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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>; <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">A</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">A</font> <a href="waybel22.html#R1" title="WAYBEL22:pred.1">is_FreeGen_set_of</a> <font color="Maroon" title="c1">S</font> holds <br/>for <font color="Olive" title="b2">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="c1">S</font>  st <font color="Olive" title="b2">h'</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Olive" title="b1">A</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Olive" title="b1">A</font> holds <br/><font color="Olive" title="b2">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font></span><br/><b>let </b><font color="Maroon" title="c2">A</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="c2">A</font> <a href="waybel22.html#R1" title="WAYBEL22:pred.1">is_FreeGen_set_of</a> <font color="Maroon" title="c1">S</font> implies 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="c1">S</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>  <a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font> )</span><br/>



<b>assume </b><a NAME="E1:13"/><i><font color="Green" title="E12">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>
 ; <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">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="c1">S</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>  <a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font> holds <br/><font color="Olive" title="b1">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font></span><br/>

<b>set </b><font color="Maroon" title="c3">L</font> = <font color="Maroon" title="c1">S</font>;<br/>
<a NAME="E2:13"/><i><font color="Green" title="E13">A2</font></i>: 
<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="#E1:13"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="waybel22.html#T7" target="_self" title="WAYBEL22:th.7">Th7</a></i>;<br/>
<a NAME="E3:13"/>
(  <a href="relat_1.html#NK2" title="RELAT_1:NK.2">dom</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> &amp;  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">A</font> )
 
<b>by </b><i><a class="ref" href="relat_1.html#T71" title="RELAT_1:th.71">RELAT_1:71</a></i>;<br/>
<b>then reconsider </b><font color="Maroon" title="c4">f</font> =  <a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font> as   <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="c1">S</font> <b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a>, <a class="ref" href="relset_1.html#T11" title="RELSET_1:th.11">RELSET_1:11</a></i>;<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="c1">S</font><b> such that </b><br/><a NAME="E6:13"/>
<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="E7:13"/><i><font color="Green" title="E14">A3</font></i>: 
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="c1">S</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="#E1:13"><i><font color="Green" title="E12">A1</font></i></a>, <a class="ref" href="waybel22.html#D1" target="_self" title="WAYBEL22:def.1">Def1</a></i>;<br/>
<b>let </b><font color="Maroon" title="c6">h'</font> be    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c6">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>  <a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font> implies <font color="Maroon" title="c6">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font> )</span><br/>

<b>assume </b><a NAME="E8:13"/><i><font color="Green" title="E15">A4</font></i>: 
<font color="Maroon" title="c6">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>  <a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c6">h'</font> <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a>  <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font></span><br/>

<a NAME="E9:13"/><i><font color="Green" title="E16">A5</font></i>: 
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font> is    <a href="waybel16.html#M1" title="WAYBEL16:mode.1">CLHomomorphism</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c1">S</font>
 
<b>by </b><i><a class="ref" href="waybel22.html#T5" target="_self" title="WAYBEL22:th.5">Th5</a></i>;<br/>
<a NAME="E10:13"/><i><font color="Green" title="E17">A6</font></i>: 
<span class="p1">(<span class="default"><a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font></span>)</span> <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>  <a href="pralg_3.html#K1" title="PRALG_3:func.1">id</a> <font color="Maroon" title="c2">A</font>
 
<b>by </b><i><a class="txt" href="#E2:13"><i><font color="Green" title="E13">A2</font></i></a>, <a class="ref" href="funct_3.html#T1" title="FUNCT_3:th.1">FUNCT_3:1</a></i>;<br/>
<b>thus </b><font color="Maroon" title="c6">h'</font> = 
<font color="Maroon" title="c5">h</font>
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="#E8:13"><i><font color="Green" title="E15">A4</font></i></a></i>
<br/>.= 
 <a href="struct_0.html#K3" title="STRUCT_0:func.3">id</a> <font color="Maroon" title="c1">S</font>
<b>by </b><i><a class="txt" href="#E7:13"><i><font color="Green" title="E14">A3</font></i></a>, <a class="txt" href="#E9:13"><i><font color="Green" title="E16">A5</font></i></a>, <a class="txt" href="#E10:13"><i><font color="Green" title="E17">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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