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<span class="kw">let </span><font color="Maroon" title="c1">S</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="orders_2.html#V3" title="ORDERS_2:attr.3">reflexive</a>   <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">D</font> being   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font> holds <br/> (  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Olive" title="b1">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Olive" title="b1">D</font> &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Olive" title="b1">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">D</font> &amp;  <a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Olive" title="b1">D</font> is   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">S</font> )</span><br/><span class="kw">let </span><font color="Maroon" title="c2">D</font> be   non  <a href="xboole_0.html#V1" title="XBOOLE_0:attr.1">empty</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">S</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c2">D</font> &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D</font> &amp;  <a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font> is   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">S</font> )</span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">N</font> =  <a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font>;<br/>
<a NAME="E1:41"/><span class="lab"><font color="Green" title="E22">A1</font></span>: 
 <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></span>;<br/>
<a NAME="E2:41"/>
 <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="relat_1.html#T45" title="RELAT_1:th.45">RELAT_1:45</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">g</font> =  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c2">D</font> as   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <font color="Maroon" title="c2">D</font>, the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:41"><span class="lab"><font color="Green" title="E22">A1</font></span></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#T4" title="RELSET_1:th.4">RELSET_1:4</a></span>;<br/>
<a NAME="E4:41"/>
<span class="p1">(<span class="default"><a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a>  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">S</font></span>)</span> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> <font color="Maroon" title="c2">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c2">D</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_3.html#T1" title="FUNCT_3:th.1">FUNCT_3:1</a></span>;<br/>
<a NAME="E5:41"/><span class="kw">then </span><span class="lab"><font color="Green" title="E23">A2</font></span>: 
 <a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel_0.html#G1" title="WAYBEL_0:aggr.1">NetStr</a>(# <font color="Maroon" title="c2">D</font>,<span class="p1">(<span class="default"> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font> <a href="toler_1.html#K1" title="TOLER_1:func.1">|_2</a> <font color="Maroon" title="c2">D</font></span>)</span>,<font color="Maroon" title="c4">g</font> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel17.html#D4" title="WAYBEL17:def.4">WAYBEL17:def 4</a></span>;<br/>
<a NAME="E6:41"/><span class="kw">then </span>
 the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="relset_1.html#R1" title="RELSET_1:pred.1">c=</a>  the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c1">S</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="xboole_1.html#T17" title="XBOOLE_1:th.17">XBOOLE_1:17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E7:41"/>
(  the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="partfun1.html#K6" title="PARTFUN1:func.6">id</a> <font color="Maroon" title="c2">D</font> &amp;  the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">D</font> &amp;  <a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Maroon" title="c2">D</font> is   <a href="yellow_0.html#V4" title="YELLOW_0:attr.4">full</a>   <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c1">S</font> )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:41"><span class="lab"><font color="Green" title="E23">A2</font></span></a>, <a class="ref" href="yellow_0.html#D13" title="YELLOW_0:def.13">YELLOW_0:def 13</a>, <a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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