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<b>consider </b><font color="Maroon" title="c2">S'</font> being  non <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> <a href="catalg_1.html#NM1" title="CATALG_1:NM.1">Signature</a>;<br/>
<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:58_1_1_1"/>
( <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> or  not <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_1"><b>suppose </b></a><a NAME="E1:58_1_1_1_1"/>
<font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S</font> st <br/>( not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> )</span><br/><div class="add"><a NAME="E2:58_1_1_1_1"/><b>then </b>
<font color="Maroon" title="c2">S'</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S</font>
 <b>by </b><i><a class="ref" href="algspec1.html#T53" target="_self" title="ALGSPEC1:th.53">Th53</a></i>;<br/><b>hence </b><a NAME="E3:58_1_1_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being   <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S</font> st <br/>( not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</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><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="58_1_1_1_2"><b>suppose </b></a><a NAME="E1:58_1_1_1_2"/>
not <font color="Maroon" title="c1">S</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive">b<sub>1</sub></font> being   <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S</font> st <br/>( not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> &amp; <font color="Olive">b<sub>1</sub></font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> )</span><br/><div class="add"><b>then reconsider </b><font color="Maroon" title="c3">S1</font> = <font color="Maroon" title="c1">S</font> as  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> ;<br/><b>reconsider </b><font color="Maroon" title="c4">E</font> = <font color="Maroon" title="c2">S'</font> <a href="circcomb.html#K4" title="CIRCCOMB:func.4">+*</a> <font color="Maroon" title="c3">S1</font> as    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S</font> <b>by </b><i><a class="ref" href="algspec1.html#T50" target="_self" title="ALGSPEC1:th.50">Th50</a></i>;<br/><b>take </b>
<font color="Maroon" title="c4">E</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="c4">E</font> is <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> &amp; not <font color="Maroon" title="c4">E</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> &amp; <font color="Maroon" title="c4">E</font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> )</span><br/><b>consider </b><font color="Maroon" title="c5">s</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c2">S'</font>, <font color="Maroon" title="c6">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S'</font>;<br/><b>thus </b><a NAME="E5:58_1_1_1_2"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">E</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D1" title="STRUCT_0:def.1">STRUCT_0:def 1</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( not <font color="Maroon" title="c4">E</font> is <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a> &amp; <font color="Maroon" title="c4">E</font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> )</span><br/><b>thus </b><a NAME="E6:58_1_1_1_2"/>
not the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c4">E</font> is <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="struct_0.html#D13" title="STRUCT_0:def.13">STRUCT_0:def 13</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c4">E</font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a></span><br/><b>thus </b><a NAME="E7:58_1_1_1_2"/>
<font color="Maroon" title="c4">E</font> is <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</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></div><b>end;</b></div>

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