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<div class="add">

<b>let </b><font color="Maroon" title="c6">term</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"> (  ex <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>  st <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font> or  ex <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> st <br/>( <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K5" title="SCM_COMP:func.5">+</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K6" title="SCM_COMP:func.6">-</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K7" title="SCM_COMP:func.7">*</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K8" title="SCM_COMP:func.8">div</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K9" title="SCM_COMP:func.9">mod</a> <font color="Olive" title="b2">tr</font> ) )</span><br/>

<a NAME="E1:11"/>
 <a href="bintree1.html#K1" title="BINTREE1:func.1">root-label</a> <font color="Maroon" title="c6">term</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> 
 
;<br/>
<a NAME="E2:11"/><b>then </b>
<font color="Maroon" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> 
 
<b>by </b><i><a class="ref" href="bintree1.html#D1" title="BINTREE1:def.1">BINTREE1:def 1</a></i>;<br/>
<a NAME="E3:11"/><b>then </b><i><font color="Green" title="E8">A1</font></i>: 
<font color="Maroon" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K6" title="DTCONSTR:func.6">Terminals</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> </span>)</span> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> <span class="p1">(<span class="default"><a href="dtconstr.html#K7" title="DTCONSTR:func.7">NonTerminals</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="lang1.html#T1" title="LANG1:th.1">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" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dtconstr.html#K6" title="DTCONSTR:func.6">Terminals</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  or <font color="Maroon" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dtconstr.html#K7" title="DTCONSTR:func.7">NonTerminals</a> <a href="scm_comp.html#K1" title="SCM_COMP:func.1">SCM-AE</a>  )
 </span><b>by </b><i><a class="txt" href="#E3:11"><i><font color="Green" title="E8">A1</font></i></a>, <a class="ref" href="xboole_0.html#D3" title="XBOOLE_0:def.3">XBOOLE_0:def 3</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" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dtconstr.html#K6" title="DTCONSTR:func.6">Terminals</a> <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"> (  ex <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>  st <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font> or  ex <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> st <br/>( <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K5" title="SCM_COMP:func.5">+</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K6" title="SCM_COMP:func.6">-</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K7" title="SCM_COMP:func.7">*</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K8" title="SCM_COMP:func.8">div</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K9" title="SCM_COMP:func.9">mod</a> <font color="Olive" title="b2">tr</font> ) )</span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c7">t</font> = <font color="Maroon" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <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>  ;<br/><a NAME="E3:11_1_1"/>
<font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Maroon" title="c7">t</font>
 <b>by </b><i><a class="ref" href="dtconstr.html#T9" title="DTCONSTR:th.9">DTCONSTR:9</a></i>;<br/><b>hence </b><a NAME="E4:11_1_1"/>
(  ex <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>  st <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font> or  ex <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> st <br/>( <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K5" title="SCM_COMP:func.5">+</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K6" title="SCM_COMP:func.6">-</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K7" title="SCM_COMP:func.7">*</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K8" title="SCM_COMP:func.8">div</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K9" title="SCM_COMP:func.9">mod</a> <font color="Olive" title="b2">tr</font> ) )
