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<b>let </b><font color="Maroon" title="c1">F</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</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">V</font> being <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font><br/> for <font color="Olive" title="b2">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">k</font> &amp; <font color="Olive" title="b2">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Olive" title="b1">V</font> holds <br/> <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">k</font> is <a href="pencil_1.html#V6" title="PENCIL_1:attr.6">identifying_close_blocks</a></span><br/><b>let </b><font color="Maroon" title="c2">V</font> be  <a href="matrlin.html#V2" title="MATRLIN:attr.2">finite-dimensional</a> <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">F</font>; <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">k</font> being  <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>  st 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">k</font> &amp; <font color="Olive" title="b1">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font> holds <br/> <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Olive" title="b1">k</font> is <a href="pencil_1.html#V6" title="PENCIL_1:attr.6">identifying_close_blocks</a></span><br/><b>let </b><font color="Maroon" title="c3">k</font> be   <a href="nat_1.html#NM1" title="NAT_1:NM.1">Nat</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font> implies  <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font> is <a href="pencil_1.html#V6" title="PENCIL_1:attr.6">identifying_close_blocks</a> )</span><br/>





<b>assume </b><a NAME="E1:25"/><i><font color="Green" title="E23">A1</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">k</font> &amp; <font color="Maroon" title="c3">k</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c2">V</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font> is <a href="pencil_1.html#V6" title="PENCIL_1:attr.6">identifying_close_blocks</a></span><br/>

<b>set </b><font color="Maroon" title="c4">S</font> =  <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font>;<br/>
<b>thus </b><a NAME="E2:25"/>
 <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font> is <a href="pencil_1.html#V6" title="PENCIL_1:attr.6">identifying_close_blocks</a>
  <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><div><a class="txt" onclick="hs2(this)" href="javascript:()" title="25_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c5">X</font>, <font color="Maroon" title="c6">Y</font> be   <a href="pencil_1.html#NM1" title="PENCIL_1:NM.1">Block</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D7" title="PENCIL_1:def.7">PENCIL_1:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not 2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">Y</font></span>)</span> or <font color="Maroon" title="c5">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Y</font> )</span><br/>

<b>assume </b><a NAME="E1:25_1"/>
2 <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="card_1.html#K1" title="CARD_1:func.1">Card</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">Y</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#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Y</font></span><br/>

<b>then consider </b><font color="Maroon" title="c7">P</font>, <font color="Maroon" title="c8">Q</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E3:25_1"/><i><font color="Green" title="E24">A2</font></i>: 
( <font color="Maroon" title="c7">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">Y</font> &amp; <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font> <a href="xboole_0.html#K3" title="XBOOLE_0:func.3">/\</a> <font color="Maroon" title="c6">Y</font> &amp; <font color="Maroon" title="c7">P</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a> <font color="Maroon" title="c8">Q</font> )
 <b>by </b><i><a class="ref" href="pencil_1.html#T2" title="PENCIL_1:th.2">PENCIL_1:2</a></i>;<br/>
<a NAME="E4:25_1"/><i><font color="Green" title="E25">A3</font></i>: 
( <font color="Maroon" title="c7">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font> &amp; <font color="Maroon" title="c7">P</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y</font> &amp; <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">X</font> &amp; <font color="Maroon" title="c8">Q</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c6">Y</font> )
 
<b>by </b><i><a class="txt" href="pencil_4.html#E3:25_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</a></i>;<br/>
<a NAME="E5:25_1"/><i><font color="Green" title="E26">A4</font></i>: 
not  <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="pencil_4.html#T18" target="_self" title="PENCIL_4:th.18">Th18</a></i>;<br/>
<a NAME="E6:25_1"/>
not  <a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font> is <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="ref" href="pencil_4.html#T19" target="_self" title="PENCIL_4:th.19">Th19</a></i>;<br/>
<a NAME="E7:25_1"/><b>then </b><i><font color="Green" title="E27">A5</font></i>: 
not the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="ref" href="pencil_1.html#D4" title="PENCIL_1:def.4">PENCIL_1:def 4</a></i>;<br/>
<a NAME="E8:25_1"/><b>then </b>
( <font color="Maroon" title="c5">X</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font></span>)</span> &amp; <font color="Maroon" title="c6">Y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="pre_topc.html#U1" title="PRE_TOPC:sel.1">topology</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font></span>)</span> )
 
