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

<b>let </b><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="msualg_1.html#V2" title="MSUALG_1:attr.2">void</a>  <a href="msualg_1.html#L1" title="MSUALG_1:struct.1">ManySortedSign</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">A</font> being <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <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">R</font> being  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Olive" title="b1">A</font> holds  <font color="Olive" title="b2">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Olive" title="b2">R</font>,<font color="Olive" title="b1">A</font></span><br/><b>let </b><font color="Maroon" title="c2">A</font> be  <a href="msualg_1.html#V5" title="MSUALG_1:attr.5">non-empty</a>  <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:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">R</font> being  <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font> holds  <font color="Olive" title="b1">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Olive" title="b1">R</font>,<font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c3">R</font> be   <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">R</font> <a href="pboole.html#R2" title="PBOOLE:pred.2">c=</a>  <a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">A</font></span><br/><b>let </b><font color="Maroon" title="c4">i</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pboole.html#D5" title="PBOOLE:def.5">PBOOLE:def 5</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">i</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 <font color="Maroon" title="c1">S</font> or <font color="Maroon" title="c3">R</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> )</span><br/>







<b>assume </b><a NAME="E1:70"/>
<font color="Maroon" title="c4">i</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 <font color="Maroon" title="c1">S</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">R</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font></span><br/>

<b>then reconsider </b><font color="Maroon" title="c5">s</font> = <font color="Maroon" title="c4">i</font> as   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font> ;<br/>
<a NAME="E3:70"/>
<span class="p1">(<span class="default"><a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <font color="Maroon" title="c5">s</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a>  <a href="msualg_5.html#K1" title="MSUALG_5:func.1">EqCl</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">R</font> <a href="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Maroon" title="c5">s</font></span>)</span>
 
<b>by </b><i><a class="ref" href="msualg_5.html#D3" title="MSUALG_5:def.3">MSUALG_5:def 3</a></i>;<br/>
<b>hence </b><a NAME="E4:70"/>
<font color="Maroon" title="c3">R</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> <span class="p1">(<span class="default"><a href="msualg_6.html#K9" title="MSUALG_6:func.9">EqCl</a> <font color="Maroon" title="c3">R</font>,<font color="Maroon" title="c2">A</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">i</font>
 <b>by </b><i><a class="ref" href="msualg_5.html#D1" title="MSUALG_5:def.1">MSUALG_5:def 1</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>
