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<span class="kw">let </span><font color="Maroon" title="c1">i</font>, <font color="Maroon" title="c2">j</font>, <font color="Maroon" title="c3">m</font>, <font color="Maroon" title="c4">n</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <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">  for <font color="Olive" title="b1">E</font> being   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>   non  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>   non  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</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>  st <font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> &amp; 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Olive" title="b1">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> &amp; 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Olive" title="b1">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> holds <br/> for <font color="Olive" title="b2">i1</font>, <font color="Olive" title="b3">j1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">i1</font> &amp; <font color="Olive" title="b2">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b3">j1</font> &amp; <font color="Olive" title="b3">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 holds <br/> <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Olive" title="b1">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>,<font color="Olive" title="b2">i1</font>,<font color="Olive" title="b3">j1</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Olive" title="b1">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span><br/><span class="kw">let </span><font color="Maroon" title="c5">E</font> be   <a href="compts_1.html#V2" title="COMPTS_1:attr.2">compact</a>   non  <a href="sppol_1.html#V1" title="SPPOL_1:attr.1">horizontal</a>   non  <a href="sppol_1.html#V2" title="SPPOL_1:attr.2">vertical</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="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font> &amp; 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> &amp; <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> &amp; 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> &amp; <font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> implies  for <font color="Olive" title="b1">i1</font>, <font color="Olive" title="b2">j1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i1</font> &amp; <font color="Olive" title="b1">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j1</font> &amp; <font color="Olive" title="b2">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 holds <br/> <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>,<font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">j1</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>) )</span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">G</font> =  <a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>);<br/>
<span class="kw">set </span><font color="Maroon" title="c7">G1</font> =  <a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>);<br/>
<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:60"/><span class="lab"><font color="Green" title="E38">A1</font></span>: 
<font color="Maroon" title="c3">m</font> <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c4">n</font>
 <span class="kw">and </span><br/><a NAME="E2:60"/><span class="lab"><font color="Green" title="E39">A2</font></span>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font>
 <span class="kw">and </span><br/><a NAME="E3:60"/><span class="lab"><font color="Green" title="E40">A3</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>
 <span class="kw">and </span><br/><a NAME="E4:60"/><span class="lab"><font color="Green" title="E41">A4</font></span>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font>
 <span class="kw">and </span><br/><a NAME="E5:60"/><span class="lab"><font color="Green" title="E42">A5</font></span>: 
<font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</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">  for <font color="Olive" title="b1">i1</font>, <font color="Olive" title="b2">j1</font> being   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>  st <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b1">i1</font> &amp; <font color="Olive" title="b1">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Olive" title="b2">j1</font> &amp; <font color="Olive" title="b2">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 holds <br/> <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>,<font color="Olive" title="b1">i1</font>,<font color="Olive" title="b2">j1</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span><br/>

<span class="kw">set </span><font color="Maroon" title="c8">i2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c9">j2</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c10">i3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2;<br/>
<span class="kw">set </span><font color="Maroon" title="c11">j3</font> = <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2;<br/>
<span class="kw">let </span><font color="Maroon" title="c12">i1</font>, <font color="Maroon" title="c13">j1</font> be   <a href="ordinal1.html#NM6" title="ORDINAL1:NM.6">Nat</a>; <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"> ( <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">i1</font> &amp; <font color="Maroon" title="c12">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 &amp; <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">j1</font> &amp; <font color="Maroon" title="c13">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 implies  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>,<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>) )</span><br/>

