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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> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="relat_1.html#V2">V5</a>  <a href="pboole.html#M1">ManySortedSet</a> of the <a href="struct_0.html#U1">carrier</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="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="finseq_1.html#NM1">FinSequence</a>;<br/>







<a NAME="E1:9"/><i><font color="Green">E6</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="msaterm.html#K1" target="_self">-Terms</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R1">=</a>  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5">DTConMSA</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
;<br/>
<a NAME="E2:9"/><i><font color="Green">E7</font></i>: 
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="hidden.html#R1">=</a>  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="msafree.html#D11">MSAFREE:def 11</a></i>;<br/>
<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:9_1"/>
<span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="msaterm.html#K1" target="_self">-Terms</a> <font color="Maroon">c<sub>2</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>4</sub></font> as    <a href="dtconstr.html#M1">Element</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5">DTConMSA</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> ;<br/><b>assume </b><a NAME="E3:9_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>4</sub></font> is <a href="trees_3.html#V6">DTree-yielding</a>
 ;<br/><a NAME="E4:9_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span>
 <b>by </b><i><a class="ref" href="trees_4.html#D4">TREES_4:def 4</a></i>;<br/><b>then consider </b><font color="Maroon">c<sub>6</sub></font> being    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5">DTConMSA</a> <font color="Maroon">c<sub>2</sub></font></span>)</span><b> such that </b><br/><a NAME="E6:9_1"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="trees_4.html#K12">-tree</a> <font color="Maroon">c<sub>6</sub></font> &amp;  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1">roots</a> <font color="Maroon">c<sub>6</sub></font> )
 <b>by </b><i><a class="txt" href="msaterm.html#E2:9"><i><font color="Green">E7</font></i></a>, <a class="ref" href="dtconstr.html#T10">DTCONSTR:10</a></i>;<br/><a NAME="E7:9_1"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 <b>by </b><i><a class="txt" href="msaterm.html#E3:9_1"><i><font color="Green">E8</font></i></a>, <a class="txt" href="msaterm.html#E6:9_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="trees_4.html#T15">TREES_4:15</a></i>;<br/><a NAME="E8:9_1"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> is    <a href="dtconstr.html#M2">SubtreeSeq</a> of  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="msaterm.html#E6:9_1"><i><font color="Green">E9</font></i></a>, <a class="ref" href="dtconstr.html#D9">DTCONSTR:def 9</a></i>;<br/><b>hence </b><a NAME="E9:9_1"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="msaterm.html#M1" target="_self">ArgumentSeq</a> of  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="msaterm.html#E1:9"><i><font color="Green">E6</font></i></a>, <a class="ref" href="msaterm.html#D2" target="_self">Def2</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E4:9"/>
<font color="Maroon">c<sub>4</sub></font> is    <a href="msaterm.html#M1" target="_self">ArgumentSeq</a> of  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 ;<br/>

<b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as    <a href="msaterm.html#M1" target="_self">ArgumentSeq</a> of  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> ;<br/>
<b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as    <a href="trees_4.html#M1">FinSequence</a> of  <a href="dtconstr.html#K4">TS</a> <span class="p1">(<span class="default"><a href="msafree.html#K5">DTConMSA</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <b>by </b><i><a class="ref" href="msaterm.html#D1" target="_self">Def1</a></i>;<br/>
<a NAME="E7:9"/>
<font color="Maroon">c<sub>6</sub></font> is    <a href="dtconstr.html#M2">SubtreeSeq</a> of  <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font>
 
<b>by </b><i><a class="ref" href="msaterm.html#D2" target="_self">Def2</a></i>;<br/>
<a NAME="E8:9"/><b>then </b>
 <a href="msaterm.html#K2" target="_self">Sym</a> <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="lang1.html#R1">==&gt;</a>  <a href="dtconstr.html#K1">roots</a> <font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="ref" href="dtconstr.html#D9">DTCONSTR:def 9</a></i>;<br/>
<b>hence </b><a NAME="E9:9"/>
( <span class="p1"><a href="tarski.html#K4">[</a><span class="default"><font color="Maroon">c<sub>3</sub></font>,the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font></span><a href="tarski.html#K4">]</a></span> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> <font color="Maroon">c<sub>1</sub></font> <a href="msaterm.html#K1" target="_self">-Terms</a> <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Maroon">c<sub>4</sub></font> is <a href="trees_3.html#V6">DTree-yielding</a> )
 <b>by </b><i><a class="txt" href="msaterm.html#E2:9"><i><font color="Green">E7</font></i></a>, <a class="ref" href="dtconstr.html#D4">DTCONSTR:def 4</a></i>;<br/>


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