;<br/>
<b>then reconsider </b><font color="Maroon" title="c9">P</font> = <font color="Maroon" title="c7">P</font>, <font color="Maroon" title="c10">Q</font> = <font color="Maroon" title="c8">Q</font> as   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font></span>)</span> <b>by </b><i><a class="txt" href="pencil_4.html#E4:25_1"><i><font color="Green" title="E25">A3</font></i></a></i>;<br/>
<a NAME="E10:25_1"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E5:25_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c11">P1</font> being  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E12:25_1"/><i><font color="Green" title="E28">A6</font></i>: 
( <font color="Maroon" title="c11">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">P</font> &amp;  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c11">P1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="ref" href="vectsp_9.html#D3" title="VECTSP_9:def.3">VECTSP_9:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c12">P</font> = <font color="Maroon" title="c9">P</font> as  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="pencil_4.html#E12:25_1"><i><font color="Green" title="E28">A6</font></i></a></i>;<br/>
<a NAME="E14:25_1"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="pencil_4.html#K5" title="PENCIL_4:func.5">PencilSpace</a> <font color="Maroon" title="c2">V</font>,<font color="Maroon" title="c3">k</font></span>)</span> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 
<b>by </b><i><a class="txt" href="pencil_4.html#E5:25_1"><i><font color="Green" title="E26">A4</font></i></a>, <a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a></i>;<br/>
<b>then consider </b><font color="Maroon" title="c13">Q1</font> being  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E16:25_1"/><i><font color="Green" title="E29">A7</font></i>: 
( <font color="Maroon" title="c13">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c10">Q</font> &amp;  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c13">Q1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="ref" href="vectsp_9.html#D3" title="VECTSP_9:def.3">VECTSP_9:def 3</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c14">Q</font> = <font color="Maroon" title="c10">Q</font> as  <a href="vectsp_1.html#V7" title="VECTSP_1:attr.7">strict</a>  <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font> <b>by </b><i><a class="txt" href="pencil_4.html#E16:25_1"><i><font color="Green" title="E29">A7</font></i></a></i>;<br/>
<b>consider </b><font color="Maroon" title="c15">W1</font>, <font color="Maroon" title="c16">W2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E19:25_1"/><i><font color="Green" title="E30">A8</font></i>: 
( <font color="Maroon" title="c15">W1</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c16">W2</font> &amp; <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c15">W1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> &amp;  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c16">W2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c5">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pencil_4.html#K3" title="PENCIL_4:func.3">pencil</a> <font color="Maroon" title="c15">W1</font>,<font color="Maroon" title="c16">W2</font>,<font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="txt" href="pencil_4.html#E7:25_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="pencil_4.html#D4" target="_self" title="PENCIL_4:def.4">Def4</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c17">U1</font>, <font color="Maroon" title="c18">U2</font> being    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c2">V</font><b> such that </b><br/><a NAME="E21:25_1"/><i><font color="Green" title="E31">A9</font></i>: 
( <font color="Maroon" title="c17">U1</font> is    <a href="vectsp_4.html#M1" title="VECTSP_4:mode.1">Subspace</a> of <font color="Maroon" title="c18">U2</font> &amp; <span class="p1">(<span class="default"><a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c17">U1</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> &amp;  <a href="vectsp_9.html#K1" title="VECTSP_9:func.1">dim</a> <font color="Maroon" title="c18">U2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">k</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 &amp; <font color="Maroon" title="c6">Y</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pencil_4.html#K3" title="PENCIL_4:func.3">pencil</a> <font color="Maroon" title="c17">U1</font>,<font color="Maroon" title="c18">U2</font>,<font color="Maroon" title="c3">k</font> )
 <b>by </b><i><a class="txt" href="pencil_4.html#E7:25_1"><i><font color="Green" title="E27">A5</font></i></a>, <a class="ref" href="pencil_4.html#D4" target="_self" title="PENCIL_4:def.4">Def4</a></i>;<br/>
<i><font color="Green" title="E32">A10</font></i>:  <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c15">W1</font> = 
<font color="Maroon" title="c12">P</font> <a href="vectsp_5.html#K2" title="VECTSP_5:func.2">/\</a> <font color="Maroon" title="c14">Q</font>
<b>by </b><i><a class="txt" href="pencil_4.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="pencil_4.html#E3:25_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="pencil_4.html#E4:25_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="pencil_4.html#E19:25_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="pencil_4.html#T12" target="_self" title="PENCIL_4:th.12">Th12</a></i>
<br/>.= 
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c17">U1</font>
<b>by </b><i><a class="txt" href="pencil_4.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="pencil_4.html#E3:25_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="pencil_4.html#E4:25_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="pencil_4.html#E21:25_1"><i><font color="Green" title="E31">A9</font></i></a>, <a class="ref" href="pencil_4.html#T12" target="_self" title="PENCIL_4:th.12">Th12</a></i>
;<br/>
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c16">W2</font> = 
<font color="Maroon" title="c12">P</font> <a href="vectsp_5.html#K1" title="VECTSP_5:func.1">+</a> <font color="Maroon" title="c14">Q</font>
<b>by </b><i><a class="txt" href="pencil_4.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="pencil_4.html#E3:25_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="pencil_4.html#E4:25_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="pencil_4.html#E19:25_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="ref" href="pencil_4.html#T12" target="_self" title="PENCIL_4:th.12">Th12</a></i>
<br/>.= 
 <a href="vectsp_4.html#K2" title="VECTSP_4:func.2">(Omega).</a> <font color="Maroon" title="c18">U2</font>
<b>by </b><i><a class="txt" href="pencil_4.html#E1:25"><i><font color="Green" title="E23">A1</font></i></a>, <a class="txt" href="pencil_4.html#E3:25_1"><i><font color="Green" title="E24">A2</font></i></a>, <a class="txt" href="pencil_4.html#E4:25_1"><i><font color="Green" title="E25">A3</font></i></a>, <a class="txt" href="pencil_4.html#E21:25_1"><i><font color="Green" title="E31">A9</font></i></a>, <a class="ref" href="pencil_4.html#T12" target="_self" title="PENCIL_4:th.12">Th12</a></i>
;<br/>
<b>hence </b><a NAME="E24:25_1"/>
<font color="Maroon" title="c5">X</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c6">Y</font>
 <b>by </b><i><a class="txt" href="pencil_4.html#E19:25_1"><i><font color="Green" title="E30">A8</font></i></a>, <a class="txt" href="pencil_4.html#E21:25_1"><i><font color="Green" title="E31">A9</font></i></a>, <a class="txt" href="pencil_4.html#E22:25_1"><i><font color="Green" title="E32">A10</font></i></a>, <a class="ref" href="pencil_4.html#T7" target="_self" title="PENCIL_4:th.7">Th7</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>
