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<span class="kw">let </span><font color="Maroon" title="c1">D</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">f</font>, <font color="Olive" title="b2">g</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</font>  st <font color="Olive" title="b2">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Olive" title="b1">f</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/><font color="Olive" title="b2">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Olive" title="b1">f</font>,1</span><br/><span class="kw">let </span><font color="Maroon" title="c2">f</font>, <font color="Maroon" title="c3">g</font> be    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of <font color="Maroon" title="c1">D</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="c3">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Maroon" title="c2">f</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  implies <font color="Maroon" title="c3">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Maroon" title="c2">f</font>,1 )</span><br/>



<span class="kw">reconsider </span><font color="Maroon" title="c4">n</font> =  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  as   <a href="abian.html#V1" title="ABIAN:attr.1">even</a>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#NK1" title="NUMBERS:NK.1">NAT</a>  ;<br/>
<span class="kw">assume </span><a NAME="E2:11"/>
<font color="Maroon" title="c3">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Maroon" title="c2">f</font>, <a href="numbers.html#K5" title="NUMBERS:func.5">0</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="c3">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Maroon" title="c2">f</font>,1</span><br/>

<a NAME="E3:11"/><span class="kw">then </span>
<font color="Maroon" title="c3">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Maroon" title="c2">f</font>,<font color="Maroon" title="c4">n</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="glib_006.html#T12" target="_self" onmouseover="rs('glib_006/T12')" onmouseout="rh()">Th16</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:11"/>
<font color="Maroon" title="c3">g</font> <a href="glib_006.html#R1" title="GLIB_006:pred.1">is_odd_substring_of</a> <font color="Maroon" title="c2">f</font>,1
 ; <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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