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<b>let </b><font color="Maroon">F1</font> be    <a href="lattice4.html#M1">Homomorphism</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="lattice2.html#K1">.:</a> , <a href="conlat_1.html#K11">ConceptLattice</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="conlat_2.html#K7" target="_self">.:</a> </span>)</span>, <font color="Maroon">F2</font> be    <a href="lattice4.html#M1">Homomorphism</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="lattice2.html#K1">.:</a> , <a href="conlat_1.html#K11">ConceptLattice</a> <span class="p1">(<span class="default"><font color="Maroon">C</font> <a href="conlat_2.html#K7" target="_self">.:</a> </span>)</span>;<br/>

<b>assume </b><a NAME="E1:34_1_2"/><i><font color="Green">E166</font></i>: 
for <font color="Olive">CP</font> being <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> holds  <font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">CP</font> <a href="hidden.html#R1">=</a> <font color="Olive">CP</font> <a href="conlat_2.html#K9" target="_self">.:</a> 
 ;<br/>

<b>assume </b><a NAME="E2:34_1_2"/><i><font color="Green">E167</font></i>: 
for <font color="Olive">CP</font> being <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> holds  <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">CP</font> <a href="hidden.html#R1">=</a> <font color="Olive">CP</font> <a href="conlat_2.html#K9" target="_self">.:</a> 
 ;<br/>

<a NAME="E3:34_1_2"/><i><font color="Green">E168</font></i>: 
for <font color="Olive">u</font> being   <a href="hidden.html#M1">set</a>   st <font color="Olive">u</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="lattice2.html#K1">.:</a> </span>)</span> holds <br/><font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Olive">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Olive">u</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="34_1_2_1"><b>proof </b></a><div class="add">

<b>let </b><font color="Maroon">u</font> be    <a href="hidden.html#M1">set</a> ;<br/>

<b>assume </b><a NAME="E1:34_1_2_1"/><i><font color="Green">E169</font></i>: 
<font color="Maroon">u</font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="lattice2.html#K1">.:</a> </span>)</span>
 ;<br/>

<a NAME="E2:34_1_2_1"/>
 <a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font> <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="conlat_1.html#K8">B-carrier</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10">B-join</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9">B-meet</a> <font color="Maroon">C</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="conlat_1.html#D23">CONLAT_1:def 23</a></i>;<br/>
<a NAME="E3:34_1_2_1"/><b>then </b>
<span class="p1">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="lattice2.html#K1">.:</a>  <a href="hidden.html#R1">=</a>  <a href="lattices.html#G3">LattStr</a>(# <span class="p1">(<span class="default"><a href="conlat_1.html#K8">B-carrier</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9">B-meet</a> <font color="Maroon">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10">B-join</a> <font color="Maroon">C</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="lattice2.html#D2">LATTICE2:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon">u</font> = <font color="Maroon">u</font> as  <a href="conlat_1.html#V6">strict</a> <a href="conlat_1.html#NM4">FormalConcept</a> of <font color="Maroon">C</font> <b>by </b><i>, <a class="ref" href="conlat_1.html#T35">CONLAT_1:35</a></i>;<br/>
<font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font> = 
<font color="Maroon">u</font> <a href="conlat_2.html#K9" target="_self">.:</a> 
<b>by </b><i/>
<br/>.= 
<font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font>
<b>by </b><i/>
;<br/>
<b>hence </b><a NAME="E6:34_1_2_1"/>
<font color="Maroon">F1</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font> <a href="funct_1.html#K1">.</a> <font color="Maroon">u</font>
 ;<br/>


</div><b>end;</b></div>
<a NAME="E4:34_1_2"/><i><font color="Green">E170</font></i>: 
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="lattice2.html#K1">.:</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:34_1_2"/>
 <a href="relset_1.html#K4">dom</a> <font color="Maroon">F2</font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11">ConceptLattice</a> <font color="Maroon">C</font></span>)</span> <a href="lattice2.html#K1">.:</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:34_1_2"/>
<font color="Maroon">F1</font> <a href="hidden.html#R1">=</a> <font color="Maroon">F2</font>
 <b>by </b><i>, , <a class="ref" href="funct_1.html#T9">FUNCT_1:9</a></i>;<br/>


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