#K2" title="XXREAL_3:func.2">-</a> 1 implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> ) &amp; ( ( <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  or  not <font color="Maroon" title="c1">K</font> is  <a href="matroid0.html#V4" title="MATROID0:attr.4">finite-degree</a>  ) &amp; not <font color="Maroon" title="c1">K</font> is  <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  &amp; <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  &amp; <font color="Maroon" title="c3">D2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xxreal_0.html#K1" title="XXREAL_0:func.1">+infty</a>  implies <font color="Maroon" title="c2">D1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">D2</font> ) )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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