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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="trees_1.html#NM1">Tree</a>;<br/>

<b>assume </b><a NAME="E1:8"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> holds  <a href="trees_2.html#K1">succ</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default">0</span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default">1</span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span><a href="domain_1.html#K7">}</a></span>
 ;<br/>

<a NAME="E2:8"/><b>then </b>
for <font color="Olive">b<sub>1</sub></font> being   <a href="trees_1.html#M1">Element</a> of <font color="Maroon">c<sub>1</sub></font> st not <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a>  <a href="trees_1.html#K3">Leaves</a> <font color="Maroon">c<sub>1</sub></font> holds <br/> <a href="trees_2.html#K1">succ</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="domain_1.html#K7">{</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default">0</span><a href="binarith.html#K13">*&gt;</a></span></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="binarith.html#K13">&lt;*</a><span class="default">1</span><a href="binarith.html#K13">*&gt;</a></span></span>)</span></span><a href="domain_1.html#K7">}</a></span>
 
;<br/>
<b>hence </b><a NAME="E3:8"/>
<font color="Maroon">c<sub>1</sub></font> is <a href="bintree1.html#V1">binary</a>
 <b>by </b><i><a class="ref" href="bintree1.html#D2">BINTREE1:def 2</a></i>;<br/>


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