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<span class="kw">let </span><font color="Maroon" title="c1">X</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>   <a href="hidden.html#M2" title="HIDDEN:mode.2">set</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">x</font> being    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</font> holds  <span class="p1">(<span class="default"><a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <span class="p2">(<span class="default"><a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="bspace.html#K11" title="BSPACE:func.11">@</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span><br/><span class="kw">let </span><font color="Maroon" title="c2">x</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <font color="Maroon" title="c1">X</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"> <span class="p1">(<span class="default"><a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <span class="p2">(<span class="default"><a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="bspace.html#K11" title="BSPACE:func.11">@</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <a href="bspace.html#K2" title="BSPACE:func.2">Z_2</a></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">V</font> =  <a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c4">L</font> = <span class="p1">(<span class="default"><a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <span class="p2">(<span class="default"><a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="bspace.html#K11" title="BSPACE:func.11">@</a> <font color="Maroon" title="c2">x</font>;<br/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <span class="p3">(<span class="default"><a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="bspace.html#K11" title="BSPACE:func.11">@</a> <font color="Maroon" title="c2">x</font></span>)</span> = 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <span class="p2">(<span class="default"><a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="bspace.html#D9" target="_self" onmouseover="rs('bspace/D9')" onmouseout="rh()">Def9</a></span>
<br/>.= 
 <a href="numbers.html#K5" title="NUMBERS:func.5">0</a> 

;<br/>
<span class="kw">hence </span><a NAME="E2:36"/>
<span class="p1">(<span class="default"><a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</a> <span class="p2">(<span class="default"><a href="bspace.html#K7" title="BSPACE:func.7">bspace</a> <font color="Maroon" title="c1">X</font></span>)</span></span>)</span> <a href="bspace.html#K11" title="BSPACE:func.11">@</a> <font color="Maroon" title="c2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bspace.html#K1" title="BSPACE:func.1">&lt;*&gt;</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"> verum</span><br/>


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