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<b>let </b><font color="Maroon" title="c1">CL</font> be   <a href="lattices.html#NM7" title="LATTICES:NM.7">C_Lattice</a>;<br/><b>let </b><font color="Maroon" title="c2">IL</font> be  <a href="filter_0.html#V3" title="FILTER_0:attr.3">implicative</a> <a href="lattices.html#NM1" title="LATTICES:NM.1">Lattice</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be    <a href="lattice4.html#M1" title="LATTICE4:mode.1">Homomorphism</a> of <font color="Maroon" title="c2">IL</font>,<font color="Maroon" title="c1">CL</font>;<br/><b>let </b><font color="Maroon" title="c4">i</font>, <font color="Maroon" title="c5">k</font>, <font color="Maroon" title="c6">j</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">IL</font>;<br/>











<b>assume </b><a NAME="E1:37"/><i><font color="Green" title="E37">A1</font></i>: 
<font color="Maroon" title="c3">f</font> is <a href="lattice4.html#V1" title="LATTICE4:attr.1">monomorphism</a>
 ;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:37_1"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">i</font></span>)</span> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">j</font>
 ;<br/><a NAME="E2:37_1"/><b>then </b>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">k</font></span>)</span> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c6">j</font>
 <b>by </b><i><a class="ref" href="lattice4.html#D1" target="_self" title="LATTICE4:def.1">Def1</a></i>;<br/><a NAME="E3:37_1"/><b>then </b>
<font color="Maroon" title="c4">i</font> <a href="lattices.html#K4" title="LATTICES:func.4">"/\"</a> <font color="Maroon" title="c5">k</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c6">j</font>
 <b>by </b><i><a class="txt" href="lattice4.html#E1:37"><i><font color="Green" title="E37">A1</font></i></a>, <a class="ref" href="lattice4.html#T8" target="_self" title="LATTICE4:th.8">Th8</a></i>;<br/><a NAME="E4:37_1"/><b>then </b>
<font color="Maroon" title="c5">k</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c4">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">j</font>
 <b>by </b><i><a class="ref" href="filter_0.html#D8" title="FILTER_0:def.8">FILTER_0:def 8</a></i>;<br/><b>hence </b><a NAME="E5:37_1"/>
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c5">k</font> <a href="lattices.html#R3" title="LATTICES:pred.3">[=</a> <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">i</font> <a href="filter_0.html#K4" title="FILTER_0:func.4">=&gt;</a> <font color="Maroon" title="c6">j</font></span>)</span>
 <b>by </b><i><a class="ref" href="lattice4.html#T7" target="_self" title="LATTICE4:th.7">Th7</a></i>;<br/></div>
<b>end;</b></div>


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