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<b>let </b><font color="Maroon" title="c1">s</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="prelamb.html#L1" title="PRELAMB:struct.1">typealg</a> ;<br/><b>let </b><font color="Maroon" title="c2">p</font> be    <a href="prelamb.html#M1" title="PRELAMB:mode.1">Proof</a> of <font color="Maroon" title="c1">s</font>;<br/><b>let </b><font color="Maroon" title="c3">v</font> be    <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font>;<br/>





<a NAME="E1:24"/><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c3">v</font> is <a href="prelamb.html#V2" title="PRELAMB:attr.2">correct</a>
 
<b>by </b><i><a class="ref" href="prelamb.html#D13" target="_self" title="PRELAMB:def.13">Def13</a></i>;<br/>
<b>assume </b><a NAME="E2:24"/><i><font color="Green" title="E9">A2</font></i>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="mcart_1.html#K2" title="MCART_1:func.2">`2</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 4
 ;<br/>

<a NAME="E3:24"/><b>then </b><i><font color="Green" title="E10">A3</font></i>: 
 ex <font color="Olive" title="b1">T</font>, <font color="Olive" title="b2">X</font>, <font color="Olive" title="b3">Y</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> ex <font color="Olive" title="b4">x</font>, <font color="Olive" title="b5">y</font>, <font color="Olive" title="b6">z</font> being  <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font> st <br/>( <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b1">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b5">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b4">x</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span>,<font color="Olive" title="b6">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><font color="Olive" title="b1">T</font>,<font color="Olive" title="b5">y</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <span class="p2">(<span class="default"><font color="Maroon" title="c3">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p3"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b2">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b4">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">Y</font></span>)</span>,<font color="Olive" title="b6">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> )
 
<b>by </b><i><a class="txt" href="prelamb.html#E1:24"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="prelamb.html#D5" target="_self" title="PRELAMB:def.5">Def5</a></i>;<br/>
<a NAME="E4:24"/>
 <a href="trees_2.html#K10" title="TREES_2:func.10">branchdeg</a> <font color="Maroon" title="c3">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 
<b>by </b><i><a class="txt" href="prelamb.html#E1:24"><i><font color="Green" title="E8">A1</font></i></a>, <a class="txt" href="prelamb.html#E2:24"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="prelamb.html#D5" target="_self" title="PRELAMB:def.5">Def5</a></i>;<br/>
<a NAME="E5:24"/><b>then </b>
( <font color="Maroon" title="c3">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font> &amp; <font color="Maroon" title="c3">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font> )
 
<b>by </b><i><a class="ref" href="prelamb.html#T2" target="_self" title="PRELAMB:th.2">Th2</a></i>;<br/>
<b>hence </b><a NAME="E6:24"/>
 ex <font color="Olive" title="b1">w</font>, <font color="Olive" title="b2">u</font> being   <a href="trees_1.html#M1" title="TREES_1:mode.1">Element</a> of  <a href="relat_1.html#K1" title="RELAT_1:func.1">dom</a> <font color="Maroon" title="c2">p</font> ex <font color="Olive" title="b3">T</font>, <font color="Olive" title="b4">X</font>, <font color="Olive" title="b5">Y</font> being   <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">s</font> ex <font color="Olive" title="b6">x</font>, <font color="Olive" title="b7">y</font>, <font color="Olive" title="b8">z</font> being  <a href="prelamb.html#NM1" title="PRELAMB:NM.1">type</a> of <font color="Maroon" title="c1">s</font> st <br/>( <font color="Olive" title="b1">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">0</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> &amp; <font color="Olive" title="b2">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">v</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p1"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default">1</span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Maroon" title="c3">v</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><span class="p4">(<span class="default"><font color="Olive" title="b4">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b3">T</font></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><span class="p5">(<span class="default"><font color="Olive" title="b7">y</font> <a href="prelamb.html#K1" title="PRELAMB:func.1">\</a> <font color="Olive" title="b6">x</font></span>)</span></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b5">Y</font></span>)</span>,<font color="Olive" title="b8">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Olive" title="b1">w</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><font color="Olive" title="b3">T</font>,<font color="Olive" title="b7">y</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">p</font> <a href="trees_2.html#K3" title="TREES_2:func.3">.</a> <font color="Olive" title="b2">u</font></span>)</span> <a href="mcart_1.html#K1" title="MCART_1:func.1">`1</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="prelamb.html#K6" title="PRELAMB:func.6">[</a><span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b4">X</font> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <span class="p4"><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">&lt;*</a><span class="default"><font color="Olive" title="b6">x</font></span><a href="finseq_1.html#K12" title="FINSEQ_1:func.12">*&gt;</a></span></span>)</span> <a href="finseq_1.html#K8" title="FINSEQ_1:func.8">^</a> <font color="Olive" title="b5">Y</font></span>)</span>,<font color="Olive" title="b8">z</font></span><a href="prelamb.html#K6" title="PRELAMB:func.6">]</a></span> )
 <b>by </b><i><a class="txt" href="prelamb.html#E3:24"><i><font color="Green" title="E10">A3</font></i></a></i>;<br/>


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