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<b>let </b><font color="Maroon">c<sub>10</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>11</sub></font>, <font color="Maroon">c<sub>12</sub></font> be   <a href="scm_comp.html#NM1">bin-term</a>;<br/><b>let </b><font color="Maroon">c<sub>13</sub></font> be   <a href="nat_1.html#NM1">Nat</a>;<br/><b>let </b><font color="Maroon">c<sub>14</sub></font>, <font color="Maroon">c<sub>15</sub></font> be   <a href="lang1.html#NM1">Symbol</a> of <a href="scm_comp.html#K1" target="_self">SCM-AE</a> ;<br/>







<b>assume </b><a NAME="E1:22"/>
( <font color="Maroon">c<sub>14</sub></font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>15</sub></font> <a href="hidden.html#R1">=</a>  <a href="bintree1.html#K1">root-label</a> <font color="Maroon">c<sub>12</sub></font> &amp; <font color="Maroon">c<sub>10</sub></font> <a href="lang1.html#R1">==&gt;</a> <span class="p1"><a href="lang1.html#K4">&lt;*</a><span class="default"><font color="Maroon">c<sub>14</sub></font>,<font color="Maroon">c<sub>15</sub></font></span><a href="lang1.html#K4">*&gt;</a></span> )
 ;<br/>

<b>then consider </b><font color="Maroon">c<sub>16</sub></font>, <font color="Maroon">c<sub>17</sub></font>, <font color="Maroon">c<sub>18</sub></font> being   <a href="funct_2.html#NM1">Function</a> of  <a href="numbers.html#K5">NAT</a> ,the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a> <b> such that </b><br/><a NAME="E3:22"/><i><font color="Green">E17</font></i>: 
( <font color="Maroon">c<sub>16</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span> &amp; <font color="Maroon">c<sub>17</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>11</sub></font> &amp; <font color="Maroon">c<sub>18</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>9</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>12</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="nat_1.html#NM1">Nat</a> holds <font color="Maroon">c<sub>16</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <font color="Olive">b<sub>1</sub></font></span>)</span> <a href="lang1.html#K1">^</a> <span class="p2">(<span class="default"><font color="Maroon">c<sub>18</sub></font> <a href="funct_2.html#K3">.</a> <span class="p3">(<span class="default"><font color="Olive">b<sub>1</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="lang1.html#K1">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" target="_self">Selfwork</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Olive">b<sub>1</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="scm_comp.html#E27"><i><font color="Green">Lemma14</font></i></a></i>;<br/>
<b>reconsider </b><font color="Maroon">c<sub>19</sub></font> = <font color="Maroon">c<sub>17</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>13</sub></font>, <font color="Maroon">c<sub>20</sub></font> = <font color="Maroon">c<sub>18</sub></font> <a href="funct_2.html#K3">.</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> as    <a href="finseq_2.html#M2">Element</a> of the <a href="ami_1.html#U4">Instructions</a> of <a href="ami_3.html#K1">SCM</a>  <a href="finseq_2.html#K3">*</a>  ;<br/>
<a NAME="E5:22"/>
(  <a href="scm_comp.html#K15" target="_self">SCM-Compile</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>19</sub></font> &amp;  <a href="scm_comp.html#K15" target="_self">SCM-Compile</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p1">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>20</sub></font> )
 
<b>by </b><i><a class="txt" href="scm_comp.html#E3:22"><i><font color="Green">E17</font></i></a>, <a class="ref" href="scm_comp.html#D11" target="_self">Def11</a>, <a class="txt" href="scm_comp.html#E27"><i><font color="Green">Lemma14</font></i></a></i>;<br/>
<a NAME="E6:22"/><b>then </b>
<font color="Maroon">c<sub>16</sub></font> <a href="funct_2.html#K3">.</a> <font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K15" target="_self">SCM-Compile</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K15" target="_self">SCM-Compile</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" target="_self">Selfwork</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>13</sub></font></span>)</span>
 
<b>by </b><i><a class="txt" href="scm_comp.html#E3:22"><i><font color="Green">E17</font></i></a></i>;<br/>
<b>hence </b><a NAME="E7:22"/>
 <a href="scm_comp.html#K15" target="_self">SCM-Compile</a> <span class="p1">(<span class="default"><font color="Maroon">c<sub>10</sub></font> <a href="scm_comp.html#K2" target="_self">-tree</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>12</sub></font></span>)</span>,<font color="Maroon">c<sub>13</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="scm_comp.html#K15" target="_self">SCM-Compile</a> <font color="Maroon">c<sub>11</sub></font>,<font color="Maroon">c<sub>13</sub></font></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p2">(<span class="default"><a href="scm_comp.html#K15" target="_self">SCM-Compile</a> <font color="Maroon">c<sub>12</sub></font>,<span class="p3">(<span class="default"><font color="Maroon">c<sub>13</sub></font> <a href="nat_1.html#K1">+</a> 1</span>)</span></span>)</span></span>)</span> <a href="finseq_1.html#K8">^</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K14" target="_self">Selfwork</a> <font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>13</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="scm_comp.html#E3:22"><i><font color="Green">E17</font></i></a>, <a class="ref" href="scm_comp.html#D11" target="_self">Def11</a>, <a class="txt" href="scm_comp.html#E27"><i><font color="Green">Lemma14</font></i></a></i>;<br/>


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