<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E6:60"/><span class="lab"><font color="Green" title="E43">A6</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">i1</font>
 <span class="kw">and </span><br/><a NAME="E7:60"/><span class="lab"><font color="Green" title="E44">A7</font></span>: 
<font color="Maroon" title="c12">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 <span class="kw">and </span><br/><a NAME="E8:60"/><span class="lab"><font color="Green" title="E45">A8</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">j1</font>
 <span class="kw">and </span><br/><a NAME="E9:60"/><span class="lab"><font color="Green" title="E46">A9</font></span>: 
<font color="Maroon" title="c13">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 ; <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="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>,<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>) <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span><br/>

<a NAME="E10:60"/><span class="lab"><font color="Green" title="E47">A10</font></span>: 
<font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<a NAME="E11:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E48">A11</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E5:60"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="ref" href="jordan1a.html#T35" target="_self" onmouseover="rs('jordan1a/T35')" onmouseout="rh()">Th35</a></span>;<br/>
<a NAME="E12:60"/><span class="lab"><font color="Green" title="E49">A12</font></span>: 
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c1">i</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E13:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E50">A13</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<a NAME="E14:60"/>
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T29" onmouseover="rs('xreal_1/T29')" onmouseout="rh()">XREAL_1:29</a></span>;<br/>
<a NAME="E15:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E51">A14</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E16:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E52">A15</font></span>: 
1 <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">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="jordan1a.html#T31" target="_self" onmouseover="rs('jordan1a/T31')" onmouseout="rh()">Th31</a></span>;<br/>
<a NAME="E17:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E53">A16</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c12">i1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E18:60"/>
<font color="Maroon" title="c13">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:60"><span class="lab"><font color="Green" title="E46">A9</font></span></a>, <a class="txt" href="#E10:60"><span class="lab"><font color="Green" title="E47">A10</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E19:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E54">A17</font></span>: 
( <font color="Maroon" title="c13">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 or <font color="Maroon" title="c13">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/>
<span class="kw">let </span><font color="Maroon" title="c14">e</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tarski.html#D3" onmouseover="rs('tarski/D3')" onmouseout="rh()">TARSKI:def 3</a> <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"> (  not <font color="Maroon" title="c14">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>,<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>) or <font color="Maroon" title="c14">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>) )</span><br/>

<span class="kw">assume </span><a NAME="E20:60"/><span class="lab"><font color="Green" title="E55">A18</font></span>: 
<font color="Maroon" title="c14">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>,<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>)
 ; <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="c14">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c15">p</font> = <font color="Maroon" title="c14">e</font> as   <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> ;<br/>
<a NAME="E22:60"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="jordan1a.html#T34" target="_self" onmouseover="rs('jordan1a/T34')" onmouseout="rh()">Th34</a></span>;<br/>
<a NAME="E23:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E56">A19</font></span>: 
<font color="Maroon" title="c12">i1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:60"><span class="lab"><font color="Green" title="E44">A7</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E24:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E57">A20</font></span>: 
<font color="Maroon" title="c12">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<span class="lab"><font color="Green" title="E58">A21</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1

<br/>.= 
<font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>
;<br/>
<a NAME="E26:60"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="xreal_1.html#T29" onmouseover="rs('xreal_1/T29')" onmouseout="rh()">XREAL_1:29</a></span>;<br/>
<a NAME="E27:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E59">A22</font></span>: 
<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,<span class="p1">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E5:60"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="#E15:60"><span class="lab"><font color="Green" title="E51">A14</font></span></a>, <a class="txt" href="#E25:60"><span class="lab"><font color="Green" title="E58">A21</font></span></a>, <a class="txt" href="#E13:60"><span class="lab"><font color="Green" title="E50">A13</font></span></a>, <a class="ref" href="jordan1a.html#T33" target="_self" onmouseover="rs('jordan1a/T33')" onmouseout="rh()">Th33</a></span>;<br/>
