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<span class="kw">set </span><font color="Maroon" title="c2">L</font> =  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font>;<br/>
<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font>,   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> =  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default">$1 <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> $2</span>)</span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c3">j</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E2:59_1_1"/><span class="lab"><font color="Green" title="E47">A1</font></span>: 
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c3">j</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S4" onmouseover="rs('binop_1/S4')" onmouseout="rh()">BINOP_1:sch 4</a>();<br/></span>
<span class="kw">deffunc </span><font color="Maroon">H<sub>2</sub></font>(   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font>,   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> =  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default">$1 <a href="normform.html#K10" title="NORMFORM:func.10">^</a> $2</span>)</span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c4">m</font> being   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span><span class="kw"> such that </span><br/><a NAME="E4:59_1_1"/><span class="lab"><font color="Green" title="E48">A2</font></span>: 
 for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> holds  <font color="Maroon" title="c4">m</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> (<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>2</sub></font>(<font color="Olive" title="b1">x</font>,<font color="Olive" title="b2">y</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="binop_1.html#S4" onmouseover="rs('binop_1/S4')" onmouseout="rh()">BINOP_1:sch 4</a>();<br/></span>
<span class="kw">take </span>
 <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">m</font> #)
; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">m</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> &amp; (  for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">C</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> holds <br/> (  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">m</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Olive" title="b2">C</font></span>)</span> &amp;  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">m</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Olive" title="b2">C</font></span>)</span> ) ) )</span><br/>

<span class="kw">thus </span><a NAME="E5:59_1_1"/>
(  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">m</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> &amp; (  for <font color="Olive" title="b1">B</font>, <font color="Olive" title="b2">C</font> being    <a href="subset_1.html#M2" title="SUBSET_1:mode.2">Element</a> of  <a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font> holds <br/> (  the <a href="lattices.html#U2" title="LATTICES:sel.2">L_join</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">m</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="setwiseo.html#K5" title="SETWISEO:func.5">\/</a> <font color="Olive" title="b2">C</font></span>)</span> &amp;  the <a href="lattices.html#U1" title="LATTICES:sel.1">L_meet</a> of <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<span class="default"><a href="normform.html#K8" title="NORMFORM:func.8">Normal_forms_on</a> <font color="Maroon" title="c1">A</font></span>)</span>,<font color="Maroon" title="c3">j</font>,<font color="Maroon" title="c4">m</font> #) <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> (<font color="Olive" title="b1">B</font>,<font color="Olive" title="b2">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="normform.html#K9" title="NORMFORM:func.9">mi</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">B</font> <a href="normform.html#K10" title="NORMFORM:func.10">^</a> <font color="Olive" title="b2">C</font></span>)</span> ) ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:59_1_1"><span class="lab"><font color="Green" title="E47">A1</font></span></a>, <a class="txt" href="#E4:59_1_1"><span class="lab"><font color="Green" title="E48">A2</font></span></a></span>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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