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<span class="kw">consider </span><font color="Maroon" title="c2">S9</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="60_1_1_1"><span class="kw">per </span></a><a class="txt" onclick="hs(this)" href="javascript:()"><span class="kw">cases </span></a><span class="hide"><a NAME="E1:60_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="60_1_1_1_1"><span class="kw">suppose </span></a><a NAME="E1:60_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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="E2:60_1_1_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c2">S9</font> is    <a href="algspec1.html#M2" title="ALGSPEC1:mode.2">Extension</a> of <font color="Maroon" title="c1">S</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T53" target="_self" title="ALGSPEC1:th.53">Th53</a></span>;<br/><span class="kw">hence </span><a NAME="E3:60_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="60_1_1_1_2"><span class="kw">suppose </span></a><a NAME="E1:60_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:()"><span class="comment"><font color="Red">::  thesis: </font></span></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"><span class="kw">then </span><span class="kw">reconsider </span><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/><span class="kw">consider </span><font color="Maroon" title="c4">s</font> being   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c2">S9</font>, <font color="Maroon" title="c5">o</font> being   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c2">S9</font>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c6">E</font> = <font color="Maroon" title="c2">S9</font> <a href="circcomb.html#K2" title="CIRCCOMB:func.2">+*</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> <span class="kw">by</span> <span class="lab"><a class="ref" href="algspec1.html#T50" target="_self" title="ALGSPEC1:th.50">Th50</a></span>;<br/><span class="kw">take </span>
<font color="Maroon" title="c6">E</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c6">E</font> is  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  &amp; not <font color="Maroon" title="c6">E</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp; <font color="Maroon" title="c6">E</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  )</span><br/><span class="kw">thus </span><a NAME="E5:60_1_1_1_2"/>
not the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c6">E</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( not <font color="Maroon" title="c6">E</font> is  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>  &amp; <font color="Maroon" title="c6">E</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a>  )</span><br/><span class="kw">thus </span><a NAME="E6:60_1_1_1_2"/>
not the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c6">E</font> is  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a> 
 ; <span class="comment"><font color="Red">:: according to </font></span><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:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c6">E</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> </span><br/><span class="kw">thus </span><a NAME="E7:60_1_1_1_2"/>
<font color="Maroon" title="c6">E</font> is  <a href="msualg_1.html#V1" title="MSUALG_1:attr.1">strict</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div></div><span class="kw">end;</span></div>

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