<a NAME="E28:60"/><span class="lab"><font color="Green" title="E60">A23</font></span>: 
<font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<a NAME="E29:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E61">A24</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="ref" href="jordan1a.html#T34" target="_self" onmouseover="rs('jordan1a/T34')" onmouseout="rh()">Th34</a></span>;<br/>
<a NAME="E30:60"/>
<font color="Maroon" title="c12">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <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">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:60"><span class="lab"><font color="Green" title="E44">A7</font></span></a>, <a class="txt" href="#E28:60"><span class="lab"><font color="Green" title="E60">A23</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E31:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E62">A25</font></span>: 
( <font color="Maroon" title="c12">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 or <font color="Maroon" title="c12">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/>
<a NAME="E32:60"/><span class="lab"><font color="Green" title="E63">A26</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:60"><span class="lab"><font color="Green" title="E49">A12</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<span class="lab"><font color="Green" title="E64">A27</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> <span class="p1">(<span class="default">1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span> = 
<font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1

<br/>.= 
<font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>
;<br/>
<a NAME="E34:60"/><span class="lab"><font color="Green" title="E65">A28</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:60"><span class="lab"><font color="Green" title="E49">A12</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<a NAME="E35:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E66">A29</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="txt" href="#E23:60"><span class="lab"><font color="Green" title="E56">A19</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E36:60"/>
<font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T29" onmouseover="rs('xreal_1/T29')" onmouseout="rh()">XREAL_1:29</a></span>;<br/>
<a NAME="E37:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E67">A30</font></span>: 
<font color="Maroon" title="c2">j</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:60"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E38:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E68">A31</font></span>: 
1 <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">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="jordan1a.html#T32" target="_self" onmouseover="rs('jordan1a/T32')" onmouseout="rh()">Th32</a></span>;<br/>
<a NAME="E39:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E69">A32</font></span>: 
1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c13">j1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:60"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E40:60"/><span class="kw">then </span>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c13">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E41:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E70">A33</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60"><span class="lab"><font color="Green" title="E56">A19</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E11:60"><span class="lab"><font color="Green" title="E48">A11</font></span></a>, <a class="txt" href="#E19:60"><span class="lab"><font color="Green" title="E54">A17</font></span></a>, <a class="ref" href="goboard5.html#T4" onmouseover="rs('goboard5/T4')" onmouseout="rh()">GOBOARD5:4</a></span>;<br/>
<a NAME="E42:60"/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 1</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E5:60"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="ref" href="jordan1a.html#T35" target="_self" onmouseover="rs('jordan1a/T35')" onmouseout="rh()">Th35</a></span>;<br/>
<a NAME="E43:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E71">A34</font></span>: 
<font color="Maroon" title="c13">j1</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:60"><span class="lab"><font color="Green" title="E46">A9</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E44:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E72">A35</font></span>: 
<font color="Maroon" title="c13">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E45:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E73">A36</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">p</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:60"><span class="lab"><font color="Green" title="E55">A18</font></span></a>, <a class="txt" href="#E24:60"><span class="lab"><font color="Green" title="E57">A20</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="ref" href="jordan9.html#T17" onmouseover="rs('jordan9/T17')" onmouseout="rh()">JORDAN9:17</a></span>;<br/>
<a NAME="E46:60"/><span class="lab"><font color="Green" title="E74">A37</font></span>: 
1 <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c2">j</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E47:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A38</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<a NAME="E48:60"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c13">j1</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">j1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:60"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/>
