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<b>let </b><font color="Maroon">term</font> be   <a href="scm_comp.html#NM1">bin-term</a>;<br/>

<a NAME="E1:11"/>
 <a href="bintree1.html#K1">root-label</a> <font color="Maroon">term</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> 
 
;<br/>
<a NAME="E2:11"/><b>then </b>
<font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> 
 
<b>by </b><i><a class="ref" href="bintree1.html#D1">BINTREE1:def 1</a></i>;<br/>
<a NAME="E3:11"/><b>then </b><i><font color="Green">E34</font></i>: 
<font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K6">Terminals</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> </span>)</span> <a href="subset_1.html#K4">\/</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K7">NonTerminals</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="lang1.html#T1">LANG1:1</a></i>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:11_1"/>
( <font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K6">Terminals</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  or <font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K7">NonTerminals</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  )
 </span><b>by </b><i>, <a class="ref" href="xboole_0.html#D2">XBOOLE_0:def 2</a></i>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_1"><b>suppose </b></a><a NAME="E1:11_1_1"/>
<font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K6">Terminals</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">t</font> = <font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  as   <a href="dtconstr.html#NM2">Terminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  ;<br/><a NAME="E3:11_1_1"/>
<font color="Maroon">term</font> <a href="hidden.html#R1">=</a>  <a href="scm_comp.html#K3" target="_self">root-tree</a> <font color="Maroon">t</font>
 <b>by </b><i><a class="ref" href="dtconstr.html#T9">DTCONSTR:9</a></i>;<br/><b>hence </b><a NAME="E4:11_1_1"/>
(  ex <font color="Olive">t</font> being  <a href="dtconstr.html#NM2">Terminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  st <font color="Maroon">term</font> <a href="hidden.html#R1">=</a>  <a href="scm_comp.html#K3" target="_self">root-tree</a> <font color="Olive">t</font> or  ex <font color="Olive">tl</font>, <font color="Olive">tr</font> being  <a href="scm_comp.html#NM1">bin-term</a> st <br/>( <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K5" target="_self">+</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K6" target="_self">-</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K7" target="_self">*</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K8" target="_self">div</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K9" target="_self">mod</a> <font color="Olive">tr</font> ) )
 ;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="11_1_2"><b>suppose </b></a><a NAME="E1:11_1_2"/>
<font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  <a href="hidden.html#R2">in</a>  <a href="dtconstr.html#K7">NonTerminals</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> 
 ;<br/><div class="add"><b>then reconsider </b><font color="Maroon">nt</font> = <font color="Maroon">term</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  as   <a href="dtconstr.html#NM3">NonTerminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  ;<br/><b>consider </b><font color="Maroon">ts</font> being    <a href="finseq_1.html#M2">FinSequence</a> of  <a href="dtconstr.html#K4">TS</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> <b> such that </b><br/><a NAME="E4:11_1_2"/><i><font color="Green">E35</font></i>: 
( <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Maroon">nt</font> <a href="trees_4.html#K4">-tree</a> <font color="Maroon">ts</font> &amp; <font color="Maroon">nt</font> <a href="lang1.html#R1">==&gt;</a>  <a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font> )
 <b>by </b><i><a class="ref" href="dtconstr.html#T10">DTCONSTR:10</a></i>;<br/><b>consider </b><font color="Maroon">x1</font> being   <a href="lang1.html#NM1">Symbol</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> , <font color="Maroon">x2</font> being   <a href="lang1.html#NM1">Symbol</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> <b> such that </b><br/><a NAME="E6:11_1_2"/><i><font color="Green">E36</font></i>: 
 <a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">x1</font>,<font color="Maroon">x2</font></span><a href="lang1.html#K4">*&gt;</a></span>
 <b>by </b><i>, <a class="ref" href="bintree1.html#D4">BINTREE1:def 4</a></i>;<br/><a NAME="E7:11_1_2"/><i><font color="Green">E38</font></i>: 
(  <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">ts</font> &amp; ( for <font color="Olive">i</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="numbers.html#K5">NAT</a>   st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">ts</font> holds <br/> ex <font color="Olive">T</font> being  <a href="trees_2.html#NM4">DecoratedTree</a> st <br/>( <font color="Olive">T</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ts</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> <a href="hidden.html#R1">=</a> <font color="Olive">T</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  ) ) )
 <b>by </b><i><a class="ref" href="trees_3.html#D18">TREES_3:def 18</a></i>;<br/><a NAME="E8:11_1_2"/>
 <a href="finseq_1.html#K3">len</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font></span>)</span> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i>, <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/><a NAME="E9:11_1_2"/><b>then </b><i><font color="Green">E39</font></i>: 
