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<b>defpred </b><font color="Maroon">S<sub>1</sub></font>[  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>,  <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>,   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ] <b>means </b> ex <font color="Olive" title="b1">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <br/>( $3 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">O</font>,<font color="Olive" title="b2">A</font> #) &amp; <font color="Olive" title="b1">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of $1 <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of $2</span>)</span></span>)</span> &amp; <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of $1 <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of $2 );<br/>
<a NAME="E1:71_1_1"/><i><font color="Green" title="E37">A1</font></i>: 
for <font color="Olive" title="b1">CP1</font>, <font color="Olive" title="b2">CP2</font> being   <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font>  ex <font color="Olive" title="b3">CP</font> being   <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">CP1</font>,<font color="Olive" title="b2">CP2</font>,<font color="Olive" title="b3">CP</font>]
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c2">CP1</font>, <font color="Maroon" title="c3">CP2</font> be    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">CP</font> being   <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">CP1</font>,<font color="Maroon" title="c3">CP2</font>,<font color="Olive" title="b1">CP</font>]</span><br/>



<b>set </b><font color="Maroon" title="c4">O</font> = <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span>;<br/>
<b>set </b><font color="Maroon" title="c5">A</font> = the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font>;<br/>
<b>reconsider </b><font color="Maroon" title="c6">O'</font> = the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font> as   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E2:71_1_1_1"/><i><font color="Green" title="E38">A2</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_1_1"><b>proof </b></a><div class="add">

<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">O'</font>
<b>by </b><i><a class="ref" href="conlat_1.html#T7" target="_self" title="CONLAT_1:th.7">Th7</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font></span>)</span> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#T16" target="_self" title="CONLAT_1:th.16">Th16</a></i>
<br/>.= 
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></i>
<br/>.= 
the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font>
<b>by </b><i><a class="ref" href="conlat_1.html#D13" target="_self" title="CONLAT_1:def.13">Def13</a></i>
;<br/>
<b>hence </b><a NAME="E2:71_1_1_1_1"/>
<span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<a NAME="E3:71_1_1_1"/><b>then </b><i><font color="Green" title="E39">A3</font></i>: 
<span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default">the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span>
 
<b>by </b><i><a class="ref" href="conlat_1.html#T7" target="_self" title="CONLAT_1:th.7">Th7</a></i>;<br/>
<a NAME="E4:71_1_1_1"/><b>then </b><i><font color="Green" title="E40">A4</font></i>: 
not  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default">the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span> #) is <a href="conlat_1.html#V7" title="CONLAT_1:attr.7">empty</a>
 
<b>by </b><i><a class="txt" href="conlat_1.html#E2:71_1_1_1"><i><font color="Green" title="E38">A2</font></i></a>, <a class="txt" href="conlat_1.html#E32"><i><font color="Green" title="E22">Lm1</font></i></a></i>;<br/>
<b>set </b><font color="Maroon" title="c7">CP</font> =  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default">the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span> #);<br/>
<a NAME="E5:71_1_1_1"/>
 <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p3">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span></span>)</span></span>)</span>,<span class="p1">(<span class="default">the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c2">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c3">CP2</font></span>)</span> #) <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) where <font color="Olive" title="b1">E</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font>, <font color="Olive" title="b2">I</font> is   <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> : ( not  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">E</font>,<font color="Olive" title="b2">I</font> #) is <a href="conlat_1.html#V7" title="CONLAT_1:attr.7">empty</a> &amp; <span class="p1">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">E</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">I</font> &amp; <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">I</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">E</font> ) </span>}</span> 
 
<b>by </b><i><a class="txt" href="conlat_1.html#E2:71_1_1_1"><i><font color="Green" title="E38">A2</font></i></a>, <a class="txt" href="conlat_1.html#E3:71_1_1_1"><i><font color="Green" title="E39">A3</font></i></a>, <a class="txt" href="conlat_1.html#E4:71_1_1_1"><i><font color="Green" title="E40">A4</font></i></a></i>;<br/>
<b>hence </b><a NAME="E6:71_1_1_1"/>
 ex <font color="Olive" title="b1">CP</font> being   <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> st <font color="Maroon">S<sub>1</sub></font>[<font color="Maroon" title="c2">CP1</font>,<font color="Maroon" title="c3">CP2</font>,<font color="Olive" title="b1">CP</font>]
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>consider </b><font color="Maroon" title="c2">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p2">(<span class="default"><a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font></span>)</span></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font><b> such that </b><br/><a NAME="E3:71_1_1"/><i><font color="Green" title="E38">A5</font></i>: 
for <font color="Olive" title="b1">CP1</font>, <font color="Olive" title="b2">CP2</font> being   <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> holds  <font color="Maroon">S<sub>1</sub></font>[<font color="Olive" title="b1">CP1</font>,<font color="Olive" title="b2">CP2</font>,<font color="Maroon" title="c2">f</font> <a href="binop_1.html#K4" title="BINOP_1:func.4">.</a> <font color="Olive" title="b1">CP1</font>,<font color="Olive" title="b2">CP2</font>]
 <b>from </b><i><a class="ref" href="binop_1.html#S3" title="BINOP_1:sch.3">BINOP_1:sch 3</a>(<a class="txt" href="conlat_1.html#E1:71_1_1"><i><font color="Green" title="E37">A1</font></i></a>);<br/></i>
<b>reconsider </b><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c2">f</font> as   <a href="binop_1.html#NM2" title="BINOP_1:NM.2">BinOp</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> ;<br/>
<a NAME="E5:71_1_1"/><i><font color="Green" title="E39">A6</font></i>: 
for <font color="Olive" title="b1">CP1</font>, <font color="Olive" title="b2">CP2</font> being <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>  ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b4">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">CP1</font>,<font color="Olive" title="b2">CP2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b3">O</font>,<font color="Olive" title="b4">A</font> #) &amp; <font color="Olive" title="b3">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Olive" title="b1">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Olive" title="b2">CP2</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Olive" title="b1">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Olive" title="b2">CP2</font> )
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="71_1_1_2"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon" title="c4">CP1</font>, <font color="Maroon" title="c5">CP2</font> be  <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide">  ex <font color="Olive" title="b1">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">CP1</font>,<font color="Maroon" title="c5">CP2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">O</font>,<font color="Olive" title="b2">A</font> #) &amp; <font color="Olive" title="b1">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c4">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c5">CP2</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c4">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c5">CP2</font> )</span><br/>