 ; <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><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" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="dtconstr.html#K7" title="DTCONSTR:func.7">NonTerminals</a> <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"> (  ex <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>  st <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font> or  ex <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> st <br/>( <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K5" title="SCM_COMP:func.5">+</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K6" title="SCM_COMP:func.6">-</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K7" title="SCM_COMP:func.7">*</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K8" title="SCM_COMP:func.8">div</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K9" title="SCM_COMP:func.9">mod</a> <font color="Olive" title="b2">tr</font> ) )</span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c7">nt</font> = <font color="Maroon" title="c6">term</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  as   <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/><b>consider </b><font color="Maroon" title="c8">ts</font> being    <a href="finseq_1.html#M2" title="FINSEQ_1:mode.2">FinSequence</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> <b> such that </b><br/><a NAME="E4:11_1_2"/><i><font color="Green" title="E9">A2</font></i>: 
( <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">nt</font> <a href="trees_4.html#K4" title="TREES_4:func.4">-tree</a> <font color="Maroon" title="c8">ts</font> &amp; <font color="Maroon" title="c7">nt</font> <a href="lang1.html#R1" title="LANG1:pred.1">==&gt;</a>  <a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font> )
 <b>by </b><i><a class="ref" href="dtconstr.html#T10" title="DTCONSTR:th.10">DTCONSTR:10</a></i>;<br/><b>consider </b><font color="Maroon" title="c9">x1</font>, <font color="Maroon" title="c10">x2</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> <b> such that </b><br/><a NAME="E6:11_1_2"/><i><font color="Green" title="E10">A3</font></i>: 
 <a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c9">x1</font>,<font color="Maroon" title="c10">x2</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E4:11_1_2"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="bintree1.html#D4" title="BINTREE1:def.4">BINTREE1:def 4</a></i>;<br/><a NAME="E7:11_1_2"/><i><font color="Green" title="E11">A4</font></i>: 
(  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">ts</font> &amp; ( for <font color="Olive" title="b1">i</font> being   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="ami_2.html#K5" title="AMI_2:func.5">NAT</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <font color="Maroon" title="c8">ts</font> holds <br/> ex <font color="Olive" title="b2">T</font> being  <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a> st <br/>( <font color="Olive" title="b2">T</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> &amp; <span class="p1">(<span class="default"><a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">T</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  ) ) )
 <b>by </b><i><a class="ref" href="trees_3.html#D18" title="TREES_3:def.18">TREES_3:def 18</a></i>;<br/><a NAME="E8:11_1_2"/>
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <b>by </b><i><a class="txt" href="#E6:11_1_2"><i><font color="Green" title="E10">A3</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/><a NAME="E9:11_1_2"/><b>then </b><i><font color="Green" title="E12">A5</font></i>: 
 <a href="finseq_1.html#K4" title="FINSEQ_1:func.4">dom</a> <span class="p1">(<span class="default"><a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2
 <b>by </b><i><a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E10:11_1_2"/><b>then </b><i><font color="Green" title="E13">A6</font></i>: 
 <a href="finseq_1.html#K3" title="FINSEQ_1:func.3">len</a> <font color="Maroon" title="c8">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 2
 <b>by </b><i><a class="txt" href="#E7:11_1_2"><i><font color="Green" title="E11">A4</font></i></a>, <a class="ref" href="finseq_1.html#D3" title="FINSEQ_1:def.3">FINSEQ_1:def 3</a></i>;<br/><a NAME="E11:11_1_2"/><i><font color="Green" title="E14">A7</font></i>: 
( 1 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 &amp; 2 <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="finseq_1.html#K2" title="FINSEQ_1:func.2">Seg</a> 2 )
 <b>by </b><i><a class="ref" href="finseq_1.html#T4" title="FINSEQ_1:th.4">FINSEQ_1:4</a>, <a class="ref" href="tarski.html#D2" title="TARSKI:def.2">TARSKI:def 2</a></i>;<br/><b>then consider </b><font color="Maroon" title="c11">tl</font> being   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a><b> such that </b><br/><a NAME="E13:11_1_2"/><i><font color="Green" title="E15">A8</font></i>: 
( <font color="Maroon" title="c11">tl</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 &amp; <span class="p1">(<span class="default"><a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">tl</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="txt" href="#E7:11_1_2"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="#E9:11_1_2"><i><font color="Green" title="E12">A5</font></i></a></i>;<br/><b>consider </b><font color="Maroon" title="c12">tr</font> being   <a href="trees_2.html#NM4" title="TREES_2:NM.4">DecoratedTree</a><b> such that </b><br/><a NAME="E15:11_1_2"/><i><font color="Green" title="E16">A9</font></i>: 
