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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be   <a href="yellow_0.html#V1" title="YELLOW_0:attr.1">lower-bounded</a>   <a href="waybel_3.html#V3" title="WAYBEL_3:attr.3">continuous</a>  <a href="waybel_0.html#NM7" title="WAYBEL_0:NM.7">sup-Semilattice</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">B</font> being  <a href="waybel23.html#V6" title="WAYBEL23:attr.6">with_bottom</a>   <a href="waybel23.html#M1" title="WAYBEL23:mode.1">CLbasis</a> of <font color="Maroon" title="c1">L</font> holds   <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p3">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Olive" title="b1">B</font></span>)</span></span>)</span></span>)</span>, <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Olive" title="b1">B</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">B</font> be   <a href="waybel23.html#V6" title="WAYBEL23:attr.6">with_bottom</a>   <a href="waybel23.html#M1" title="WAYBEL23:mode.1">CLbasis</a> of <font color="Maroon" title="c1">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p3">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span></span>)</span>, <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> </span><br/>



<span class="kw">deffunc </span><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span>) <span class="kw">-&gt; </span>   <a href="subset_1.html#M1" title="SUBSET_1:mode.1">Element</a> of <a href="zfmisc_1.html#K1" title="ZFMISC_1:func.1">K10</a>(the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span>) =  <a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> $1;<br/>
<a NAME="E1:109"/><span class="lab"><font color="Green" title="E61">A1</font></span>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>) is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p4">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span></span>)</span></span>)</span>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="109_1"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">x</font>) is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p4">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span></span>)</span></span>)</span></span><br/>

<a NAME="E1:109_1"/>
 <a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Maroon" title="c3">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><a href="waybel_0.html#K5" title="WAYBEL_0:func.5">downarrow</a> <font color="Olive" title="b1">b</font></span>)</span> where <font color="Olive" title="b1">b</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> : verum </span>}</span> 
 
;<br/>
<span class="kw">hence </span><a NAME="E2:109_1"/>
<font color="Maroon">H<sub>1</sub></font>(<font color="Maroon" title="c3">x</font>) is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p4">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel23.html#T69" target="_self" title="WAYBEL23:th.69">Th69</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


</div><span class="kw">end;</span></div>
<span class="kw">consider </span><font color="Maroon" title="c3">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span>,<span class="p1">(<span class="default"><a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p2">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p3">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p4">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span></span>)</span></span>)</span><span class="kw"> such that </span><br/><a NAME="E3:109"/><span class="lab"><font color="Green" title="E62">A2</font></span>: 
for <font color="Olive" title="b1">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span> holds  <font color="Maroon" title="c3">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">x</font>)
 <span class="kw">from</span> <span class="lab"><a class="ref" href="funct_2.html#S9" title="FUNCT_2:sch.9">FUNCT_2:sch 9</a>(<a class="txt" href="#E1:109"><span class="lab"><font color="Green" title="E61">A1</font></span></a>);<br/></span>
<a NAME="E4:109"/>
<font color="Maroon" title="c3">f</font> is  <a href="waybel_0.html#V23" title="WAYBEL_0:attr.23">isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:109"><span class="lab"><font color="Green" title="E62">A2</font></span></a>, <a class="ref" href="waybel13.html#T13" title="WAYBEL13:th.13">WAYBEL13:13</a></span>;<br/>
<a NAME="E5:109"/><span class="kw">then </span>
 <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font>, <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p3">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span></span>)</span> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_1.html#D8" title="WAYBEL_1:def.8">WAYBEL_1:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E6:109"/>
 <a href="waybel_8.html#K1" title="WAYBEL_8:func.1">CompactSublatt</a> <span class="p1">(<span class="default"><a href="yellow_1.html#K2" title="YELLOW_1:func.2">InclPoset</a> <span class="p2">(<span class="default"><a href="waybel_0.html#K7" title="WAYBEL_0:func.7">Ids</a> <span class="p3">(<span class="default"><a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font></span>)</span></span>)</span></span>)</span>, <a href="yellow_0.html#K5" title="YELLOW_0:func.5">subrelstr</a> <font color="Maroon" title="c2">B</font> <a href="waybel_1.html#R5" title="WAYBEL_1:pred.5">are_isomorphic</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_1.html#T7" title="WAYBEL_1:th.7">WAYBEL_1:7</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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