 <a href="finseq_1.html#K4">dom</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font></span>)</span> <a href="hidden.html#R1">=</a>  <a href="finseq_1.html#K2">Seg</a> 2
 <b>by </b><i><a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E10:11_1_2"/><b>then </b><i><font color="Green">E40</font></i>: 
 <a href="finseq_1.html#K3">len</a> <font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> 2
 <b>by </b><i>, <a class="ref" href="finseq_1.html#D3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E11:11_1_2"/><i><font color="Green">E41</font></i>: 
( 1 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 2 &amp; 2 <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K2">Seg</a> 2 )
 <b>by </b><i><a class="ref" href="finseq_1.html#T4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2">TARSKI:def 2</a></i>;<br/><b>then consider </b><font color="Maroon">tl</font> being   <a href="trees_2.html#NM4">DecoratedTree</a><b> such that </b><br/><a NAME="E13:11_1_2"/><i><font color="Green">E42</font></i>: 
( <font color="Maroon">tl</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ts</font> <a href="funct_1.html#K1">.</a> 1 &amp; <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font></span>)</span> <a href="funct_1.html#K1">.</a> 1 <a href="hidden.html#R1">=</a> <font color="Maroon">tl</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, </i>;<br/><b>consider </b><font color="Maroon">tr</font> being   <a href="trees_2.html#NM4">DecoratedTree</a><b> such that </b><br/><a NAME="E15:11_1_2"/><i><font color="Green">E43</font></i>: 
( <font color="Maroon">tr</font> <a href="hidden.html#R1">=</a> <font color="Maroon">ts</font> <a href="funct_1.html#K1">.</a> 2 &amp; <span class="p1">(<span class="default"><a href="trees_3.html#K16">roots</a> <font color="Maroon">ts</font></span>)</span> <a href="funct_1.html#K1">.</a> 2 <a href="hidden.html#R1">=</a> <font color="Maroon">tr</font> <a href="funct_1.html#K1">.</a> <a href="xboole_0.html#K1">{}</a>  )
 <b>by </b><i>, , </i>;<br/><b>reconsider </b><font color="Maroon">tl</font> = <font color="Maroon">tl</font>, <font color="Maroon">tr</font> = <font color="Maroon">tr</font> as   <a href="scm_comp.html#NM1">bin-term</a> <b>by </b><i>, , , , , <a class="ref" href="finseq_2.html#T13">FINSEQ_2:13</a></i>;<br/><a NAME="E17:11_1_2"/>
<font color="Maroon">ts</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">tl</font>,<font color="Maroon">tr</font></span><a href="lang1.html#K4">*&gt;</a></span>
 <b>by </b><i>, , , <a class="ref" href="finseq_1.html#T61">FINSEQ_1:61</a></i>;<br/><a NAME="E18:11_1_2"/><b>then </b><i><font color="Green">E44</font></i>: 
<font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Maroon">nt</font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Maroon">tl</font>,<font color="Maroon">tr</font>
 <b>by </b><i>, <a class="ref" href="trees_4.html#D6">TREES_4:def 6</a></i>;<br/><a NAME="E19:11_1_2"/>
( <font color="Maroon">nt</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,0</span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">nt</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,1</span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">nt</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,2</span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">nt</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,3</span><a href="tarski.html#K4">]</a></span> or <font color="Maroon">nt</font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="tarski.html#K4">[</a><span class="default">0,4</span><a href="tarski.html#K4">]</a></span> )
 <b>by </b><i/>;<br/><a NAME="E20:11_1_2"/><b>then </b>
( <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Maroon">tl</font> <a href="scm_comp.html#K5" target="_self">+</a> <font color="Maroon">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Maroon">tl</font> <a href="scm_comp.html#K6" target="_self">-</a> <font color="Maroon">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Maroon">tl</font> <a href="scm_comp.html#K7" target="_self">*</a> <font color="Maroon">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Maroon">tl</font> <a href="scm_comp.html#K8" target="_self">div</a> <font color="Maroon">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Maroon">tl</font> <a href="scm_comp.html#K9" target="_self">mod</a> <font color="Maroon">tr</font> )
 <b>by </b><i/>;<br/><b>hence </b><a NAME="E21:11_1_2"/>
(  ex <font color="Olive">t</font> being  <a href="dtconstr.html#NM2">Terminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  st <font color="Maroon">term</font> <a href="hidden.html#R1">=</a>  <a href="scm_comp.html#K3" target="_self">root-tree</a> <font color="Olive">t</font> or  ex <font color="Olive">tl</font>, <font color="Olive">tr</font> being  <a href="scm_comp.html#NM1">bin-term</a> st <br/>( <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K5" target="_self">+</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K6" target="_self">-</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K7" target="_self">*</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K8" target="_self">div</a> <font color="Olive">tr</font> or <font color="Maroon">term</font> <a href="hidden.html#R1">=</a> <font color="Olive">tl</font> <a href="scm_comp.html#K9" target="_self">mod</a> <font color="Olive">tr</font> ) )
 ;<br/></div><b>end;</b></div></div><b>end;</b></div>

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