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

<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[   <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font>,   <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font>,   <a href="hidden.html#M1">set</a> ] <b>means </b><font color="Maroon">a<sub>3</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">a<sub>2</sub></font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">a<sub>1</sub></font>;<br/>
<a NAME="E1:17_1_1"/><i><font color="Green">E32</font></i>: 
for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font>  ex <font color="Olive">m</font> being   <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">m</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">x</font> be    <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font>, <font color="Maroon">y</font> be    <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font>;<br/>

<b>reconsider </b><font color="Maroon">xx</font> = <font color="Maroon">x</font>, <font color="Maroon">yy</font> = <font color="Maroon">y</font> as   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">U1</font>,<font color="Maroon">U1</font> ;<br/>
<b>reconsider </b><font color="Maroon">m</font> = <font color="Maroon">yy</font> <a href="msualg_3.html#K3">**</a> <font color="Maroon">xx</font> as    <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font> <b>by </b><i/>;<br/>
<b>take </b>
<font color="Maroon">m</font>
;<br/>

<b>thus </b><a NAME="E3:17_1_1_1"/>
<font color="Maroon">S<sub>1</sub></font>[<font color="Maroon">x</font>,<font color="Maroon">y</font>,<font color="Maroon">m</font>]
 ;<br/>


</div><b>end;</b></div>
<a NAME="E2:17_1_1"/>
 ex <font color="Olive">B</font> being  <a href="binop_1.html#NM2">BinOp</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font> st <br/>for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive">x</font>,<font color="Olive">y</font>,<font color="Olive">B</font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font>]
 
<b>from </b><i><a class="ref" href="binop_1.html#S3">BINOP_1:sch 3</a>();<br/></i>
<b>hence </b><a NAME="E3:17_1_1"/>
 ex <font color="Olive">b<sub>1</sub></font> being  <a href="binop_1.html#NM2">BinOp</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font> st <br/>for <font color="Olive">x</font>, <font color="Olive">y</font> being   <a href="autalg_1.html#M2">Element</a> of  <a href="endalg.html#K4" target="_self">MSAEnd</a> <font color="Maroon">U1</font> holds  <font color="Olive">b<sub>1</sub></font> <a href="binop_1.html#K2">.</a> <font color="Olive">x</font>,<font color="Olive">y</font> <a href="hidden.html#R1">=</a> <font color="Olive">y</font> <a href="msualg_3.html#K3">**</a> <font color="Olive">x</font>
 ;<br/>


</div>