<a NAME="E49:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E76">A39</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60"><span class="lab"><font color="Green" title="E56">A19</font></span></a>, <a class="txt" href="#E43:60"><span class="lab"><font color="Green" title="E71">A34</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E38:60"><span class="lab"><font color="Green" title="E68">A31</font></span></a>, <a class="txt" href="#E47:60"><span class="lab"><font color="Green" title="E75">A38</font></span></a>, <a class="ref" href="goboard5.html#T4" onmouseover="rs('goboard5/T4')" onmouseout="rh()">GOBOARD5:4</a></span>;<br/>
<a NAME="E50:60"/><span class="lab"><font color="Green" title="E77">A40</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="xcmplx_0.html#K6" title="XCMPLX_0:func.6">-</a> 2</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E46:60"><span class="lab"><font color="Green" title="E74">A37</font></span></a>, <a class="ref" href="xreal_1.html#T233" onmouseover="rs('xreal_1/T233')" onmouseout="rh()">XREAL_1:233</a></span>;<br/>
<a NAME="E51:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E78">A41</font></span>: 
<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E15:60"><span class="lab"><font color="Green" title="E51">A14</font></span></a>, <a class="txt" href="#E37:60"><span class="lab"><font color="Green" title="E67">A30</font></span></a>, <a class="txt" href="#E34:60"><span class="lab"><font color="Green" title="E65">A28</font></span></a>, <a class="ref" href="jordan1a.html#T33" target="_self" onmouseover="rs('jordan1a/T33')" onmouseout="rh()">Th33</a></span>;<br/>
<a NAME="E52:60"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="ref" href="xreal_1.html#T29" onmouseover="rs('xreal_1/T29')" onmouseout="rh()">XREAL_1:29</a></span>;<br/>
<a NAME="E53:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E79">A42</font></span>: 
<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p1">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p4">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p3">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:60"><span class="lab"><font color="Green" title="E38">A1</font></span></a>, <a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E37:60"><span class="lab"><font color="Green" title="E67">A30</font></span></a>, <a class="txt" href="#E33:60"><span class="lab"><font color="Green" title="E64">A27</font></span></a>, <a class="txt" href="#E47:60"><span class="lab"><font color="Green" title="E75">A38</font></span></a>, <a class="ref" href="jordan1a.html#T33" target="_self" onmouseover="rs('jordan1a/T33')" onmouseout="rh()">Th33</a></span>;<br/>
<a NAME="E54:60"/><span class="lab"><font color="Green" title="E80">A43</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:60"><span class="lab"><font color="Green" title="E55">A18</font></span></a>, <a class="txt" href="#E24:60"><span class="lab"><font color="Green" title="E57">A20</font></span></a>, <a class="txt" href="#E44:60"><span class="lab"><font color="Green" title="E72">A35</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="ref" href="jordan9.html#T17" onmouseover="rs('jordan9/T17')" onmouseout="rh()">JORDAN9:17</a></span>;<br/>
<a NAME="E55:60"/>
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="ref" href="nat_1.html#T13" onmouseover="rs('nat_1/T13')" onmouseout="rh()">NAT_1:13</a></span>;<br/>
<a NAME="E56:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E81">A44</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c12">i1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:60"><span class="lab"><font color="Green" title="E71">A34</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="txt" href="#E29:60"><span class="lab"><font color="Green" title="E61">A24</font></span></a>, <a class="txt" href="#E31:60"><span class="lab"><font color="Green" title="E62">A25</font></span></a>, <a class="ref" href="goboard5.html#T3" onmouseover="rs('goboard5/T3')" onmouseout="rh()">GOBOARD5:3</a></span>;<br/>
<a NAME="E57:60"/><span class="lab"><font color="Green" title="E82">A45</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:60"><span class="lab"><font color="Green" title="E55">A18</font></span></a>, <a class="txt" href="#E24:60"><span class="lab"><font color="Green" title="E57">A20</font></span></a>, <a class="txt" href="#E44:60"><span class="lab"><font color="Green" title="E72">A35</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="ref" href="jordan9.html#T17" onmouseover="rs('jordan9/T17')" onmouseout="rh()">JORDAN9:17</a></span>;<br/>
<a NAME="E58:60"/><span class="lab"><font color="Green" title="E83">A46</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a>  <a href="matrix_0.html#K1" title="MATRIX_0:func.1">width</a> <span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:60"><span class="lab"><font color="Green" title="E45">A8</font></span></a>, <a class="txt" href="#E43:60"><span class="lab"><font color="Green" title="E71">A34</font></span></a>, <a class="txt" href="#E50:60"><span class="lab"><font color="Green" title="E77">A40</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60"><span class="lab"><font color="Green" title="E56">A19</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E38:60"><span class="lab"><font color="Green" title="E68">A31</font></span></a>, <a class="txt" href="#E47:60"><span class="lab"><font color="Green" title="E75">A38</font></span></a>, <a class="ref" href="goboard5.html#T1" onmouseover="rs('goboard5/T1')" onmouseout="rh()">GOBOARD5:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:60"><span class="lab"><font color="Green" title="E52">A15</font></span></a>, <a class="txt" href="#E38:60"><span class="lab"><font color="Green" title="E68">A31</font></span></a>, <a class="txt" href="#E35:60"><span class="lab"><font color="Green" title="E66">A29</font></span></a>, <a class="txt" href="#E58:60"><span class="lab"><font color="Green" title="E83">A46</font></span></a>, <a class="txt" href="#E32:60"><span class="lab"><font color="Green" title="E63">A26</font></span></a>, <a class="txt" href="#E47:60"><span class="lab"><font color="Green" title="E75">A38</font></span></a>, <a class="ref" href="goboard5.html#T1" onmouseover="rs('goboard5/T1')" onmouseout="rh()">GOBOARD5:1</a></span>
