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<div class="add">

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:10_2_1_1"/>
( <font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> or <font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T5" onmouseover="rs('bspace/T5')" onmouseout="rh()">BSPACE:5</a>, <a class="ref" href="bspace.html#T6" onmouseover="rs('bspace/T6')" onmouseout="rh()">BSPACE:6</a>, <a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:10_2_1_1_1"/><span class="lab"><font color="Green" title="E6">A2</font></span>: 
<font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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"> <font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_1_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:10_2_1_1_1_1"/>
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> or <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T5" onmouseover="rs('bspace/T5')" onmouseout="rh()">BSPACE:5</a>, <a class="ref" href="bspace.html#T6" onmouseover="rs('bspace/T6')" onmouseout="rh()">BSPACE:6</a>, <a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:10_2_1_1_1_1_1"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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"> <font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><span class="kw">then </span><font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> = 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span>)</span>

<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T5" onmouseover="rs('bspace/T5')" onmouseout="rh()">BSPACE:5</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:10_2_1_1_1_1_1"/>
<font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_1_1_1"><span class="lab"><font color="Green" title="E6">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:10_2_1_1_1_1_2"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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"> <font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> = 
<span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_1_1_1"><span class="lab"><font color="Green" title="E6">A2</font></span></a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T5" onmouseover="rs('bspace/T5')" onmouseout="rh()">BSPACE:5</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:10_2_1_1_1_1_2"/>
<font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_1_1_1"><span class="lab"><font color="Green" title="E6">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:10_2_1_1_2"/><span class="lab"><font color="Green" title="E6">A3</font></span>: 
<font color="Maroon" title="c1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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"> <font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_2_1"><span class="kw">per </span></a><a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:10_2_1_1_2_1"/>
( <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> or <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a> )
 </span><span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T5" onmouseover="rs('bspace/T5')" onmouseout="rh()">BSPACE:5</a>, <a class="ref" href="bspace.html#T6" onmouseover="rs('bspace/T6')" onmouseout="rh()">BSPACE:6</a>, <a class="ref" href="xboolean.html#D3" onmouseover="rs('xboolean/D3')" onmouseout="rh()">XBOOLEAN:def 3</a></span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_2_1_1"><span class="kw">suppose </span></a><a NAME="E1:10_2_1_1_2_1_1"/><span class="lab"><font color="Green" title="E7">A4</font></span>: 
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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"> <font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><span class="kw">then </span><font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> = 
<span class="p1">(<span class="default"><a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span>)</span> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <span class="p1">(<span class="default"><a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span>)</span>

<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 
<span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#T5" onmouseover="rs('bspace/T5')" onmouseout="rh()">BSPACE:5</a></span>
;<br/><span class="kw">hence </span><a NAME="E3:10_2_1_1_2_1_1"/>
<font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_1_1_2_1_1"><span class="lab"><font color="Green" title="E7">A4</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="10_2_1_1_2_1_2"><span class="kw">suppose </span></a><a NAME="E1:10_2_1_1_2_1_2"/>
<font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K5" title="STRUCT_0:func.5">1.</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</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"> <font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font></span><br/><div class="add"><span class="kw">hence </span><a NAME="E2:10_2_1_1_2_1_2"/>
<font color="Maroon" title="c1">u</font> <a href="group_1.html#K8" title="GROUP_1:func.8">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c1">u</font> <a href="xboolean.html#K4" title="XBOOLEAN:func.4">'&amp;'</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:10_2_1_1_2"><span class="lab"><font color="Green" title="E6">A3</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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