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<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#V1" target="_self">normalized</a>  <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="E1:13"/><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>
 ;<br/>

<div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1"><b>per </b></a><a class="txt" onclick="hs(this)" href="javascript:()"><b>cases </b></a><span class="hide"><a NAME="E1:13_1"/>
( <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> or <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font> )
 </span>;<br/><div class="add"><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_1"><b>suppose </b></a><a NAME="E1:13_1_1"/>
<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/><div class="add"><b>hence </b><a NAME="E2:13_1_1"/>
<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> <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>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:13"><i><font color="Green">E9</font></i></a>, <a class="ref" href="msalimit.html#T3" target="_self">Th3</a></i>;<br/></div><b>end;</b></div><div><a class="txt" onclick="hsNdiv(this)" href="javascript:()" title="13_1_2"><b>suppose </b></a><a NAME="E1:13_1_2"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>6</sub></font>
 ;<br/><div class="add"><a NAME="E2:13_1_2"/>
<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="txt" href="msalimit.html#E1:13"><i><font color="Green">E9</font></i></a>, <a class="ref" href="msalimit.html#D5" target="_self">Def5</a></i>;<br/><a NAME="E3:13_1_2"/><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="msualg_3.html#K2">id</a> the <a href="msualg_1.html#U4">Sorts</a> of <span class="p1">(<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>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:13_1_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="cqc_lang.html#D1">CQC_LANG:def 1</a></i>;<br/><b>hence </b><a NAME="E4:13_1_2"/>
<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> <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>
 <b>by </b><i><a class="txt" href="msalimit.html#E1:13_1_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="msalimit.html#D4" target="_self">Def4</a></i>;<br/></div><b>end;</b></div></div><b>end;</b></div>

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