;<br/>
<a NAME="E60:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E84">A47</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E57:60"><span class="lab"><font color="Green" title="E82">A45</font></span></a>, <a class="txt" href="#E51:60"><span class="lab"><font color="Green" title="E78">A41</font></span></a>, <a class="txt" href="#E49:60"><span class="lab"><font color="Green" title="E76">A39</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E61:60"/><span class="lab"><font color="Green" title="E85">A48</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c13">j1</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:60"><span class="lab"><font color="Green" title="E55">A18</font></span></a>, <a class="txt" href="#E24:60"><span class="lab"><font color="Green" title="E57">A20</font></span></a>, <a class="txt" href="#E44:60"><span class="lab"><font color="Green" title="E72">A35</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="ref" href="jordan9.html#T17" onmouseover="rs('jordan9/T17')" onmouseout="rh()">JORDAN9:17</a></span>;<br/>
<a NAME="E62:60"/><span class="lab"><font color="Green" title="E86">A49</font></span>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:60"><span class="lab"><font color="Green" title="E46">A9</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="txt" href="#E10:60"><span class="lab"><font color="Green" title="E47">A10</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (1,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60"><span class="lab"><font color="Green" title="E56">A19</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E11:60"><span class="lab"><font color="Green" title="E48">A11</font></span></a>, <a class="ref" href="goboard5.html#T1" onmouseover="rs('goboard5/T1')" onmouseout="rh()">GOBOARD5:1</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:60"><span class="lab"><font color="Green" title="E52">A15</font></span></a>, <a class="txt" href="#E35:60"><span class="lab"><font color="Green" title="E66">A29</font></span></a>, <a class="txt" href="#E13:60"><span class="lab"><font color="Green" title="E50">A13</font></span></a>, <a class="txt" href="#E11:60"><span class="lab"><font color="Green" title="E48">A11</font></span></a>, <a class="txt" href="#E62:60"><span class="lab"><font color="Green" title="E86">A49</font></span></a>, <a class="ref" href="goboard5.html#T1" onmouseover="rs('goboard5/T1')" onmouseout="rh()">GOBOARD5:1</a></span>
;<br/>
<a NAME="E64:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E87">A50</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,<span class="p2">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>)</span>)</span> <a href="euclid.html#K18" title="EUCLID:func.18">`2</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E61:60"><span class="lab"><font color="Green" title="E85">A48</font></span></a>, <a class="txt" href="#E27:60"><span class="lab"><font color="Green" title="E59">A22</font></span></a>, <a class="txt" href="#E41:60"><span class="lab"><font color="Green" title="E70">A33</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<a NAME="E65:60"/>
( <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Maroon" title="c12">i1</font> or <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">i1</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E6:60"><span class="lab"><font color="Green" title="E43">A6</font></span></a>, <a class="txt" href="#E34:60"><span class="lab"><font color="Green" title="E65">A28</font></span></a>, <a class="ref" href="xxreal_0.html#T1" onmouseover="rs('xxreal_0/T1')" onmouseout="rh()">XXREAL_0:1</a></span>;<br/>
<a NAME="E66:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E88">A51</font></span>: 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c12">i1</font>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E23:60"><span class="lab"><font color="Green" title="E56">A19</font></span></a>, <a class="txt" href="#E43:60"><span class="lab"><font color="Green" title="E71">A34</font></span></a>, <a class="txt" href="#E16:60"><span class="lab"><font color="Green" title="E52">A15</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="txt" href="#E34:60"><span class="lab"><font color="Green" title="E65">A28</font></span></a>, <a class="ref" href="goboard5.html#T3" onmouseover="rs('goboard5/T3')" onmouseout="rh()">GOBOARD5:3</a></span>;<br/>
<a NAME="E67:60"/><span class="lab"><font color="Green" title="E89">A52</font></span>: 
1 <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p3">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E7:60"><span class="lab"><font color="Green" title="E44">A7</font></span></a>, <a class="txt" href="#E17:60"><span class="lab"><font color="Green" title="E53">A16</font></span></a>, <a class="txt" href="#E28:60"><span class="lab"><font color="Green" title="E60">A23</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">then </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,1)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:60"><span class="lab"><font color="Green" title="E71">A34</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="txt" href="#E29:60"><span class="lab"><font color="Green" title="E61">A24</font></span></a>, <a class="ref" href="goboard5.html#T2" onmouseover="rs('goboard5/T2')" onmouseout="rh()">GOBOARD5:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 1</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E38:60"><span class="lab"><font color="Green" title="E68">A31</font></span></a>, <a class="txt" href="#E58:60"><span class="lab"><font color="Green" title="E83">A46</font></span></a>, <a class="txt" href="#E47:60"><span class="lab"><font color="Green" title="E75">A38</font></span></a>, <a class="txt" href="#E29:60"><span class="lab"><font color="Green" title="E61">A24</font></span></a>, <a class="txt" href="#E67:60"><span class="lab"><font color="Green" title="E89">A52</font></span></a>, <a class="ref" href="goboard5.html#T2" onmouseover="rs('goboard5/T2')" onmouseout="rh()">GOBOARD5:2</a></span>
