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<b>let </b><font color="Maroon">c<sub>1</sub></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">c<sub>2</sub></font> be    <a href="prelamb.html#M1" target="_self">Proof</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>;<br/>





<a NAME="E1:27"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> is <a href="prelamb.html#V2" target="_self">correct</a>
 
<b>by </b><i><a class="ref" href="prelamb.html#D13" target="_self">Def13</a></i>;<br/>
<b>assume </b><a NAME="E2:27"/><i><font color="Green">E10</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> <a href="mcart_1.html#K2">`2</a>  <a href="hidden.html#R1">=</a> 7
 ;<br/>

<a NAME="E3:27"/><b>then </b><i><font color="Green">E11</font></i>: 
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></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"><span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<font color="Olive">b<sub>5</sub></font></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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">b<sub>1</sub></font>,<font color="Olive">b<sub>4</sub></font></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="funct_1.html#K1">.</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></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"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive">b<sub>2</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">b<sub>4</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">b<sub>3</sub></font></span>)</span>,<font color="Olive">b<sub>5</sub></font></span><a href="prelamb.html#K6" target="_self">]</a></span> )
 
<b>by </b><i><a class="txt" href="prelamb.html#E1:27"><i><font color="Green">E9</font></i></a>, <a class="ref" href="prelamb.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E4:27"/>
 <a href="trees_2.html#K10">branchdeg</a> <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> 2
 
<b>by </b><i><a class="txt" href="prelamb.html#E1:27"><i><font color="Green">E9</font></i></a>, <a class="txt" href="prelamb.html#E2:27"><i><font color="Green">E10</font></i></a>, <a class="ref" href="prelamb.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E5:27"/><b>then </b>
( <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> )
 
<b>by </b><i><a class="ref" href="prelamb.html#T2" target="_self">Th2</a></i>;<br/>
<b>hence </b><a NAME="E6:27"/>
ex <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being   <a href="trees_1.html#M1">Element</a> of  <a href="relat_1.html#K1">dom</a> <font color="Maroon">c<sub>2</sub></font>ex <font color="Olive">b<sub>3</sub></font>, <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being   <a href="finseq_1.html#M2">FinSequence</a> of the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>ex <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font> being  <a href="prelamb.html#NM1">type</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></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">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>3</sub></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">c<sub>2</sub></font> <a href="trees_2.html#K3">.</a> <font color="Maroon">c<sub>3</sub></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"><span class="p3">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <font color="Olive">b<sub>3</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">b<sub>5</sub></font></span>)</span>,<font color="Olive">b<sub>7</sub></font></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></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">b<sub>3</sub></font>,<font color="Olive">b<sub>6</sub></font></span><a href="prelamb.html#K6" target="_self">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon">c<sub>2</sub></font> <a href="trees_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></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"><span class="p3">(<span class="default"><font color="Olive">b<sub>4</sub></font> <a href="finseq_1.html#K8">^</a> <span class="p4"><a href="finseq_1.html#K12">&lt;*</a><span class="default"><font color="Olive">b<sub>6</sub></font></span><a href="finseq_1.html#K12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8">^</a> <font color="Olive">b<sub>5</sub></font></span>)</span>,<font color="Olive">b<sub>7</sub></font></span><a href="prelamb.html#K6" target="_self">]</a></span> )
 <b>by </b><i><a class="txt" href="prelamb.html#E3:27"><i><font color="Green">E11</font></i></a></i>;<br/>


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