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

<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#NM1">Poset</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="msalimit.html#M1" target="_self">OrderedAlgFam</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>4</sub></font> be    <a href="msalimit.html#M2" target="_self">Binding</a> of <font color="Maroon">c<sub>3</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font>;<br/>











<b>assume </b><a NAME="E1:10"/><i><font color="Green">E9</font></i>: 
( <font color="Maroon">c<sub>5</sub></font> <a href="orders_2.html#NR2" target="_self">&gt;=</a> <font color="Maroon">c<sub>6</sub></font> &amp; <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a> <font color="Maroon">c<sub>6</sub></font> )
 ;<br/>

<a NAME="E2:10"/><b>then </b><i><font color="Green">E10</font></i>: 
<span class="p1">(<span class="default"><a href="msalimit.html#K2" target="_self">Normalized</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="cqc_lang.html#K1">IFEQ</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msalimit.html#K1" target="_self">bind</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="msualg_3.html#K3">**</a> <span class="p2">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="msalimit.html#D5" target="_self">Def5</a></i>;<br/>
<a NAME="E3:10"/>
 <a href="cqc_lang.html#K1">IFEQ</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<span class="p1">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>,<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="msalimit.html#K1" target="_self">bind</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="msualg_3.html#K3">**</a> <span class="p2">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p3">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msalimit.html#K1" target="_self">bind</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font></span>)</span> <a href="msualg_3.html#K3">**</a> <span class="p1">(<span class="default"><a href="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p2">(<span class="default"><font color="Maroon">c<sub>3</sub></font> <a href="pralg_2.html#K6">.</a> <font color="Maroon">c<sub>5</sub></font></span>)</span></span>)</span>
 
<b>by </b><i><a class="txt" href="msalimit.html#E1:10"><i><font color="Green">E9</font></i></a>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>;<br/>
<a NAME="E4:10"/><b>then </b>
<span class="p1">(<span class="default"><a href="msalimit.html#K2" target="_self">Normalized</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a>  <a href="msalimit.html#K1" target="_self">bind</a> <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 
<b>by </b><i><a class="txt" href="msalimit.html#E2:10"><i><font color="Green">E10</font></i></a>, <a class="ref" href="msualg_3.html#T3">MSUALG_3:3</a></i>;<br/>
<b>hence </b><a NAME="E5:10"/>
<font color="Maroon">c<sub>4</sub></font> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="msalimit.html#K2" target="_self">Normalized</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> <a href="binop_1.html#K1">.</a> <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>5</sub></font>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:10"><i><font color="Green">E9</font></i></a>, <a class="ref" href="msalimit.html#D3" target="_self">Def3</a></i>;<br/>


</div>
