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<b>let </b><font color="Maroon" title="c1">GS</font> be   <a href="lexbfs.html#NM10" title="LEXBFS:NM.10">VLabelNumberingSeq</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="hidden.html#M1" title="HIDDEN:mode.1">set</a> <br/> for <font color="Olive" title="b2">m</font>, <font color="Olive" title="b3">n</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Olive" title="b1">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Olive" title="b2">m</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Olive" title="b2">m</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Olive" title="b1">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b3">n</font> holds <br/><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Olive" title="b3">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">v</font></span><br/><b>let </b><font color="Maroon" title="c2">v</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"> for <font color="Olive" title="b1">m</font>, <font color="Olive" title="b2">n</font> being <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  <a href="ordinal1.html#NM1" title="ORDINAL1:NM.1">number</a>   st <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Olive" title="b1">m</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Olive" title="b1">m</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">n</font> holds <br/><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Olive" title="b2">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font></span><br/><b>let </b><font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">n</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"> ( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> implies <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font> )</span><br/>





<b>set </b><font color="Maroon" title="c5">CSM</font> = <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font>;<br/>
<b>set </b><font color="Maroon" title="c6">VLM</font> =  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c7">j</font> = <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font>;<br/>
<b>set </b><font color="Maroon" title="c8">CJ1</font> = <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c9">VJ1</font> =  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>;<br/>
<b>assume </b><a NAME="E1:125"/><i><font color="Green" title="E56">A1</font></i>: 
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a>  &amp; <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font></span><br/>

<a NAME="E2:125"/><b>then </b><i><font color="Green" title="E57">A2</font></i>: 
( 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> &amp; <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a>  )
 
<b>by </b><i><a class="ref" href="lexbfs.html#T22" target="_self" title="LEXBFS:th.22">Th22</a></i>;<br/>
<a NAME="E3:125"/><i><font color="Green" title="E58">A3</font></i>: 
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c4">n</font>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E1:125"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="lexbfs.html#T22" target="_self" title="LEXBFS:th.22">Th22</a></i>;<br/>
<a NAME="E4:125"/><i><font color="Green" title="E59">A4</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">n</font>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E2:125"><i><font color="Green" title="E57">A2</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/>
<a NAME="E5:125"/><b>then </b><i><font color="Green" title="E60">A5</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> 
 
<b>by </b><i><a class="txt" href="lexbfs.html#E3:125"><i><font color="Green" title="E58">A3</font></i></a>, <a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></i>;<br/>
<b>set </b><font color="Maroon" title="c10">w</font> = <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span>;<br/>
<a NAME="E6:125"/><i><font color="Green" title="E61">A6</font></i>: 
<font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="glib_003.html#K14" title="GLIB_003:func.14">.labeledV()</a> 
 
<b>by </b><i><a class="txt" href="lexbfs.html#E5:125"><i><font color="Green" title="E60">A5</font></i></a>, <a class="ref" href="lexbfs.html#T18" target="_self" title="LEXBFS:th.18">Th18</a></i>;<br/>
<a NAME="E7:125"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">n</font></span>)</span>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E4:125"><i><font color="Green" title="E59">A4</font></i></a>, <a class="txt" href="lexbfs.html#E5:125"><i><font color="Green" title="E60">A5</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a></i>;<br/>
<a NAME="E8:125"/><b>then </b><i><font color="Green" title="E62">A7</font></i>: 
<span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font>
 
<b>by </b><i><a class="txt" href="lexbfs.html#E3:125"><i><font color="Green" title="E58">A3</font></i></a>, <a class="txt" href="lexbfs.html#E4:125"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="lexbfs.html#T19" target="_self" title="LEXBFS:th.19">Th19</a>, <a class="ref" href="xreal_1.html#T46" title="XREAL_1:th.46">XREAL_1:46</a></i>;<br/>
<a NAME="E9:125"/><i><font color="Green" title="E63">A8</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span> is <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>
 
