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<b>let </b><font color="Maroon">c<sub>7</sub></font> be   <a href="ami_1.html#NM4">State</a> of <a href="ami_3.html#K1">SCM</a> ;<br/><b>let </b><font color="Maroon">c<sub>8</sub></font> be   <a href="dtconstr.html#NM3">NonTerminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> ;<br/><b>let </b><font color="Maroon">c<sub>9</sub></font>, <font color="Maroon">c<sub>10</sub></font> be   <a href="scm_comp.html#NM1">bin-term</a>;<br/>





<b>consider </b><font color="Maroon">c<sub>11</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="dtconstr.html#K4">TS</a> <a href="scm_comp.html#K1" target="_self">SCM-AE</a> , <a href="numbers.html#K4">INT</a> <b> such that </b><br/><a NAME="E2:17"/><i><font color="Green">E12</font></i>: 
( <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="scm_comp.html#K13" target="_self">@</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="dtconstr.html#NM2">Terminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  holds <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" target="_self">root-tree</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>7</sub></font> <a href="scm_comp.html#K11" target="_self">.</a> <font color="Olive">b<sub>1</sub></font> ) &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="dtconstr.html#NM3">NonTerminal</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> <br/>for <font color="Olive">b<sub>2</sub></font>, <font color="Olive">b<sub>3</sub></font> being  <a href="scm_comp.html#NM1">bin-term</a><br/>for <font color="Olive">b<sub>4</sub></font>, <font color="Olive">b<sub>5</sub></font> being  <a href="lang1.html#NM1">Symbol</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a>  st <font color="Olive">b<sub>4</sub></font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Olive">b<sub>3</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Olive">b<sub>4</sub></font>,<font color="Olive">b<sub>5</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> holds <br/>for <font color="Olive">b<sub>6</sub></font>, <font color="Olive">b<sub>7</sub></font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K4">INT</a>  st <font color="Olive">b<sub>6</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>2</sub></font> &amp; <font color="Olive">b<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>3</sub></font> holds <br/><font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Olive">b<sub>2</sub></font>,<font color="Olive">b<sub>3</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>1</sub></font> <a href="scm_comp.html#K10" target="_self">-Meaning_on</a> <font color="Olive">b<sub>6</sub></font>,<font color="Olive">b<sub>7</sub></font> ) )
 <b>by </b><i><a class="ref" href="scm_comp.html#D9" target="_self">Def9</a></i>;<br/>
<a NAME="E3:17"/>
( <font color="Maroon">c<sub>9</sub></font> <a href="scm_comp.html#K13" target="_self">@</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>9</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="scm_comp.html#K13" target="_self">@</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>11</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>10</sub></font> &amp; <font color="Maroon">c<sub>8</sub></font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="bintree1.html#K1">root-label</a> <font color="Maroon">c<sub>9</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="bintree1.html#K1">root-label</a> <font color="Maroon">c<sub>10</sub></font></span>)</span></span><a href="lang1.html#K4">*&gt;</a></span> )
 
<b>by </b><i><a class="txt" href="scm_comp.html#E2:17"><i><font color="Green">E12</font></i></a>, <a class="ref" href="scm_comp.html#D1" target="_self">Def1</a>, <a class="ref" href="scm_comp.html#D9" target="_self">Def9</a>, <a class="txt" href="scm_comp.html#E6"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E4:17"/>
<span class="p1">(<span class="default"><font color="Maroon">c<sub>8</sub></font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Maroon">c<sub>9</sub></font>,<font color="Maroon">c<sub>10</sub></font></span>)</span> <a href="scm_comp.html#K13" target="_self">@</a> <font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>8</sub></font> <a href="scm_comp.html#K10" target="_self">-Meaning_on</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>9</sub></font> <a href="scm_comp.html#K13" target="_self">@</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="scm_comp.html#K13" target="_self">@</a> <font color="Maroon">c<sub>7</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scm_comp.html#E2:17"><i><font color="Green">E12</font></i></a></i>;<br/>


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