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<div class="add">

<b>let </b><font color="Maroon" title="c1">T</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">F</font> being  <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> holds   <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Olive" title="b1">F</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Olive" title="b1">F</font></span>)</span></span><br/><b>let </b><font color="Maroon" title="c2">F</font> be   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span><br/>



<a NAME="E1:37"/><i><font color="Green" title="E24">A1</font></i>: 
 <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> :  ex <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b2">B</font></span>)</span> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T31" target="_self" title="TDLAT_2:th.31">Th31</a></i>;<br/>
<b>set </b><font color="Maroon" title="c3">H</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> :  ex <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b2">B</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) </span>}</span> ;<br/>
<a NAME="E2:37"/>
 <a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> :  ex <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b2">B</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) </span>}</span> 
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T34" target="_self" title="TDLAT_2:th.34">Th34</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">H</font> = <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> :  ex <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b2">B</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) </span>}</span>  as   <a href="struct_0.html#NM3" title="STRUCT_0:NM.3">Subset-Family</a> of <font color="Maroon" title="c1">T</font> ;<br/>
<a NAME="E4:37"/><i><font color="Green" title="E25">A2</font></i>: 
 <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <font color="Maroon" title="c4">H</font>
 
<b>by </b><i><a class="ref" href="tdlat_2.html#T34" target="_self" title="TDLAT_2:th.34">Th34</a></i>;<br/>
<a NAME="E5:37"/>
for <font color="Olive" title="b1">X</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span> iff <font color="Olive" title="b1">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">X</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span> iff <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span> )</span><br/>