<b>by </b><i><a class="ref" href="lexbfs.html#T25" target="_self" title="LEXBFS:th.25">Th25</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="125_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:125_1"/>
( <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font> or <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">m</font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="125_1_1"><b>suppose </b></a><a NAME="E1:125_1_1"/><i><font color="Green" title="E64">A9</font></i>: 
<font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><a NAME="E2:125_1_1"/><b>then </b>
<font color="Maroon" title="c3">m</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="txt" href="lexbfs.html#E4:125"><i><font color="Green" title="E59">A4</font></i></a>, <a class="ref" href="xreal_1.html#T8" title="XREAL_1:th.8">XREAL_1:8</a></i>;<br/><a NAME="E3:125_1_1"/><b>then </b><i><font color="Green" title="E65">A10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Maroon" title="c3">m</font></span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="ref" href="xreal_1.html#T11" title="XREAL_1:th.11">XREAL_1:11</a></i>;<br/><a NAME="E4:125_1_1"/><i><font color="Green" title="E66">A11</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <font color="Maroon" title="c3">m</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="txt" href="lexbfs.html#E5:125"><i><font color="Green" title="E60">A5</font></i></a>, <a class="txt" href="lexbfs.html#E1:125_1_1"><i><font color="Green" title="E64">A9</font></i></a>, <a class="ref" href="binarith.html#T50" title="BINARITH:th.50">BINARITH:50</a>, <a class="ref" href="xxreal_0.html#T2" title="XXREAL_0:th.2">XXREAL_0:2</a></i>;<br/><a NAME="E5:125_1_1"/><i><font color="Green" title="E67">A12</font></i>: 
<font color="Maroon" title="c4">n</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:125"><i><font color="Green" title="E56">A1</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/><a NAME="E6:125_1_1"/>
 <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span></span>)</span> <a href="subset_1.html#K7" title="SUBSET_1:func.7">\</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="lexbfs.html#T21" target="_self" title="LEXBFS:th.21">Th21</a></i>;<br/><b>hence </b><a NAME="E7:125_1_1"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E3:125_1_1"><i><font color="Green" title="E65">A10</font></i></a>, <a class="txt" href="lexbfs.html#E4:125_1_1"><i><font color="Green" title="E66">A11</font></i></a>, <a class="txt" href="lexbfs.html#E5:125_1_1"><i><font color="Green" title="E67">A12</font></i></a>, <a class="ref" href="lexbfs.html#T5" target="_self" title="LEXBFS:th.5">Th5</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="hsNdiv(this)" href="javascript:()" title="125_1_2"><b>suppose </b></a><a NAME="E1:125_1_2"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c3">m</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><a NAME="E2:125_1_2"/><b>then </b>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c3">m</font>
 <b>by </b><i><a class="ref" href="nat_1.html#T13" title="NAT_1:th.13">NAT_1:13</a></i>;<br/><a NAME="E3:125_1_2"/><b>then </b><i><font color="Green" title="E64">A13</font></i>: 
 <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span>
 <b>by </b><i><a class="ref" href="lexbfs.html#T24" target="_self" title="LEXBFS:th.24">Th24</a></i>;<br/><a NAME="E4:125_1_2"/><b>then </b><i><font color="Green" title="E65">A14</font></i>: 
 <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><span class="p5">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span>
 <b>by </b><i><a class="ref" href="relat_1.html#T25" title="RELAT_1:th.25">RELAT_1:25</a></i>;<br/><a NAME="E5:125_1_2"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span>,<font color="Maroon" title="c4">n</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">+</a> 1</span>)</span></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E6:125"><i><font color="Green" title="E61">A6</font></i></a>, <a class="txt" href="lexbfs.html#E8:125"><i><font color="Green" title="E62">A7</font></i></a>, <a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/><a NAME="E6:125_1_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="glib_003.html#K7" title="GLIB_003:func.7">the_VLabel_of</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K8" title="LEXBFS:func.8">.</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="recdef_1.html#K1" title="RECDEF_1:func.1">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">n</font>
 <b>by </b><i><a class="txt" href="lexbfs.html#E6:125"><i><font color="Green" title="E61">A6</font></i></a>, <a class="txt" href="lexbfs.html#E3:125_1_2"><i><font color="Green" title="E64">A13</font></i></a>, <a class="txt" href="lexbfs.html#E4:125_1_2"><i><font color="Green" title="E65">A14</font></i></a>, <a class="ref" href="funct_1.html#D4" title="FUNCT_1:def.4">FUNCT_1:def 4</a></i>;<br/><b>hence </b><a NAME="E7:125_1_2"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">GS</font> <a href="lexbfs.html#K10" title="LEXBFS:func.10">.PickedAt</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c1">GS</font> <a href="glib_000.html#K40" title="GLIB_000:func.40">.Lifespan()</a> </span>)</span> <a href="binarith.html#K3" title="BINARITH:func.3">-'</a> <font color="Maroon" title="c4">n</font></span>)</span>
 <b>by </b><i><a class="txt" href="lexbfs.html#E1:125"><i><font color="Green" title="E56">A1</font></i></a>, <a class="txt" href="lexbfs.html#E6:125"><i><font color="Green" title="E61">A6</font></i></a>, <a class="txt" href="lexbfs.html#E9:125"><i><font color="Green" title="E63">A8</font></i></a>, <a class="txt" href="lexbfs.html#E4:125_1_2"><i><font color="Green" title="E65">A14</font></i></a>, <a class="ref" href="funct_1.html#D8" title="FUNCT_1:def.8">FUNCT_1:def 8</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><b>end;</b></div>

</div>
