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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">A</font> be  <a href="msualg_1.html#V5">non-empty</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">s1</font> be   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>, <font color="Maroon">s2</font> be   <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>;<br/>





<b>assume </b><a NAME="E1:26"/><i><font color="Green">E32</font></i>: 
 <a href="msualg_6.html#K3" target="_self">TranslationRel</a> <font color="Maroon">S</font> <a href="rewrite1.html#R1">reduces</a> <font color="Maroon">s1</font>,<font color="Maroon">s2</font>
 ;<br/>

<b>let </b><font color="Maroon">q</font> be    <a href="rewrite1.html#M1">RedSequence</a> of  <a href="msualg_6.html#K3" target="_self">TranslationRel</a> <font color="Maroon">S</font>;<br/><b>let </b><font color="Maroon">p</font> be  <a href="funcop_1.html#V1">Function-yielding</a> <a href="finseq_1.html#NM1">FinSequence</a>;<br/>



<b>assume </b><b>that </b><br/><a NAME="E2:26"/><i><font color="Green">E34</font></i>: 
(  <a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">p</font></span>)</span> <a href="nat_1.html#K1">+</a> 1 &amp; <font color="Maroon">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> 1 &amp; <font color="Maroon">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><a href="finseq_1.html#K3">len</a> <font color="Maroon">q</font></span>)</span> )
 <b>and </b><br/><a NAME="E3:26"/><i><font color="Green">E43</font></i>: 
for <font color="Olive">i</font> being   <a href="subset_1.html#M1">Element</a> of  <a href="numbers.html#K5">NAT</a> <br/> for <font color="Olive">f</font> being  <a href="funct_1.html#NM1">Function</a><br/> for <font color="Olive">s1</font>, <font color="Olive">s2</font> being  <a href="msualg_1.html#NM1">SortSymbol</a> of <font color="Maroon">S</font>  st <font color="Olive">i</font> <a href="hidden.html#R2">in</a>  <a href="finseq_1.html#K4">dom</a> <font color="Maroon">p</font> &amp; <font color="Olive">f</font> <a href="hidden.html#R1">=</a> <font color="Maroon">p</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <font color="Olive">s1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <font color="Olive">i</font> &amp; <font color="Olive">s2</font> <a href="hidden.html#R1">=</a> <font color="Maroon">q</font> <a href="funct_1.html#K1">.</a> <span class="p1">(<span class="default"><font color="Olive">i</font> <a href="nat_1.html#K1">+</a> 1</span>)</span> holds <br/><font color="Olive">f</font> <a href="msualg_6.html#R1" target="_self">is_e.translation_of</a> <font color="Maroon">A</font>,<font color="Olive">s1</font>,<font color="Olive">s2</font>
 ;<br/>

<a NAME="E4:26"/>
 <a href="funct_7.html#K4">compose</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s1</font></span>)</span> is   <a href="funct_2.html#NM1">Function</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s1</font>,the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s2</font>
 
<b>by </b><i>, , , </i>;<br/>
<b>hence </b><a NAME="E5:26"/>
 <a href="funct_7.html#K4">compose</a> <font color="Maroon">p</font>,<span class="p1">(<span class="default">the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">s1</font></span>)</span> is    <a href="msualg_6.html#M2" target="_self">Translation</a> of <font color="Maroon">A</font>,<font color="Maroon">s1</font>,<font color="Maroon">s2</font>
 <b>by </b><i>, , , </i>;<br/>


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