<div><i><font color="Green" title="E26">A3</font></i>: <a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_1"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1_1"/><i><font color="Green" title="E27">A4</font></i>: 
<font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span><br/><b>then reconsider </b><font color="Maroon" title="c6">C</font> = <font color="Maroon" title="c5">X</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> ;<br/><b>consider </b><font color="Maroon" title="c7">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E4:37_1_1"/><i><font color="Green" title="E28">A5</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <font color="Maroon" title="c7">B</font>
 <b>and </b><br/><a NAME="E5:37_1_1"/><i><font color="Green" title="E29">A6</font></i>: 
<font color="Maroon" title="c7">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">A</font> where <font color="Olive" title="b1">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> :  ex <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b2">B</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) </span>}</span> 
 <b>by </b><i><a class="txt" href="tdlat_2.html#E4:37"><i><font color="Green" title="E25">A2</font></i></a>, <a class="txt" href="tdlat_2.html#E1:37_1_1"><i><font color="Green" title="E27">A4</font></i></a>, <a class="ref" href="pcomps_1.html#D3" title="PCOMPS_1:def.3">PCOMPS_1:def 3</a></i>;<br/><a NAME="E6:37_1_1"/>
 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">T</font> st <br/>( <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">B</font> &amp;  ex <font color="Olive" title="b2">R</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">S</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b2">R</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">R</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) )
 <b>by </b><i><a class="txt" href="tdlat_2.html#E5:37_1_1"><i><font color="Green" title="E29">A6</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c8">D</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E8:37_1_1"/><i><font color="Green" title="E30">A7</font></i>: 
<font color="Maroon" title="c7">B</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c8">D</font></span>)</span></span>)</span>
 <b>and </b><br/><a NAME="E9:37_1_1"/><i><font color="Green" title="E31">A8</font></i>: 
<font color="Maroon" title="c8">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 ;<br/><a NAME="E10:37_1_1"/><i><font color="Green" title="E32">A9</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c8">D</font></span>)</span>
 <b>by </b><i><a class="txt" href="tdlat_2.html#E4:37_1_1"><i><font color="Green" title="E28">A5</font></i></a>, <a class="txt" href="tdlat_2.html#E8:37_1_1"><i><font color="Green" title="E30">A7</font></i></a>, <a class="ref" href="tops_1.html#T58" title="TOPS_1:th.58">TOPS_1:58</a></i>;<br/><a NAME="E11:37_1_1"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c8">D</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="txt" href="tdlat_2.html#E9:37_1_1"><i><font color="Green" title="E31">A8</font></i></a>, <a class="ref" href="tdlat_2.html#D1" target="_self" title="TDLAT_2:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E12:37_1_1"/>
<font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="txt" href="tdlat_2.html#E10:37_1_1"><i><font color="Green" title="E32">A9</font></i></a>, <a class="ref" href="pcomps_1.html#D3" title="PCOMPS_1:def.3">PCOMPS_1:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="37_1_2"><b>now </b></a><div class="add"><b>assume </b><a NAME="E1:37_1_2"/><i><font color="Green" title="E27">A10</font></i>: 
<font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span></span><br/><b>then reconsider </b><font color="Maroon" title="c6">C</font> = <font color="Maroon" title="c5">X</font> as   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> ;<br/><a NAME="E3:37_1_2"/>
 ex <font color="Olive" title="b1">D</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">C</font> &amp;  ex <font color="Olive" title="b2">B</font> being  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Olive" title="b2">B</font></span>)</span> &amp; <font color="Olive" title="b2">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font> ) )
 <b>by </b><i><a class="txt" href="tdlat_2.html#E1:37"><i><font color="Green" title="E24">A1</font></i></a>, <a class="txt" href="tdlat_2.html#E1:37_1_2"><i><font color="Green" title="E27">A10</font></i></a></i>;<br/><b>then consider </b><font color="Maroon" title="c7">B</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">T</font><b> such that </b><br/><a NAME="E5:37_1_2"/><i><font color="Green" title="E28">A11</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c7">B</font></span>)</span>
 <b>and </b><br/><a NAME="E6:37_1_2"/><i><font color="Green" title="E29">A12</font></i>: 
<font color="Maroon" title="c7">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">F</font>
 ;<br/><a NAME="E7:37_1_2"/><i><font color="Green" title="E30">A13</font></i>: 
<font color="Maroon" title="c6">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p2">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p3">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c7">B</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="tdlat_2.html#E5:37_1_2"><i><font color="Green" title="E28">A11</font></i></a>, <a class="ref" href="tops_1.html#T58" title="TOPS_1:th.58">TOPS_1:58</a></i>;<br/><a NAME="E8:37_1_2"/>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c7">B</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font>
 <b>by </b><i><a class="txt" href="tdlat_2.html#E6:37_1_2"><i><font color="Green" title="E29">A12</font></i></a>, <a class="ref" href="tdlat_2.html#D1" target="_self" title="TDLAT_2:def.1">Def1</a></i>;<br/><a NAME="E9:37_1_2"/><b>then </b>
 <a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p1">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c7">B</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="pcomps_1.html#D3" title="PCOMPS_1:def.3">PCOMPS_1:def 3</a></i>;<br/><a NAME="E10:37_1_2"/><b>then </b>
 <a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" title="PRE_TOPC:func.2">Cl</a> <span class="p2">(<span class="default"><a href="tops_1.html#K1" title="TOPS_1:func.1">Int</a> <font color="Maroon" title="c7">B</font></span>)</span></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="tdlat_2.html#D1" target="_self" title="TDLAT_2:def.1">Def1</a></i>;<br/><b>hence </b><a NAME="E11:37_1_2"/>
<font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="tdlat_2.html#E7:37_1_2"><i><font color="Green" title="E30">A13</font></i></a>, <a class="ref" href="pcomps_1.html#D3" title="PCOMPS_1:def.3">PCOMPS_1:def 3</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:37_1"/>
( <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span> iff <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span> )
 <b>by </b><i><a class="txt" href="tdlat_2.html#E1:37_1"><i><font color="Green" title="E26">A3</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>hence </b><a NAME="E6:37"/>
 <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <span class="p2">(<span class="default"><a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p3">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="tdlat_2.html#NK1" title="TDLAT_2:NK.1">Cl</a> <span class="p1">(<span class="default"><a href="tdlat_2.html#K1" title="TDLAT_2:func.1">Int</a> <font color="Maroon" title="c2">F</font></span>)</span>
 <b>by </b><i><a class="ref" href="tarski.html#T2" title="TARSKI:th.2">TARSKI:2</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div>
