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<b>let </b><font color="Maroon" title="c1">T</font> be  <a href="bintree1.html#V1" title="BINTREE1:attr.1">binary</a> <a href="trees_1.html#NM1" title="TREES_1:NM.1">Tree</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">n</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> <br/> for <font color="Olive" title="b2">t</font> being   <a href="bintree2.html#M1" title="BINTREE2:mode.1">Element</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b2">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> <a href="trees_2.html#K2" title="TREES_2:func.2">-level</a> <font color="Olive" title="b1">n</font> holds <br/><font color="Olive" title="b2">t</font> is   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <font color="Olive" title="b1">n</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span><br/><b>let </b><font color="Maroon" title="c2">n</font> be    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="numbers.html#K5" title="NUMBERS:func.5">NAT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">t</font> being   <a href="bintree2.html#M1" title="BINTREE2:mode.1">Element</a> of <font color="Maroon" title="c1">T</font>  st <font color="Olive" title="b1">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> <a href="trees_2.html#K2" title="TREES_2:func.2">-level</a> <font color="Maroon" title="c2">n</font> holds <br/><font color="Olive" title="b1">t</font> is   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <font color="Maroon" title="c2">n</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span><br/><b>let </b><font color="Maroon" title="c3">t</font> be    <a href="bintree2.html#M1" title="BINTREE2:mode.1">Element</a> of <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"> ( <font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> <a href="trees_2.html#K2" title="TREES_2:func.2">-level</a> <font color="Maroon" title="c2">n</font> implies <font color="Maroon" title="c3">t</font> is   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <font color="Maroon" title="c2">n</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a>  )</span><br/>





<b>assume </b><a NAME="E1:6"/>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c1">T</font> <a href="trees_2.html#K2" title="TREES_2:func.2">-level</a> <font color="Maroon" title="c2">n</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">t</font> is   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <font color="Maroon" title="c2">n</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> </span><br/>

<a NAME="E2:6"/><b>then </b>
<font color="Maroon" title="c3">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <font color="Olive" title="b1">w</font> where <font color="Olive" title="b1">w</font> is    <a href="bintree2.html#M1" title="BINTREE2:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> :  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> </span>}</span> 
 
<b>by </b><i><a class="ref" href="trees_2.html#D6" title="TREES_2:def.6">TREES_2:def 6</a></i>;<br/>
<a NAME="E3:6"/><b>then </b>
 ex <font color="Olive" title="b1">t2</font> being   <a href="bintree2.html#M1" title="BINTREE2:mode.1">Element</a> of <font color="Maroon" title="c1">T</font> st <br/>( <font color="Olive" title="b1">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">t</font> &amp;  <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Olive" title="b1">t2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">n</font> )
 
;<br/>
<b>hence </b><a NAME="E4:6"/>
<font color="Maroon" title="c3">t</font> is   <a href="binarith.html#NM1" title="BINARITH:NM.1">Tuple</a> of <font color="Maroon" title="c2">n</font>,<a href="margrel1.html#K6" title="MARGREL1:func.6">BOOLEAN</a> 
 <b>by </b><i><a class="ref" href="finseq_2.html#T110" title="FINSEQ_2:th.110">FINSEQ_2:110</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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