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<b>let </b><font color="Maroon" title="c4">s</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> <a href="trees_1.html#K5" title="TREES_1:func.5">with-replacement</a> <font color="Maroon" title="c2">t</font>,<font color="Maroon" title="c3">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="trees_3.html#D14" target="_self" title="TREES_3:def.14">TREES_3:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> or  ex <font color="Olive" title="b1">l</font> being   <a href="trees_3.html#M8" title="TREES_3:mode.8">Leaf</a> of <font color="Maroon" title="c1">T</font> st <font color="Olive" title="b1">l</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c4">s</font> )</span><br/>

<b>assume </b><a NAME="E1:99_1_1"/><i><font color="Green" title="E41">A1</font></i>: 
not <font color="Maroon" title="c4">s</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">l</font> being   <a href="trees_3.html#M8" title="TREES_3:mode.8">Leaf</a> of <font color="Maroon" title="c1">T</font> st <font color="Olive" title="b1">l</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c4">s</font></span><br/>

<b>then consider </b><font color="Maroon" title="c5">t1</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <b> such that </b><br/><a NAME="E3:99_1_1"/><i><font color="Green" title="E42">A2</font></i>: 
( <font color="Maroon" title="c5">t1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">S</font> &amp; <font color="Maroon" title="c4">s</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> <font color="Maroon" title="c2">t</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Maroon" title="c5">t1</font> )
 <b>by </b><i><a class="ref" href="trees_1.html#D12" title="TREES_1:def.12">TREES_1:def 12</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c2">t</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">t</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c4">s</font></span><br/>

<a NAME="E4:99_1_1"/>
<font color="Maroon" title="c2">t</font> <a href="finseq_1.html#K7" title="FINSEQ_1:func.7">^</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">t</font>
 
<b>by </b><i><a class="ref" href="finseq_1.html#T47" title="FINSEQ_1:th.47">FINSEQ_1:47</a></i>;<br/>
<a NAME="E5:99_1_1"/><b>then </b>
<font color="Maroon" title="c5">t1</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a> 
 
<b>by </b><i><a class="txt" href="#E1:99_1_1"><i><font color="Green" title="E41">A1</font></i></a>, <a class="txt" href="#E3:99_1_1"><i><font color="Green" title="E42">A2</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:99_1_1"/>
<font color="Maroon" title="c2">t</font> <a href="trees_1.html#NR3" title="TREES_1:NR.3">is_a_proper_prefix_of</a> <font color="Maroon" title="c4">s</font>
 <b>by </b><i><a class="txt" href="#E3:99_1_1"><i><font color="Green" title="E42">A2</font></i></a>, <a class="ref" href="trees_1.html#T33" title="TREES_1:th.33">TREES_1:33</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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