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<b>let </b><font color="Maroon">s</font> be  non <a href="struct_0.html#V3">empty</a>  <a href="prelamb.html#L1" target="_self">typealg</a> ;<br/><b>let </b><font color="Maroon">p</font> be    <a href="prelamb.html#M1" target="_self">Proof</a> of <font color="Maroon">s</font>;<br/><b>let </b><font color="Maroon">v</font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font>;<br/>





<a NAME="E1:26"/><i><font color="Green">E36</font></i>: 
<font color="Maroon">v</font> is <a href="prelamb.html#V2" target="_self">correct</a>
 
<b>by </b><i/>;<br/>
<b>assume </b><a NAME="E2:26"/><i><font color="Green">E37</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="trees_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 6
 ;<br/>

<a NAME="E3:26"/><b>then </b><i><font color="Green">E38</font></i>: 
 ex <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">s</font> ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="trees_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="prelamb.html#K6" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Olive">y</font></span>)</span></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="prelamb.html#K6" target="_self">[</a><span class="default"><font color="Olive">X</font>,<font color="Olive">x</font></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">v</font> <a href="finseq_1.html#K8">^</a> <span class="p3"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="prelamb.html#K6" target="_self">[</a><span class="default"><font color="Olive">Y</font>,<font color="Olive">y</font></span><a href="prelamb.html#K6" target="_self">]</a></span> )
 
<b>by </b><i>, </i>;<br/>
<a NAME="E4:26"/>
 <a href="trees_2.html#K10">branchdeg</a> <font color="Maroon">v</font> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i>, , </i>;<br/>
<a NAME="E5:26"/><b>then </b>
( <font color="Maroon">v</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> &amp; <font color="Maroon">v</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> <a href="hidden.html#R2">in</a>  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> )
 
<b>by </b><i/>;<br/>
<b>hence </b><a NAME="E6:26"/>
 ex <font color="Olive">w</font>, <font color="Olive">u</font> being   <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">p</font> ex <font color="Olive">X</font>, <font color="Olive">Y</font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">s</font> ex <font color="Olive">x</font>, <font color="Olive">y</font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">s</font> st <br/>( <font color="Olive">w</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12">*&gt;</a></span> &amp; <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">v</font> <a href="finseq_1.html#K8">^</a> <span class="p1"><a href="finseq_1.html#K12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12">*&gt;</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="trees_2.html#K3">.</a> <font color="Maroon">v</font></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="prelamb.html#K6" target="_self">[</a><span class="default"><span class="p2">(<span class="default"><font color="Olive">X</font> <a href="finseq_1.html#K8">^</a> <font color="Olive">Y</font></span>)</span>,<span class="p2">(<span class="default"><font color="Olive">x</font> <a href="prelamb.html#K3" target="_self">*</a> <font color="Olive">y</font></span>)</span></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="trees_2.html#K3">.</a> <font color="Olive">w</font></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="prelamb.html#K6" target="_self">[</a><span class="default"><font color="Olive">X</font>,<font color="Olive">x</font></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">p</font> <a href="trees_2.html#K3">.</a> <font color="Olive">u</font></span>)</span> <a href="mcart_1.html#K1">`1</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="prelamb.html#K6" target="_self">[</a><span class="default"><font color="Olive">Y</font>,<font color="Olive">y</font></span><a href="prelamb.html#K6" target="_self">]</a></span> )
 <b>by </b><i/>;<br/>


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