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<b>set </b><font color="Maroon">L</font> =  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/>
<b>let </b><font color="Maroon">A1</font> be  <a href="lattices.html#V3">strict</a>  <a href="lattices.html#L3">LattStr</a> , <font color="Maroon">A2</font> be  <a href="lattices.html#V3">strict</a>  <a href="lattices.html#L3">LattStr</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:66_1_2"/><i><font color="Green">E44</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A1</font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">A</font>, <font color="Olive">B</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font> holds <br/> ( the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">A1</font> <a href="binop_1.html#K1">.</a> <font color="Olive">A</font>,<font color="Olive">B</font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="setwiseo.html#K5">\/</a> <font color="Olive">B</font></span>)</span> &amp; the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">A1</font> <a href="binop_1.html#K1">.</a> <font color="Olive">A</font>,<font color="Olive">B</font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="normform.html#K10" target="_self">^</a> <font color="Olive">B</font></span>)</span> ) ) )
 <b>and </b><br/><a NAME="E2:66_1_2"/><i><font color="Green">E45</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">A2</font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font> &amp; ( for <font color="Olive">A</font>, <font color="Olive">B</font> being   <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font> holds <br/> ( the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">A2</font> <a href="binop_1.html#K1">.</a> <font color="Olive">A</font>,<font color="Olive">B</font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="setwiseo.html#K5">\/</a> <font color="Olive">B</font></span>)</span> &amp; the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">A2</font> <a href="binop_1.html#K1">.</a> <font color="Olive">A</font>,<font color="Olive">B</font> <a href="hidden.html#R1">=</a>  <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Olive">A</font> <a href="normform.html#K10" target="_self">^</a> <font color="Olive">B</font></span>)</span> ) ) )
 ;<br/>

<b>reconsider </b><font color="Maroon">a3</font> = the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">A1</font>, <font color="Maroon">a4</font> = the <a href="lattices.html#U1">L_meet</a> of <font color="Maroon">A2</font>, <font color="Maroon">a1</font> = the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">A1</font>, <font color="Maroon">a2</font> = the <a href="lattices.html#U2">L_join</a> of <font color="Maroon">A2</font> as   <a href="binop_1.html#NM2">BinOp</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font> <b>by </b><i>, </i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_2_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/><b>thus </b><font color="Maroon">a1</font> <a href="normform.html#K11" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> = 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="setwiseo.html#K5">\/</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">a2</font> <a href="normform.html#K11" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<a NAME="E5:66_1_2"/><b>then </b><i><font color="Green">E47</font></i>: 
<font color="Maroon">a1</font> <a href="funct_2.html#R2">=</a> <font color="Maroon">a2</font>
 
<b>by </b><i><a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="66_1_2_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>, <font color="Maroon">y</font> be    <a href="subset_1.html#M2">Element</a> of  <a href="normform.html#K8" target="_self">Normal_forms_on</a> <font color="Maroon">A</font>;<br/><b>thus </b><font color="Maroon">a3</font> <a href="normform.html#K11" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font> = 
 <a href="normform.html#K9" target="_self">mi</a> <span class="p1">(<span class="default"><font color="Maroon">x</font> <a href="normform.html#K10" target="_self">^</a> <font color="Maroon">y</font></span>)</span>
<b>by </b><i/>
<br/>.= 
<font color="Maroon">a4</font> <a href="normform.html#K11" target="_self">.</a> <font color="Maroon">x</font>,<font color="Maroon">y</font>
<b>by </b><i/>
;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E7:66_1_2"/>
<font color="Maroon">A1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">A2</font>
 <b>by </b><i>, , , <a class="ref" href="binop_1.html#T2">BINOP_1:2</a></i>;<br/>


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