<?xml version="1.0"?>
<div class="add">

<span class="kw">let </span><font color="Maroon" title="c1">P</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b1">q</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 </span> } </span>  implies  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 )</span><br/>

<span class="kw">assume </span><a NAME="E1:28"/>
<font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"> { <span class="default"> <font color="Olive" title="b1">q</font> where <font color="Olive" title="b1">q</font> is   <a href="pre_topc.html#NM2" title="PRE_TOPC:NM.2">Point</a> of <span class="p1">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> : <span class="p1"><a href="euclid.html#K12" title="EUCLID:func.12">|.</a><span class="default"><font color="Olive" title="b1">q</font></span><a href="euclid.html#K12" title="EUCLID:func.12">.|</a></span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 </span> } </span> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span><br/>

<a NAME="E2:28"/><span class="kw">then </span>
<a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="jgraph_5.html#E30"><span class="lab"><font color="Green" title="E24">Lm3</font></span></a></span>;<br/>
<a NAME="E3:28"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a> <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">[.</a><span class="default"><span class="p2">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1</span>)</span>,1</span><a href="rcomp_1.html#K1" title="RCOMP_1:func.1">.]</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T129" onmouseover="rs('relat_1/T129')" onmouseout="rh()">RELAT_1:129</a></span>;<br/>
<a NAME="E4:28"/><span class="kw">then </span>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="euclid.html#K15" title="EUCLID:func.15">TOP-REAL</a> 2</span>)</span> <a href="pre_topc.html#K1" title="PRE_TOPC:func.1">|</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">P</font> &amp;  <a href="seq_4.html#K3" title="SEQ_4:func.3">lower_bound</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a> <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="relset_1.html#K7" title="RELSET_1:func.7">.:</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="jordan5a.html#T19" onmouseover="rs('jordan5a/T19')" onmouseout="rh()">JORDAN5A:19</a>, <a class="ref" href="pre_topc.html#T8" onmouseover="rs('pre_topc/T8')" onmouseout="rh()">PRE_TOPC:8</a></span>;<br/>
<a NAME="E5:28"/><span class="kw">then </span>
 <a href="pscomp_1.html#K1" title="PSCOMP_1:func.1">lower_bound</a> <span class="p1">(<span class="default"><a href="pscomp_1.html#K4" title="PSCOMP_1:func.4">proj1</a> <a href="pscomp_1.html#K3" title="PSCOMP_1:func.3">|</a> <font color="Maroon" title="c1">P</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#D1" onmouseover="rs('pscomp_1/D1')" onmouseout="rh()">PSCOMP_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:28"/>
 <a href="pscomp_1.html#K6" title="PSCOMP_1:func.6">W-bound</a> <font color="Maroon" title="c1">P</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> 1
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pscomp_1.html#D7" onmouseover="rs('pscomp_1/D7')" onmouseout="rh()">PSCOMP_1:def 7</a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div>