;<br/>
<a NAME="E69:60"/><span class="kw">then </span><span class="lab"><font color="Green" title="E90">A53</font></span>: 
<font color="Maroon" title="c15">p</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <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"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1</span>)</span>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E54:60"><span class="lab"><font color="Green" title="E80">A43</font></span></a>, <a class="txt" href="#E53:60"><span class="lab"><font color="Green" title="E79">A42</font></span></a>, <a class="txt" href="#E56:60"><span class="lab"><font color="Green" title="E81">A44</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<font color="Maroon" title="c13">j1</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,1)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E43:60"><span class="lab"><font color="Green" title="E71">A34</font></span></a>, <a class="txt" href="#E16:60"><span class="lab"><font color="Green" title="E52">A15</font></span></a>, <a class="txt" href="#E39:60"><span class="lab"><font color="Green" title="E69">A32</font></span></a>, <a class="txt" href="#E34:60"><span class="lab"><font color="Green" title="E65">A28</font></span></a>, <a class="txt" href="#E35:60"><span class="lab"><font color="Green" title="E66">A29</font></span></a>, <a class="ref" href="goboard5.html#T2" onmouseover="rs('goboard5/T2')" onmouseout="rh()">GOBOARD5:2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c4">n</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c1">i</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>,<span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default">2 <a href="newton.html#K11" title="NEWTON:func.11">|^</a> <span class="p5">(<span class="default"><font color="Maroon" title="c4">n</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> <font color="Maroon" title="c3">m</font></span>)</span></span>)</span> <a href="nat_1.html#K2" title="NAT_1:func.2">*</a> <span class="p4">(<span class="default"><font color="Maroon" title="c2">j</font> <a href="nat_d.html#K7" title="NAT_D:func.7">-'</a> 2</span>)</span></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 2</span>)</span>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E16:60"><span class="lab"><font color="Green" title="E52">A15</font></span></a>, <a class="txt" href="#E38:60"><span class="lab"><font color="Green" title="E68">A31</font></span></a>, <a class="txt" href="#E34:60"><span class="lab"><font color="Green" title="E65">A28</font></span></a>, <a class="txt" href="#E50:60"><span class="lab"><font color="Green" title="E77">A40</font></span></a>, <a class="txt" href="#E35:60"><span class="lab"><font color="Green" title="E66">A29</font></span></a>, <a class="txt" href="#E58:60"><span class="lab"><font color="Green" title="E83">A46</font></span></a>, <a class="ref" href="goboard5.html#T2" onmouseover="rs('goboard5/T2')" onmouseout="rh()">GOBOARD5:2</a></span>
;<br/>
<a NAME="E71:60"/><span class="kw">then </span>
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span> <a href="matrix_0.html#K3" title="MATRIX_0:func.3">*</a> (<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)</span>)</span> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a>  <a href="xxreal_0.html#R1" title="XXREAL_0:pred.1">&lt;=</a> <font color="Maroon" title="c15">p</font> <a href="euclid.html#K17" title="EUCLID:func.17">`1</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E45:60"><span class="lab"><font color="Green" title="E73">A36</font></span></a>, <a class="txt" href="#E51:60"><span class="lab"><font color="Green" title="E78">A41</font></span></a>, <a class="txt" href="#E66:60"><span class="lab"><font color="Green" title="E88">A51</font></span></a>, <a class="ref" href="xxreal_0.html#T2" onmouseover="rs('xxreal_0/T2')" onmouseout="rh()">XXREAL_0:2</a></span>;<br/>
<span class="kw">hence </span><a NAME="E72:60"/>
<font color="Maroon" title="c14">e</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="goboard5.html#K3" title="GOBOARD5:func.3">cell</a> (<span class="p1">(<span class="default"><a href="jordan8.html#K1" title="JORDAN8:func.1">Gauge</a> (<font color="Maroon" title="c5">E</font>,<font color="Maroon" title="c3">m</font>)</span>)</span>,<font color="Maroon" title="c1">i</font>,<font color="Maroon" title="c2">j</font>)
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:60"><span class="lab"><font color="Green" title="E39">A2</font></span></a>, <a class="txt" href="#E3:60"><span class="lab"><font color="Green" title="E40">A3</font></span></a>, <a class="txt" href="#E4:60"><span class="lab"><font color="Green" title="E41">A4</font></span></a>, <a class="txt" href="#E5:60"><span class="lab"><font color="Green" title="E42">A5</font></span></a>, <a class="txt" href="#E69:60"><span class="lab"><font color="Green" title="E90">A53</font></span></a>, <a class="txt" href="#E60:60"><span class="lab"><font color="Green" title="E84">A47</font></span></a>, <a class="txt" href="#E64:60"><span class="lab"><font color="Green" title="E87">A50</font></span></a>, <a class="ref" href="jordan9.html#T17" onmouseover="rs('jordan9/T17')" onmouseout="rh()">JORDAN9:17</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/>


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