<a NAME="E1:71_1_1_2"/>
( <font color="Maroon" title="c4">CP1</font> is    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> &amp; <font color="Maroon" title="c5">CP2</font> is    <a href="conlat_1.html#M2" title="CONLAT_1:mode.2">Element</a> of  <a href="conlat_1.html#K8" title="CONLAT_1:func.8">B-carrier</a> <font color="Maroon" title="c1">C</font> )
 
<b>by </b><i><a class="ref" href="conlat_1.html#T35" target="_self" title="CONLAT_1:th.35">Th35</a></i>;<br/>
<b>hence </b><a NAME="E2:71_1_1_2"/>
 ex <font color="Olive" title="b1">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b2">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Maroon" title="c4">CP1</font>,<font color="Maroon" title="c5">CP2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b1">O</font>,<font color="Olive" title="b2">A</font> #) &amp; <font color="Olive" title="b1">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c4">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Maroon" title="c5">CP2</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c4">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Maroon" title="c5">CP2</font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E3:71_1_1"><i><font color="Green" title="E38">A5</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


</div><b>end;</b></div>
<b>take </b>
<font color="Maroon" title="c3">f</font>
; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">CP1</font>, <font color="Olive" title="b2">CP2</font> being <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>  ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b4">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">CP1</font>,<font color="Olive" title="b2">CP2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b3">O</font>,<font color="Olive" title="b4">A</font> #) &amp; <font color="Olive" title="b3">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Olive" title="b1">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Olive" title="b2">CP2</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Olive" title="b1">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Olive" title="b2">CP2</font> )</span><br/>

<b>thus </b><a NAME="E6:71_1_1"/>
for <font color="Olive" title="b1">CP1</font>, <font color="Olive" title="b2">CP2</font> being <a href="conlat_1.html#V6" title="CONLAT_1:attr.6">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font>  ex <font color="Olive" title="b3">O</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U1" title="CONLAT_1:sel.1">Objects</a> of <font color="Maroon" title="c1">C</font> ex <font color="Olive" title="b4">A</font> being  <a href="subset_1.html#NM2" title="SUBSET_1:NM.2">Subset</a> of the <a href="conlat_1.html#U2" title="CONLAT_1:sel.2">Attributes</a> of <font color="Maroon" title="c1">C</font> st <br/>( <font color="Maroon" title="c3">f</font> <a href="binop_1.html#K1" title="BINOP_1:func.1">.</a> <font color="Olive" title="b1">CP1</font>,<font color="Olive" title="b2">CP2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="conlat_1.html#G3" title="CONLAT_1:aggr.3">ConceptStr</a>(# <font color="Olive" title="b3">O</font>,<font color="Olive" title="b4">A</font> #) &amp; <font color="Olive" title="b3">O</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="conlat_1.html#K2" title="CONLAT_1:func.2">AttributeDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K1" title="CONLAT_1:func.1">ObjectDerivation</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p2">(<span class="default">the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Olive" title="b1">CP1</font> <a href="subset_1.html#K4" title="SUBSET_1:func.4">\/</a> the <a href="conlat_1.html#U4" title="CONLAT_1:sel.4">Extent</a> of <font color="Olive" title="b2">CP2</font></span>)</span></span>)</span> &amp; <font color="Olive" title="b4">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Olive" title="b1">CP1</font> <a href="subset_1.html#K9" title="SUBSET_1:func.9">/\</a> the <a href="conlat_1.html#U5" title="CONLAT_1:sel.5">Intent</a> of <font color="Olive" title="b2">CP2</font> )
 <b>by </b><i><a class="txt" href="conlat_1.html#E5:71_1_1"><i><font color="Green" title="E39">A6</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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