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<span class="kw">let </span><font color="Maroon" title="c7">s</font> be   <a href="ami_1.html#NM5" title="AMI_1:NM.5">State</a> of <a href="ami_3.html#K1" title="AMI_3:func.1">SCM</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></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> holds  <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="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font> <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> <span class="p1">(<span class="default"><font color="Olive" title="b2">tl</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">tr</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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> holds  <span class="p1">(<span class="default"><font color="Maroon" title="c8">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="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b2">tr</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c9">tl</font>, <font color="Maroon" title="c10">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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c8">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c9">tl</font>,<font color="Maroon" title="c10">tr</font></span>)</span> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">tl</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">tr</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span></span><br/>





<span class="kw">consider </span><font color="Maroon" title="c11">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1">(<span class="default"><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> </span>)</span>,<a href="numbers.html#K4" title="NUMBERS:func.4">INT</a> <span class="kw"> such that </span><br/><a NAME="E2:17"/><span class="lab"><font color="Green" title="E12">A1</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c9">tl</font>,<font color="Maroon" title="c10">tr</font></span>)</span> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c8">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c9">tl</font>,<font color="Maroon" title="c10">tr</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E3:17"/><span class="lab"><font color="Green" title="E13">A2</font></span>: 
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="c11">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>
 <span class="kw">and </span><br/><a NAME="E4:17"/><span class="lab"><font color="Green" title="E14">A3</font></span>: 
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="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><font color="Olive" title="b4">rtl</font>,<font color="Olive" title="b5">rtr</font></span><a href="pre_poly.html#K4" title="PRE_POLY: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="c11">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="c11">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="c11">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 class="kw">by</span> <span class="lab"><a class="ref" href="scm_comp.html#D9" target="_self" title="SCM_COMP:def.9">Def9</a></span>;<br/>
<a NAME="E5:17"/><span class="lab"><font color="Green" title="E15">A4</font></span>: 
<font color="Maroon" title="c8">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a> <span class="p1"><a href="pre_poly.html#K4" title="PRE_POLY:func.4">&lt;*</a><span class="default"><span class="p2">(<span class="default"><a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c9">tl</font></span>)</span>,<span class="p2">(<span class="default"><a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c10">tr</font></span>)</span></span><a href="pre_poly.html#K4" title="PRE_POLY:func.4">*&gt;</a></span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="scm_comp.html#D1" target="_self" title="SCM_COMP:def.1">Def1</a>, <a class="txt" href="scm_comp.html#E6"><span class="lab"><font color="Green" title="E6">Lm3</font></span></a></span>;<br/>
<a NAME="E6:17"/>
( <font color="Maroon" title="c9">tl</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c9">tl</font> &amp; <font color="Maroon" title="c10">tr</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">tr</font> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:17"><span class="lab"><font color="Green" title="E13">A2</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="ref" href="scm_comp.html#D9" target="_self" title="SCM_COMP:def.9">Def9</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:17"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c9">tl</font>,<font color="Maroon" title="c10">tr</font></span>)</span> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">nt</font> <a href="scm_comp.html#K10" title="SCM_COMP:func.10">-Meaning_on</a> <span class="p1">(<span class="default"><font color="Maroon" title="c9">tl</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span>,<span class="p1">(<span class="default"><font color="Maroon" title="c10">tr</font> <a href="scm_comp.html#K13" title="SCM_COMP:func.13">@</a> <font color="Maroon" title="c7">s</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:17"><span class="lab"><font color="Green" title="E12">A1</font></span></a>, <a class="txt" href="#E4:17"><span class="lab"><font color="Green" title="E14">A3</font></span></a>, <a class="txt" href="#E5:17"><span class="lab"><font color="Green" title="E15">A4</font></span></a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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