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<b>let </b><font color="Maroon" title="c2">F1</font>, <font color="Maroon" title="c3">F2</font> be    <a href="lattice4.html#M1" title="LATTICE4:mode.1">Homomorphism</a> of <span class="p1">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> , <a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <span class="p1">(<span class="default"><font color="Maroon" title="c1">C</font> <a href="conlat_2.html#K7" title="CONLAT_2:func.7">.:</a> </span>)</span>; <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">CP</font> being <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c2">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">CP</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">CP</font> <a href="conlat_2.html#K9" title="CONLAT_2:func.9">.:</a>  ) &amp; ( for <font color="Olive" title="b1">CP</font> being <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">CP</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">CP</font> <a href="conlat_2.html#K9" title="CONLAT_2:func.9">.:</a>  ) implies <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> )</span><br/>

<b>assume </b><a NAME="E1:34_1_2"/><i><font color="Green" title="E20">A65</font></i>: 
for <font color="Olive" title="b1">CP</font> being <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c2">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">CP</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">CP</font> <a href="conlat_2.html#K9" title="CONLAT_2:func.9">.:</a> 
 ; <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#V4" title="CONLAT_1:attr.4">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> st not <font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">CP</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">CP</font> <a href="conlat_2.html#K9" title="CONLAT_2:func.9">.:</a>  or <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> )</span><br/>

<b>assume </b><a NAME="E2:34_1_2"/><i><font color="Green" title="E21">A66</font></i>: 
for <font color="Olive" title="b1">CP</font> being <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> holds  <font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">CP</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">CP</font> <a href="conlat_2.html#K9" title="CONLAT_2:func.9">.:</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font></span><br/>

<a NAME="E3:34_1_2"/><i><font color="Green" title="E22">A67</font></i>: 
for <font color="Olive" title="b1">u</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> holds <br/><font color="Maroon" title="c2">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">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" title="c4">u</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span> implies <font color="Maroon" title="c2">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">u</font> )</span><br/>

<b>assume </b><a NAME="E1:34_1_2_1"/><i><font color="Green" title="E23">A68</font></i>: 
<font color="Maroon" title="c4">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c2">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">u</font></span><br/>

<a NAME="E2:34_1_2_1"/>
 <a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<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="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="conlat_1.html#D23" title="CONLAT_1:def.23">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" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="lattices.html#G3" title="LATTICES:aggr.3">LattStr</a>(# <span class="p1">(<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="p1">(<span class="default"><a href="conlat_1.html#K9" title="CONLAT_1:func.9">B-meet</a> <font color="Maroon" title="c1">C</font></span>)</span>,<span class="p1">(<span class="default"><a href="conlat_1.html#K10" title="CONLAT_1:func.10">B-join</a> <font color="Maroon" title="c1">C</font></span>)</span> #)
 
<b>by </b><i><a class="ref" href="lattice2.html#D2" title="LATTICE2:def.2">LATTICE2:def 2</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c5">u</font> = <font color="Maroon" title="c4">u</font> as  <a href="conlat_1.html#V4" title="CONLAT_1:attr.4">strict</a> <a href="conlat_1.html#NM4" title="CONLAT_1:NM.4">FormalConcept</a> of <font color="Maroon" title="c1">C</font> <b>by </b><i><a class="txt" href="#E1:34_1_2_1"><i><font color="Green" title="E23">A68</font></i></a>, <a class="ref" href="conlat_1.html#T35" title="CONLAT_1:th.35">CONLAT_1:35</a></i>;<br/>
<font color="Maroon" title="c2">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">u</font> = 
<font color="Maroon" title="c5">u</font> <a href="conlat_2.html#K9" title="CONLAT_2:func.9">.:</a> 
<b>by </b><i><a class="txt" href="#E1:34_1_2"><i><font color="Green" title="E20">A65</font></i></a></i>
<br/>.= 
<font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c5">u</font>
<b>by </b><i><a class="txt" href="#E2:34_1_2"><i><font color="Green" title="E21">A66</font></i></a></i>
;<br/>
<b>hence </b><a NAME="E6:34_1_2_1"/>
<font color="Maroon" title="c2">F1</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">u</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="E4:34_1_2"/><i><font color="Green" title="E23">A69</font></i>: 
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<a NAME="E5:34_1_2"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">F2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="conlat_1.html#K11" title="CONLAT_1:func.11">ConceptLattice</a> <font color="Maroon" title="c1">C</font></span>)</span> <a href="lattice2.html#K1" title="LATTICE2:func.1">.:</a> </span>)</span>
 
<b>by </b><i><a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>hence </b><a NAME="E6:34_1_2"/>
<font color="Maroon" title="c2">F1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">F2</font>
 <b>by </b><i><a class="txt" href="#E3:34_1_2"><i><font color="Green" title="E22">A67</font></i></a>, <a class="txt" href="#E4:34_1_2"><i><font color="Green" title="E23">A69</font></i></a>, <a class="ref" href="funct_1.html#T9" title="FUNCT_1:th.9">FUNCT_1:9</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>
