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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="xboole_0.html#V1">empty</a>  <a href="hidden.html#M1">set</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></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">c<sub>3</sub></font> be   <a href="altcat_1.html#NM4">category</a>;<br/>





<b>assume </b><a NAME="E1:14"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a>  <a href="msinst_1.html#K4" target="_self">MSAlgCat</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="altcat_1.html#NM1">object</a> of <font color="Maroon">c<sub>3</sub></font>;<br/>

<a NAME="E2:14"/>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 
;<br/>
<a NAME="E3:14"/><b>then </b>
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R2">in</a>  <a href="msinst_1.html#K2" target="_self">MSAlg_set</a> <font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="txt" href="msinst_1.html#E1:14"><i><font color="Green">E9</font></i></a>, <a class="ref" href="msinst_1.html#D4" target="_self">Def4</a></i>;<br/>
<b>then consider </b><font color="Maroon">c<sub>5</sub></font> being  <a href="msualg_1.html#V4">strict</a> <a href="msualg_6.html#V1">feasible</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>2</sub></font><b> such that </b><br/><a NAME="E5:14"/><i><font color="Green">E10</font></i>: 
( <font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font> being  <a href="pboole.html#NM3">Component</a> of the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">c<sub>5</sub></font> holds <font color="Olive">b<sub>1</sub></font> <a href="tarski.html#R1">c=</a> <font color="Maroon">c<sub>1</sub></font> ) )
 <b>by </b><i><a class="ref" href="msinst_1.html#D2" target="_self">Def2</a></i>;<br/>
<b>thus </b><a NAME="E6:14"/>
<font color="Maroon">c<sub>4</sub></font> is  <a href="msualg_1.html#V4">strict</a> <a href="msualg_6.html#V1">feasible</a>  <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="msinst_1.html#E5:14"><i><font color="Green">E10</font></i></a></i>;<br/>


</div>
