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<span class="kw">let </span><font color="Maroon" title="c1">t</font> be   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">p</font> being  <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c1">t</font><br/> for <font color="Olive" title="b2">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Olive" title="b1">p</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b2">k</font> is   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c1">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">p</font> be   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c1">t</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">k</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a>  holds  <font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Olive" title="b1">k</font> is   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c1">t</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">k</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">k</font> is   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c1">t</font></span><br/>





<a NAME="E1:37"/>
<font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">k</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">p</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> <font color="Maroon" title="c3">k</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="finseq_1.html#D15" title="FINSEQ_1:def.15">FINSEQ_1:def 15</a></span>;<br/>
<a NAME="E2:37"/><span class="kw">then </span>
<font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">k</font> <a href="tarski.html#R1" title="TARSKI:pred.1">is_a_prefix_of</a> <font color="Maroon" title="c2">p</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="trees_1.html#D1" title="TREES_1:def.1">TREES_1:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E3:37"/>
<font color="Maroon" title="c2">p</font> <a href="finseq_1.html#K17" title="FINSEQ_1:func.17">|</a> <font color="Maroon" title="c3">k</font> is   <a href="trees_4.html#NM1" title="TREES_4:NM.1">Node</a> of <font color="Maroon" title="c1">t</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="trees_1.html#T45" title="TREES_1:th.45">TREES_1:45</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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