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<b>deffunc </b><font color="Maroon">H<sub>1</sub></font>(  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>()) <b>-&gt; </b>  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>1</sub></font>() = <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default">the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> $1</span>)</span>);<br/>
<a NAME="E1:24_1"/><i><font color="Green" title="E15">A1</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">i</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 <font color="Maroon">F<sub>1</sub></font>()
 
;<br/>
<b>consider </b><font color="Maroon" title="c1">f</font> being   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>1</sub></font>()<b> such that </b><br/><a NAME="E3:24_1"/><i><font color="Green" title="E16">A2</font></i>: 
for <font color="Olive" title="b1">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon">F<sub>2</sub></font>() holds  <font color="Maroon" title="c1">f</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">H<sub>1</sub></font>(<font color="Olive" title="b1">i</font>)
 <b>from </b><i><a class="ref" href="funct_2.html#S8" title="FUNCT_2:sch.8">FUNCT_2:sch 8</a>(<a class="txt" href="waybel_2.html#E1:24_1"><i><font color="Green" title="E15">A1</font></i></a>);<br/></i>
<b>set </b><font color="Maroon" title="c2">M</font> =  <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c1">f</font> #);<br/>
<a NAME="E4:24_1"/>
 <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c1">f</font> #) is <a href="waybel_0.html#V7" title="WAYBEL_0:attr.7">directed</a>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="24_1_1"><b>proof </b></a><div class="add">

<a NAME="E1:24_1_1"/><i><font color="Green" title="E17">A3</font></i>: 
 <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c1">f</font> #),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c1">f</font> #) #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>() #)
 
;<br/>
<a NAME="E2:24_1_1"/><i><font color="Green" title="E18">A4</font></i>: 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon">F<sub>2</sub></font>() is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 
<b>by </b><i><a class="ref" href="waybel_0.html#D6" title="WAYBEL_0:def.6">WAYBEL_0:def 6</a></i>;<br/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon">F<sub>2</sub></font>() = 
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>()
<b>by </b><i><a class="ref" href="pre_topc.html#T12" title="PRE_TOPC:th.12">PRE_TOPC:12</a></i>
<br/>.= 
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c1">f</font> #)
<b>by </b><i><a class="ref" href="pre_topc.html#T12" title="PRE_TOPC:th.12">PRE_TOPC:12</a></i>
;<br/>
<b>hence </b><a NAME="E4:24_1_1"/>
 <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c1">f</font> #) is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 <b>by </b><i><a class="txt" href="waybel_2.html#E1:24_1_1"><i><font color="Green" title="E17">A3</font></i></a>, <a class="txt" href="waybel_2.html#E2:24_1_1"><i><font color="Green" title="E18">A4</font></i></a>, <a class="ref" href="waybel_0.html#T3" title="WAYBEL_0:th.3">WAYBEL_0:3</a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="waybel_0.html#D6" title="WAYBEL_0:def.6">WAYBEL_0:def 6</a><br/>


</div><b>end;</b></div>
<b>then reconsider </b><font color="Maroon" title="c3">M</font> =  <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>(),<font color="Maroon" title="c1">f</font> #) as   <a href="waybel_0.html#NM1" title="WAYBEL_0:NM.1">prenet</a> of <font color="Maroon">F<sub>1</sub></font>() ;<br/>
<b>take </b>
<font color="Maroon" title="c3">M</font>
;<br/>

<b>thus </b><a NAME="E6:24_1"/>
(  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">M</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c3">M</font> #) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="orders_2.html#G1" title="ORDERS_2:aggr.1">RelStr</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon">F<sub>2</sub></font>(),the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon">F<sub>2</sub></font>() #) &amp; ( for <font color="Olive" title="b1">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c3">M</font> holds  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c3">M</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">i</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon">F<sub>3</sub></font>(<span class="p1">(<span class="default">the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon">F<sub>2</sub></font>() <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b1">i</font></span>)</span>) ) )
 <b>by </b><i><a class="txt" href="waybel_2.html#E3:24_1"><i><font color="Green" title="E16">A2</font></i></a></i>;<br/>


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