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<b>let </b><font color="Maroon" title="c1">S</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/><b>let </b><font color="Maroon" title="c2">A</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/>



<b>assume </b><a NAME="E1:12"/><i><font color="Green" title="E11">A1</font></i>: 
<font color="Maroon" title="c2">A</font> <a href="waybel22.html#R1" title="WAYBEL22:pred.1">is_FreeGen_set_of</a> <font color="Maroon" title="c1">S</font>
 ;<br/>

<b>consider </b><font color="Maroon" title="c3">T</font> being  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a> <a href="lattice3.html#V3" title="LATTICE3:attr.3">complete</a> <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a> <a href="orders_2.html#NM1" title="ORDERS_2:NM.1">Poset</a>;<br/>
<b>consider </b><font color="Maroon" title="c4">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">A</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">T</font>;<br/>
<b>consider </b><font color="Maroon" title="c5">h</font> being    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">T</font><b> such that </b><br/><a NAME="E5:12"/><i><font color="Green" title="E12">A2</font></i>: 
<font color="Maroon" title="c5">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font>
 <b>and </b><br/><a NAME="E6:12"/>
for <font color="Olive" title="b1">h'</font> being   <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c3">T</font>  st <font color="Olive" title="b1">h'</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">f</font> holds <br/><font color="Olive" title="b1">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <font color="Maroon" title="c5">h</font>
 <b>by </b><i><a class="txt" href="waybel22.html#E1:12"><i><font color="Green" title="E11">A1</font></i></a>, <a class="ref" href="waybel22.html#D1" target="_self" title="WAYBEL22:def.1">Def1</a></i>;<br/>
<a NAME="E7:12"/>
 <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">h</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c5">h</font></span>)</span> <a href="subset_1.html#K8" title="SUBSET_1:func.8">/\</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="ref" href="relat_1.html#T90" title="RELAT_1:th.90">RELAT_1:90</a></i>;<br/>
<b>hence </b><a NAME="E8:12"/>
<font color="Maroon" title="c2">A</font> is   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>
 <b>by </b><i><a class="txt" href="waybel22.html#E5:12"><i><font color="Green" title="E12">A2</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>


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