<?xml version="1.0"?>
<div class="add">

<b>let </b><font color="Maroon" title="c1">S1</font>, <font color="Maroon" title="c2">S2</font>, <font color="Maroon" title="c3">E</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> iff ( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> ) )</span><br/>

<b>set </b><font color="Maroon" title="c4">f1</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>;<br/>
<b>set </b><font color="Maroon" title="c5">g1</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font>;<br/>
<b>set </b><font color="Maroon" title="c6">f2</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>;<br/>
<b>set </b><font color="Maroon" title="c7">g2</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font>;<br/>
<a NAME="E1:54"/><i><font color="Green" title="E44">A1</font></i>: 
( <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> implies <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_1"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:54_1"/><i><font color="Green" title="E45">A2</font></i>: 
( <font color="Maroon" title="c1">S1</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c3">E</font> &amp; <font color="Maroon" title="c2">S2</font> is    <a href="instalg1.html#M1" title="INSTALG1:mode.1">Subsignature</a> of <font color="Maroon" title="c3">E</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">ALGSPEC1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font></span><br/>

<a NAME="E2:54_1"/><b>then </b>
( the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c3">E</font> &amp; the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c3">E</font> )
 
<b>by </b><i><a class="ref" href="instalg1.html#T12" title="INSTALG1:th.12">INSTALG1:12</a></i>;<br/>
<b>hence </b><a NAME="E3:54_1"/>
the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c1">S1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U1" title="MSUALG_1:sel.1">Arity</a> of <font color="Maroon" title="c2">S2</font>
 <b>by </b><i><a class="ref" href="partfun1.html#T131" title="PARTFUN1:th.131">PARTFUN1:131</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="circcomb.html#D1" title="CIRCCOMB:def.1">CIRCCOMB:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font></span><br/>

<a NAME="E4:54_1"/>
( the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c3">E</font> &amp; the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c3">E</font> )
 
<b>by </b><i><a class="txt" href="#E1:54_1"><i><font color="Green" title="E45">A2</font></i></a>, <a class="ref" href="instalg1.html#T12" title="INSTALG1:th.12">INSTALG1:12</a></i>;<br/>
<b>hence </b><a NAME="E5:54_1"/>
the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c1">S1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a> the <a href="msualg_1.html#U2" title="MSUALG_1:sel.2">ResultSort</a> of <font color="Maroon" title="c2">S2</font>
 <b>by </b><i><a class="ref" href="partfun1.html#T131" title="PARTFUN1:th.131">PARTFUN1:131</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>
<a NAME="E2:54"/>
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="xboole_1.html#T7" title="XBOOLE_1:th.7">XBOOLE_1:7</a></i>;<br/>
<a NAME="E3:54"/><b>then </b>
(  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font></span>)</span> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <span class="p1">(<span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font></span>)</span> )
 
<b>by </b><i><a class="ref" href="funct_4.html#T4" title="FUNCT_4:th.4">FUNCT_4:4</a></i>;<br/>
<a NAME="E4:54"/><b>then </b><i><font color="Green" title="E45">A3</font></i>: 
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="partfun1.html#R1" title="PARTFUN1:pred.1">tolerates</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>
 
<b>by </b><i><a class="ref" href="partfun1.html#T131" title="PARTFUN1:th.131">PARTFUN1:131</a></i>;<br/>
<a NAME="E5:54"/><i><font color="Green" title="E46">A4</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font> &amp; the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="xboole_0.html#K2" title="XBOOLE_0:func.2">\/</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="circcomb.html#D2" title="CIRCCOMB:def.2">CIRCCOMB:def 2</a></i>;<br/>
<a NAME="E6:54"/>
( <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> implies <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="54_2"><b>proof </b></a><div class="add">

<b>assume </b><a NAME="E1:54_2"/>
(  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font>, <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font>,<font color="Maroon" title="c3">E</font> &amp;  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font>, <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">E</font> )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="instalg1.html#D2" title="INSTALG1:def.2">INSTALG1:def 2</a>,<a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">ALGSPEC1:def 5</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span><br/>

<a NAME="E2:54_2"/><b>then </b>
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">S2</font></span>)</span>,<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">E</font>
 
<b>by </b><i><a class="txt" href="#E4:54"><i><font color="Green" title="E45">A3</font></i></a>, <a class="ref" href="algspec1.html#T51" target="_self" title="ALGSPEC1:th.51">Th51</a></i>;<br/>
<a NAME="E3:54_2"/><b>then </b>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span>,<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S1</font></span>)</span> <a href="funct_4.html#K1" title="FUNCT_4:func.1">+*</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c2">S2</font></span>)</span> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">E</font>
 
<b>by </b><i><a class="txt" href="#E5:54"><i><font color="Green" title="E46">A4</font></i></a>, <a class="ref" href="funct_4.html#T23" title="FUNCT_4:th.23">FUNCT_4:23</a></i>;<br/>
<b>hence </b><a NAME="E4:54_2"/>
 <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span>, <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font></span>)</span> <a href="pua2mss1.html#R3" title="PUA2MSS1:pred.3">form_morphism_between</a> <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font>,<font color="Maroon" title="c3">E</font>
 <b>by </b><i><a class="txt" href="#E5:54"><i><font color="Green" title="E46">A4</font></i></a>, <a class="ref" href="funct_4.html#T23" title="FUNCT_4:th.23">FUNCT_4:23</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="instalg1.html#D2" title="INSTALG1:def.2">INSTALG1:def 2</a>,<a class="ref" href="algspec1.html#D5" target="_self" title="ALGSPEC1:def.5">ALGSPEC1:def 5</a> <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>hence </b><a NAME="E7:54"/>
( <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> implies ( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> ) )
 <b>by </b><i><a class="txt" href="#E1:54"><i><font color="Green" title="E44">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> implies ( <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> ) )</span><br/>

<b>assume </b><a NAME="E8:54"/>
<font color="Maroon" title="c1">S1</font> <a href="circcomb.html#R1" title="CIRCCOMB:pred.1">tolerates</a> <font color="Maroon" title="c2">S2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> (  not <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> or ( <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> ) )</span><br/>

<a NAME="E9:54"/><b>then </b>
( <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> )
 
<b>by </b><i><a class="ref" href="algspec1.html#T49" target="_self" title="ALGSPEC1:th.49">Th49</a>, <a class="ref" href="algspec1.html#T50" target="_self" title="ALGSPEC1:th.50">Th50</a></i>;<br/>
<b>hence </b><a NAME="E10:54"/>
(  not <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c2">S2</font> or ( <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S1</font> &amp; <font color="Maroon" title="c3">E</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c2">S2</font> ) )
 <b>by </b><i><a class="ref" href="algspec1.html#T48" target="_self" title="ALGSPEC1:th.48">Th48</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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