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<b>let </b><font color="Maroon" title="c1">R</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>let </b><font color="Maroon" title="c2">S</font> be  non <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">S</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">R</font>;<br/>





<b>assume </b><a NAME="E1:48"/><i><font color="Green" title="E25">A1</font></i>: 
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font> is <a href="waybel_0.html#V1" title="WAYBEL_0:attr.1">directed</a>
 ;<br/>

<b>set </b><font color="Maroon" title="c4">N</font> =  <a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font>;<br/>
<b>let </b><font color="Maroon" title="c5">x</font>, <font color="Maroon" title="c6">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>; <i><font color="Red">:: according to </font></i><a class="ref" href="yellow_6.html#D5" title="YELLOW_6:def.5">YELLOW_6:def 5</a><br/>

<a NAME="E2:48"/><i><font color="Green" title="E26">A2</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span>
 
<b>by </b><i><a class="ref" href="waybel11.html#D10" target="_self" title="WAYBEL11:def.10">Def10</a></i>;<br/>
<a NAME="E3:48"/><b>then </b>
 <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">{<span class="default"> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Olive" title="b1">i</font></span>)</span> where <font color="Olive" title="b1">i</font> is   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> : verum </span>}</span> 
 
<b>by </b><i><a class="ref" href="waybel11.html#T19" target="_self" title="WAYBEL11:th.19">Th19</a></i>;<br/>
<a NAME="E4:48"/><b>then </b>
( <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font> &amp; <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font> )
 
;<br/>
<b>then consider </b><font color="Maroon" title="c7">p</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">R</font><b> such that </b><br/><a NAME="E6:48"/><i><font color="Green" title="E27">A3</font></i>: 
<font color="Maroon" title="c7">p</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K5" title="RELSET_1:func.5">rng</a> <font color="Maroon" title="c3">f</font>
 <b>and </b><br/><a NAME="E7:48"/><i><font color="Green" title="E28">A4</font></i>: 
( <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">p</font> &amp; <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c7">p</font> )
 <b>by </b><i><a class="txt" href="waybel11.html#E1:48"><i><font color="Green" title="E25">A1</font></i></a>, <a class="ref" href="waybel_0.html#D1" title="WAYBEL_0:def.1">WAYBEL_0:def 1</a></i>;<br/>
<b>consider </b><font color="Maroon" title="c8">z</font> being    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> <b> such that </b><br/><a NAME="E9:48"/><i><font color="Green" title="E29">A5</font></i>: 
<font color="Maroon" title="c8">z</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K4" title="RELSET_1:func.4">dom</a> <font color="Maroon" title="c3">f</font>
 <b>and </b><br/><a NAME="E10:48"/><i><font color="Green" title="E30">A6</font></i>: 
<font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">f</font> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c8">z</font>
 <b>by </b><i><a class="txt" href="waybel11.html#E6:48"><i><font color="Green" title="E27">A3</font></i></a>, <a class="ref" href="funct_1.html#D5" title="FUNCT_1:def.5">FUNCT_1:def 5</a></i>;<br/>
<b>reconsider </b><font color="Maroon" title="c9">z</font> = <font color="Maroon" title="c8">z</font> as   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <b>by </b><i><a class="txt" href="waybel11.html#E2:48"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="waybel11.html#E9:48"><i><font color="Green" title="E29">A5</font></i></a>, <a class="ref" href="funct_2.html#D1" title="FUNCT_2:def.1">FUNCT_2:def 1</a></i>;<br/>
<b>take </b>
<font color="Maroon" title="c9">z</font>
;<br/>

<a NAME="E12:48"/>
<font color="Maroon" title="c7">p</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">S</font>,<font color="Maroon" title="c3">f</font></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c9">z</font>
 
<b>by </b><i><a class="txt" href="waybel11.html#E2:48"><i><font color="Green" title="E26">A2</font></i></a>, <a class="txt" href="waybel11.html#E10:48"><i><font color="Green" title="E30">A6</font></i></a></i>;<br/>
<b>hence </b><a NAME="E13:48"/>
( <font color="Maroon" title="c5">x</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">z</font> &amp; <font color="Maroon" title="c6">y</font> <a href="orders_2.html#R1" title="ORDERS_2:pred.1">&lt;=</a> <font color="Maroon" title="c9">z</font> )
 <b>by </b><i><a class="txt" href="waybel11.html#E7:48"><i><font color="Green" title="E28">A4</font></i></a>, <a class="ref" href="waybel11.html#D10" target="_self" title="WAYBEL11:def.10">Def10</a></i>;<br/>


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