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<b>consider </b><font color="Maroon" title="c9">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> , <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <b> such that </b><br/><a NAME="E2:15_1_1"/><i><font color="Green" title="E9">A1</font></i>: 
( ( for <font color="Olive" title="b1">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  holds  <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">t</font>) ) &amp; ( for <font color="Olive" title="b1">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b2">tl</font>, <font color="Olive" title="b3">tr</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b4">rtl</font>, <font color="Olive" title="b5">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b4">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b5">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">tr</font> &amp; <font color="Olive" title="b1">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/>for <font color="Olive" title="b6">xl</font>, <font color="Olive" title="b7">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b6">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b7">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b2">tl</font>,<font color="Olive" title="b3">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">nt</font>,<font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font>,<font color="Olive" title="b6">xl</font>,<font color="Olive" title="b7">xr</font>) ) )
 <b>from </b><i><a class="ref" href="bintree1.html#S3" title="BINTREE1:sch.3">BINTREE1:sch 3</a>();<br/></i>
<b>reconsider </b><font color="Maroon" title="c10">IT</font> = <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">term</font> as    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  ;<br/>
<b>take </b>
<font color="Maroon" title="c10">IT</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">f</font> being  <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of  <a href="dtconstr.html#K4" title="DTCONSTR:func.4">TS</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> , <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>  st <br/>( <font color="Maroon" title="c10">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">term</font> &amp; ( for <font color="Olive" title="b2">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  holds  <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b2">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Olive" title="b2">t</font> ) &amp; ( for <font color="Olive" title="b2">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b3">tl</font>, <font color="Olive" title="b4">tr</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b5">rtl</font>, <font color="Olive" title="b6">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b5">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">tl</font> &amp; <font color="Olive" title="b6">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b4">tr</font> &amp; <font color="Olive" title="b2">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b5">rtl</font>,<font color="Olive" title="b6">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/>for <font color="Olive" title="b7">xl</font>, <font color="Olive" title="b8">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b7">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">tl</font> &amp; <font color="Olive" title="b8">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b4">tr</font> holds <br/><font color="Olive" title="b1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b3">tl</font>,<font color="Olive" title="b4">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b7">xl</font>,<font color="Olive" title="b8">xr</font> ) )</span><br/>

<b>take </b>
<font color="Maroon" title="c9">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c10">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">term</font> &amp; ( for <font color="Olive" title="b1">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  holds  <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Olive" title="b1">t</font> ) &amp; ( for <font color="Olive" title="b1">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b2">tl</font>, <font color="Olive" title="b3">tr</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b4">rtl</font>, <font color="Olive" title="b5">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b4">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b5">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">tr</font> &amp; <font color="Olive" title="b1">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/>for <font color="Olive" title="b6">xl</font>, <font color="Olive" title="b7">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b6">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b7">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b2">tl</font>,<font color="Olive" title="b3">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b6">xl</font>,<font color="Olive" title="b7">xr</font> ) )</span><br/>

<b>thus </b><a NAME="E4:15_1_1"/>
<font color="Maroon" title="c10">IT</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">term</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">t</font> being  <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  holds  <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Olive" title="b1">t</font> ) &amp; ( for <font color="Olive" title="b1">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b2">tl</font>, <font color="Olive" title="b3">tr</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b4">rtl</font>, <font color="Olive" title="b5">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b4">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b5">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">tr</font> &amp; <font color="Olive" title="b1">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/>for <font color="Olive" title="b6">xl</font>, <font color="Olive" title="b7">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b6">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b7">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b2">tl</font>,<font color="Olive" title="b3">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b6">xl</font>,<font color="Olive" title="b7">xr</font> ) )</span><br/>

<div><b>hereby </b> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">nt</font> being  <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> <br/> for <font color="Olive" title="b2">tl</font>, <font color="Olive" title="b3">tr</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b4">rtl</font>, <font color="Olive" title="b5">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b4">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b5">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b3">tr</font> &amp; <font color="Olive" title="b1">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/>for <font color="Olive" title="b6">xl</font>, <font color="Olive" title="b7">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b6">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">tl</font> &amp; <font color="Olive" title="b7">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b2">tl</font>,<font color="Olive" title="b3">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b6">xl</font>,<font color="Olive" title="b7">xr</font></span>
<div class="add"><b>let </b><font color="Maroon" title="c11">t</font> be   <a href="dtconstr.html#NM2" title="DTCONSTR:NM.2">Terminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Maroon" title="c11">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Maroon" title="c11">t</font></span><br/><a NAME="E1:15_1_1_1"/>
<font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Maroon" title="c11">t</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 <b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/><a NAME="E2:15_1_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> </span>)</span> <a href="scm_comp.html#K12" title="SCM_COMP:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Maroon" title="c11">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Maroon" title="c11">t</font>
 <b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/><b>hence </b><a NAME="E3:15_1_1_1"/>
<font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Maroon" title="c11">t</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">s</font> <a href="scm_comp.html#K11" title="SCM_COMP:func.11">.</a> <font color="Maroon" title="c11">t</font>
 <b>by </b><i><a class="txt" href="#E2:15_1_1"><i><font color="Green" title="E9">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/></div>
<b>end;</b></div>