( <font color="Maroon" title="c12">tr</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c8">ts</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 &amp; <span class="p1">(<span class="default"><a href="trees_3.html#K16" title="TREES_3:func.16">roots</a> <font color="Maroon" title="c8">ts</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> 2 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c12">tr</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <a href="xboole_0.html#K1" title="XBOOLE_0:func.1">{}</a>  )
 <b>by </b><i><a class="txt" href="#E7:11_1_2"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="#E9:11_1_2"><i><font color="Green" title="E12">A5</font></i></a>, <a class="txt" href="#E11:11_1_2"><i><font color="Green" title="E14">A7</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c13">tl</font> = <font color="Maroon" title="c11">tl</font>, <font color="Maroon" title="c14">tr</font> = <font color="Maroon" title="c12">tr</font> as   <a href="scm_comp.html#NM1" title="SCM_COMP:NM.1">bin-term</a> <b>by </b><i><a class="txt" href="#E7:11_1_2"><i><font color="Green" title="E11">A4</font></i></a>, <a class="txt" href="#E9:11_1_2"><i><font color="Green" title="E12">A5</font></i></a>, <a class="txt" href="#E11:11_1_2"><i><font color="Green" title="E14">A7</font></i></a>, <a class="txt" href="#E13:11_1_2"><i><font color="Green" title="E15">A8</font></i></a>, <a class="txt" href="#E15:11_1_2"><i><font color="Green" title="E16">A9</font></i></a>, <a class="ref" href="finseq_2.html#T13" title="FINSEQ_2:th.13">FINSEQ_2:13</a></i>;<br/><a NAME="E17:11_1_2"/>
<font color="Maroon" title="c8">ts</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="lang1.html#K4" title="LANG1:func.4">&lt;*</a><span class="default"><font color="Maroon" title="c13">tl</font>,<font color="Maroon" title="c14">tr</font></span><a href="lang1.html#K4" title="LANG1:func.4">*&gt;</a></span>
 <b>by </b><i><a class="txt" href="#E10:11_1_2"><i><font color="Green" title="E13">A6</font></i></a>, <a class="txt" href="#E13:11_1_2"><i><font color="Green" title="E15">A8</font></i></a>, <a class="txt" href="#E15:11_1_2"><i><font color="Green" title="E16">A9</font></i></a>, <a class="ref" href="finseq_1.html#T61" title="FINSEQ_1:th.61">FINSEQ_1:61</a></i>;<br/><a NAME="E18:11_1_2"/><b>then </b>
<font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">nt</font> <a href="scm_comp.html#K2" title="SCM_COMP:func.2">-tree</a> <font color="Maroon" title="c13">tl</font>,<font color="Maroon" title="c14">tr</font>
 <b>by </b><i><a class="txt" href="#E4:11_1_2"><i><font color="Green" title="E9">A2</font></i></a>, <a class="ref" href="trees_4.html#D6" title="TREES_4:def.6">TREES_4:def 6</a></i>;<br/><a NAME="E19:11_1_2"/><b>then </b>
( <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">tl</font> <a href="scm_comp.html#K5" title="SCM_COMP:func.5">+</a> <font color="Maroon" title="c14">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">tl</font> <a href="scm_comp.html#K6" title="SCM_COMP:func.6">-</a> <font color="Maroon" title="c14">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">tl</font> <a href="scm_comp.html#K7" title="SCM_COMP:func.7">*</a> <font color="Maroon" title="c14">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">tl</font> <a href="scm_comp.html#K8" title="SCM_COMP:func.8">div</a> <font color="Maroon" title="c14">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c13">tl</font> <a href="scm_comp.html#K9" title="SCM_COMP:func.9">mod</a> <font color="Maroon" title="c14">tr</font> )
 <b>by </b><i><a class="ref" href="scm_comp.html#T3" target="_self" title="SCM_COMP:th.3">Th3</a></i>;<br/><b>hence </b><a NAME="E20:11_1_2"/>
(  ex <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>  st <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="scm_comp.html#K3" title="SCM_COMP:func.3">root-tree</a> <font color="Olive" title="b1">t</font> or  ex <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> st <br/>( <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K5" title="SCM_COMP:func.5">+</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K6" title="SCM_COMP:func.6">-</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K7" title="SCM_COMP:func.7">*</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K8" title="SCM_COMP:func.8">div</a> <font color="Olive" title="b2">tr</font> or <font color="Maroon" title="c6">term</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">tl</font> <a href="scm_comp.html#K9" title="SCM_COMP:func.9">mod</a> <font color="Olive" title="b2">tr</font> ) )
 ; <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></div><b>end;</b></div>

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