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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  non  <a href="struct_0.html#V11" title="STRUCT_0:attr.11">void</a>   <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</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">U0</font> being   <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font><br/> for <font color="Olive" title="b2">B</font> being  <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Olive" title="b1">U0</font>  st <font color="Olive" title="b2">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Olive" title="b1">U0</font> holds <br/> <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Olive" title="b1">U0</font>,<font color="Olive" title="b2">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Olive" title="b1">U0</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">U0</font> be    <a href="msualg_1.html#L3" title="MSUALG_1:struct.3">MSAlgebra</a> of <font color="Maroon" title="c1">S</font>; <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">B</font> being  <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font>  st <font color="Olive" title="b1">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font> holds <br/> <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Olive" title="b1">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">B</font> be   <a href="msualg_2.html#NM1" title="MSUALG_2:NM.1">MSSubset</a> of <font color="Maroon" title="c2">U0</font>; <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="c3">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font> implies  <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font> )</span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">f1</font> = the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c5">f2</font> =  <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font>;<br/>
<span class="kw">assume </span><a NAME="E1:19"/><span class="lab"><font color="Green" title="E13">A1</font></span>: 
<font color="Maroon" title="c3">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U3" title="MSUALG_1:sel.3">Sorts</a> of <font color="Maroon" title="c2">U0</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font></span><br/>

<a NAME="E2:19"/>
for <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font> holds <br/>the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">x</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="19_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">x</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</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">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font> implies the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> )</span><br/>

<span class="kw">assume </span><a NAME="E1:19_1"/>
<font color="Maroon" title="c6">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U4" title="STRUCT_0:sel.4">carrier'</a> of <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font></span><br/>

<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c7">o1</font> = <font color="Maroon" title="c6">x</font> as   <a href="msualg_1.html#NM2" title="MSUALG_1:NM.2">OperSymbol</a> of <font color="Maroon" title="c1">S</font> ;<br/>
<a NAME="E3:19_1"/>
( the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="msualg_1.html#K5" title="MSUALG_1:func.5">Den</a> <font color="Maroon" title="c7">o1</font>,<font color="Maroon" title="c2">U0</font> &amp; <span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">o1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c7">o1</font> <a href="msualg_2.html#K3" title="MSUALG_2:func.3">/.</a> <font color="Maroon" title="c3">B</font> )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="msualg_2.html#D9" target="_self" title="MSUALG_2:def.9">Def9</a>, <a class="ref" href="msualg_1.html#D11" title="MSUALG_1:def.11">MSUALG_1:def 11</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:19_1"/>
the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:19"><span class="lab"><font color="Green" title="E13">A1</font></span></a>, <a class="ref" href="msualg_2.html#T4" target="_self" title="MSUALG_2:th.4">Th4</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/>


</div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E3:19"/>
 <a href="msualg_2.html#K4" title="MSUALG_2:func.4">Opers</a> <font color="Maroon" title="c2">U0</font>,<font color="Maroon" title="c3">B</font> <a href="pboole.html#R6" title="PBOOLE:pred.6">=</a> the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Charact</a> of <font color="Maroon" title="c2">U0</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="pboole.html#T3" title="PBOOLE:th.3">PBOOLE:3</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/>


</div>
