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<span class="kw">let </span><font color="Maroon" title="c1">L</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="struct_0.html#L1" title="STRUCT_0:struct.1">1-sorted</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">N</font> being non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="waybel_0.html#L1" title="WAYBEL_0:struct.1">NetStr</a> of <font color="Maroon" title="c1">L</font><br/> for <font color="Olive" title="b2">i</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Olive" title="b1">N</font> holds  <font color="Olive" title="b1">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Olive" title="b2">i</font> is   <a href="yellow_6.html#V2" title="YELLOW_6:attr.2">full</a>   <a href="yellow_6.html#M1" title="YELLOW_6:mode.1">SubNetStr</a> of <font color="Olive" title="b1">N</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">N</font> be  non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="waybel_0.html#L1" title="WAYBEL_0:struct.1">NetStr</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"> 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="c2">N</font> holds  <font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Olive" title="b1">i</font> is   <a href="yellow_6.html#V2" title="YELLOW_6:attr.2">full</a>   <a href="yellow_6.html#M1" title="YELLOW_6:mode.1">SubNetStr</a> of <font color="Maroon" title="c2">N</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">i</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font> is   <a href="yellow_6.html#V2" title="YELLOW_6:attr.2">full</a>   <a href="yellow_6.html#M1" title="YELLOW_6:mode.1">SubNetStr</a> of <font color="Maroon" title="c2">N</font></span><br/>





<a NAME="E1:43"/><span class="lab"><font color="Green" title="E21">A1</font></span>: 
the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c2">N</font> <a href="partfun1.html#K2" title="PARTFUN1:func.2">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D7" target="_self" title="WAYBEL_9:def.7">Def7</a></span>;<br/>
<a NAME="E2:43"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">N</font> <a href="toler_1.html#K1" title="TOLER_1:func.1">|_2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D7" target="_self" title="WAYBEL_9:def.7">Def7</a></span>;<br/>
<a NAME="E3:43"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A2</font></span>: 
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</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="c2">N</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/>
<a NAME="E4:43"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <span class="p1">(<span class="default"><font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font></span>)</span> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#T13" target="_self" title="WAYBEL_9:th.13">Th13</a></span>;<br/>
<a NAME="E5:43"/><span class="kw">then </span>
<font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font> is    <a href="yellow_0.html#M1" title="YELLOW_0:mode.1">SubRelStr</a> of <font color="Maroon" title="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:43"><span class="lab"><font color="Green" title="E22">A2</font></span></a>, <a class="ref" href="yellow_0.html#D13" title="YELLOW_0:def.13">YELLOW_0:def 13</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c4">K</font> = <font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font> as    <a href="yellow_6.html#M1" title="YELLOW_6:mode.1">SubNetStr</a> of <font color="Maroon" title="c2">N</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:43"><span class="lab"><font color="Green" title="E21">A1</font></span></a>, <a class="ref" href="yellow_6.html#D8" title="YELLOW_6:def.8">YELLOW_6:def 8</a></span>;<br/>
<a NAME="E7:43"/>
the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c4">K</font> <a href="relset_1.html#R2" title="RELSET_1:pred.2">=</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">N</font> <a href="toler_1.html#K1" title="TOLER_1:func.1">|_2</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c4">K</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D7" target="_self" title="WAYBEL_9:def.7">Def7</a></span>;<br/>
<a NAME="E8:43"/><span class="kw">then </span>
<font color="Maroon" title="c4">K</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="c2">N</font>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_0.html#D14" title="YELLOW_0:def.14">YELLOW_0:def 14</a>, <a class="ref" href="yellow_6.html#D8" title="YELLOW_6:def.8">YELLOW_6:def 8</a></span>;<br/>
<span class="kw">hence </span><a NAME="E9:43"/>
<font color="Maroon" title="c2">N</font> <a href="waybel_9.html#K5" title="WAYBEL_9:func.5">|</a> <font color="Maroon" title="c3">i</font> is   <a href="yellow_6.html#V2" title="YELLOW_6:attr.2">full</a>   <a href="yellow_6.html#M1" title="YELLOW_6:mode.1">SubNetStr</a> of <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="yellow_6.html#D9" title="YELLOW_6:def.9">YELLOW_6:def 9</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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