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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">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> ;<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>;<br/><b>let </b><font color="Maroon" title="c3">R</font> be  <a href="msualg_6.html#V3" title="MSUALG_6:attr.3">invariant</a> <a href="msualg_4.html#NM4" title="MSUALG_4:NM.4">ManySortedRelation</a> of <font color="Maroon" title="c2">A</font>;<br/><b>let </b><font color="Maroon" title="c4">s1</font>, <font color="Maroon" title="c5">s2</font> be   <a href="msualg_1.html#NM1" title="MSUALG_1:NM.1">SortSymbol</a> of <font color="Maroon" title="c1">S</font>; <i><font color="Red">:: according to </font></i><a class="ref" href="msualg_6.html#D8" target="_self" title="MSUALG_6:def.8">MSUALG_6:def 8</a><br/><b>let </b><font color="Maroon" title="c6">t</font> be   <a href="funct_1.html#NM1" title="FUNCT_1:NM.1">Function</a>;<br/>









<b>assume </b><a NAME="E1:76"/><i><font color="Green" title="E52">A1</font></i>: 
<font color="Maroon" title="c6">t</font> <a href="msualg_6.html#R1" title="MSUALG_6:pred.1">is_e.translation_of</a> <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">s1</font>,<font color="Maroon" title="c5">s2</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c7">t</font> = <font color="Maroon" title="c6">t</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">s1</font>,the <a href="msualg_1.html#U4" title="MSUALG_1:sel.4">Sorts</a> of <font color="Maroon" title="c2">A</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">s2</font> <b>by </b><i><a class="ref" href="msualg_6.html#T11" target="_self" title="MSUALG_6:th.11">Th11</a></i>;<br/>
<b>let </b><font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c9">b</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>

<b>assume </b><a NAME="E3:76"/><i><font color="Green" title="E53">A2</font></i>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c8">a</font>,<font color="Maroon" title="c9">b</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="msualg_4.html#K2" title="MSUALG_4:func.2">.</a> <font color="Maroon" title="c4">s1</font>
 ;<br/>

<b>then reconsider </b><font color="Maroon" title="c10">a</font> = <font color="Maroon" title="c8">a</font>, <font color="Maroon" title="c11">b</font> = <font color="Maroon" title="c9">b</font> as   <a href="msualg_6.html#NM1" title="MSUALG_6:NM.1">Element</a> of <font color="Maroon" title="c2">A</font>,<font color="Maroon" title="c4">s1</font> <b>by </b><i><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></i>;<br/>
<a NAME="E5:76"/>
<font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c11">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c3">R</font> <a href="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Maroon" title="c4">s1</font>
 
<b>by </b><i><a class="txt" href="msualg_6.html#E3:76"><i><font color="Green" title="E53">A2</font></i></a>, <a class="ref" href="msualg_6.html#T42" target="_self" title="MSUALG_6:th.42">Th42</a></i>;<br/>
<a NAME="E6:76"/><b>then </b>
<font color="Maroon" title="c7">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c10">a</font>,<font color="Maroon" title="c7">t</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c11">b</font> <a href="rewrite1.html#R2" title="REWRITE1:pred.2">are_convertible_wrt</a> <font color="Maroon" title="c3">R</font> <a href="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Maroon" title="c5">s2</font>
 
<b>by </b><i><a class="txt" href="msualg_6.html#E1:76"><i><font color="Green" title="E52">A1</font></i></a>, <a class="ref" href="msualg_6.html#T47" target="_self" title="MSUALG_6:th.47">Th47</a></i>;<br/>
<b>hence </b><a NAME="E7:76"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">a</font></span>)</span>,<span class="p2">(<span class="default"><font color="Maroon" title="c6">t</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c9">b</font></span>)</span></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="msualg_4.html#K1" title="MSUALG_4:func.1">.</a> <font color="Maroon" title="c5">s2</font>
 <b>by </b><i><a class="ref" href="msualg_6.html#T42" target="_self" title="MSUALG_6:th.42">Th42</a></i>;<br/>


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