<b>let </b><font color="Maroon" title="c11">nt</font> be   <a href="dtconstr.html#NM3" title="DTCONSTR:NM.3">NonTerminal</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">tl</font>, <font color="Olive" title="b2">tr</font> being  <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a><br/> for <font color="Olive" title="b3">rtl</font>, <font color="Olive" title="b4">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b3">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b1">tl</font> &amp; <font color="Olive" title="b4">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Olive" title="b2">tr</font> &amp; <font color="Maroon" title="c11">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b3">rtl</font>,<font color="Olive" title="b4">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/>for <font color="Olive" title="b5">xl</font>, <font color="Olive" title="b6">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b5">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">tl</font> &amp; <font color="Olive" title="b6">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Olive" title="b1">tl</font>,<font color="Olive" title="b2">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b5">xl</font>,<font color="Olive" title="b6">xr</font></span><br/><b>let </b><font color="Maroon" title="c12">tl</font>, <font color="Maroon" title="c13">tr</font> be   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">rtl</font>, <font color="Olive" title="b2">rtr</font> being  <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>   st <font color="Olive" title="b1">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Olive" title="b2">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c13">tr</font> &amp; <font color="Maroon" title="c11">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Olive" title="b1">rtl</font>,<font color="Olive" title="b2">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> holds <br/>for <font color="Olive" title="b3">xl</font>, <font color="Olive" title="b4">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b3">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Olive" title="b4">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c12">tl</font>,<font color="Maroon" title="c13">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b3">xl</font>,<font color="Olive" title="b4">xr</font></span><br/><b>let </b><font color="Maroon" title="c14">rtl</font>, <font color="Maroon" title="c15">rtr</font> be   <a href="lang1.html#NM1" title="LANG1:NM.1">Symbol</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c14">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Maroon" title="c15">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c13">tr</font> &amp; <font color="Maroon" title="c11">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c14">rtl</font>,<font color="Maroon" title="c15">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> implies for <font color="Olive" title="b1">xl</font>, <font color="Olive" title="b2">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b1">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Olive" title="b2">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c12">tl</font>,<font color="Maroon" title="c13">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b1">xl</font>,<font color="Olive" title="b2">xr</font> )</span><br/>





<b>assume </b><a NAME="E6:15_1_1"/><i><font color="Green" title="E10">A2</font></i>: 
( <font color="Maroon" title="c14">rtl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Maroon" title="c15">rtr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c13">tr</font> &amp; <font color="Maroon" title="c11">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c14">rtl</font>,<font color="Maroon" title="c15">rtr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">xl</font>, <font color="Olive" title="b2">xr</font> being   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a>   st <font color="Olive" title="b1">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Olive" title="b2">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">tr</font> holds <br/><font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c12">tl</font>,<font color="Maroon" title="c13">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Olive" title="b1">xl</font>,<font color="Olive" title="b2">xr</font></span><br/>

<b>let </b><font color="Maroon" title="c16">xl</font>, <font color="Maroon" title="c17">xr</font> be    <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c16">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Maroon" title="c17">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">tr</font> implies <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c12">tl</font>,<font color="Maroon" title="c13">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Maroon" title="c16">xl</font>,<font color="Maroon" title="c17">xr</font> )</span><br/>

<a NAME="E7:15_1_1"/>
<font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Maroon" title="c16">xl</font>,<font color="Maroon" title="c17">xr</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> 
 
<b>by </b><i><a class="ref" href="int_1.html#D2" title="INT_1:def.2">INT_1:def 2</a></i>;<br/>
<a NAME="E8:15_1_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> </span>)</span> <a href="scm_comp.html#K12" title="SCM_COMP:func.12">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Maroon" title="c16">xl</font>,<font color="Maroon" title="c17">xr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Maroon" title="c16">xl</font>,<font color="Maroon" title="c17">xr</font>
 
<b>by </b><i><a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></i>;<br/>
<b>hence </b><a NAME="E9:15_1_1"/>
( <font color="Maroon" title="c16">xl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c12">tl</font> &amp; <font color="Maroon" title="c17">xr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c13">tr</font> implies <font color="Maroon" title="c9">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c12">tl</font>,<font color="Maroon" title="c13">tr</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <font color="Maroon" title="c16">xl</font>,<font color="Maroon" title="c17">xr</font> )
 <b>by </b><i><a class="txt" href="#E2:15_1_1"><i><font color="Green" title="E9">A1</font></i></a>, <a class="txt" href="#E6:15_1_1"><i><font color="Green" title="E10">A2</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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