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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="Red">::  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   <a href="waybel17.html#K4" title="WAYBEL17:func.4">Net-Str</a> <font color="Olive" title="b1">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Olive" title="b1">D</font>,<span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Olive" title="b1">D</font></span>)</span></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="Red">::  thesis: </font></span></a><span class="hide">  <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="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">D</font>,<span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">M</font> =  <a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">D</font>,<span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span>;<br/>
<a NAME="E1:26"/><span class="lab"><font color="Green" title="E17">A1</font></span>: 
<font color="Maroon" title="c2">D</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel11.html#D10" title="WAYBEL11:def.10">WAYBEL11:def 10</a></span>;<br/>
<a NAME="E2:26"/><span class="lab"><font color="Green" title="E18">A2</font></span>: 
<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel11.html#D10" title="WAYBEL11:def.10">WAYBEL11:def 10</a></span>;<br/>
<a NAME="E3:26"/><span class="lab"><font color="Green" title="E19">A3</font></span>: 
<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font> <a href="funct_2.html#R1" title="FUNCT_2: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="E4:26"/><span class="lab"><font color="Green" title="E20">A4</font></span>: 
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> <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/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="26_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c5">y</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> ) &amp; ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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><br/><div><span class="kw">hereby </span> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> implies <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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>
<div class="add"><span class="kw">assume </span><a NAME="E1:26_1_1"/><span class="lab"><font color="Green" title="E21">A5</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span></span><br/><a NAME="E2:26_1_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A6</font></span>: 
<font color="Maroon" title="c4">x</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E3:26_1_1"/><span class="lab"><font color="Green" title="E23">A7</font></span>: 
<font color="Maroon" title="c5">y</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">D</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><span class="kw">reconsider </span><font color="Maroon" title="c6">x9</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c7">y9</font> = <font color="Maroon" title="c5">y</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E5:26_1_1"/><span class="lab"><font color="Green" title="E24">A8</font></span>: 
<font color="Maroon" title="c6">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E2:26_1_1"><span class="lab"><font color="Green" title="E22">A6</font></span></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></span>;<br/><a NAME="E6:26_1_1"/>
<font color="Maroon" title="c7">y9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="txt" href="#E3:26_1_1"><span class="lab"><font color="Green" title="E23">A7</font></span></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></span>;<br/><a NAME="E7:26_1_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">x9</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c7">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E4:26"><span class="lab"><font color="Green" title="E20">A4</font></span></a>, <a class="txt" href="#E1:26_1_1"><span class="lab"><font color="Green" title="E21">A5</font></span></a>, <a class="txt" href="#E5:26_1_1"><span class="lab"><font color="Green" title="E24">A8</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E8:26_1_1"/><span class="kw">then </span>
<font color="Maroon" title="c6">x9</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel11.html#D10" title="WAYBEL11:def.10">WAYBEL11:def 10</a></span>;<br/><span class="kw">hence </span><a NAME="E9:26_1_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2: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/></div>
<span class="kw">end;</span></div><span class="kw">assume </span><a NAME="E2:26_1"/><span class="lab"><font color="Green" title="E21">A9</font></span>: 
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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><br/><span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c6">x9</font> = <font color="Maroon" title="c4">x</font>, <font color="Maroon" title="c7">y9</font> = <font color="Maroon" title="c5">y</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">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="zfmisc_1.html#T106" title="ZFMISC_1:th.106">ZFMISC_1:106</a></span>;<br/><a NAME="E4:26_1"/>
<font color="Maroon" title="c6">x9</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <font color="Maroon" title="c7">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="ref" href="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E5:26_1"/><span class="kw">then </span>
<span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">x9</font> <a href="orders_2.html#R3" title="ORDERS_2:pred.3">&lt;=</a> <span class="p1">(<span class="default"><a href="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">D</font>,<span class="p2">(<span class="default"><span class="p3">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c7">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="waybel11.html#D10" title="WAYBEL11:def.10">WAYBEL11:def 10</a></span>;<br/><a NAME="E6:26_1"/><span class="kw">then </span><span class="lab"><font color="Green" title="E22">A10</font></span>: 
<span class="p1"><a href="domain_1.html#K1" title="DOMAIN_1:func.1">[</a><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">D</font>,<span class="p4">(<span class="default"><span class="p5">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c6">x9</font></span>)</span>,<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">D</font>,<span class="p4">(<span class="default"><span class="p5">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span></span>)</span> <a href="waybel_0.html#K2" title="WAYBEL_0:func.2">.</a> <font color="Maroon" title="c7">y9</font></span>)</span></span><a href="domain_1.html#K1" title="DOMAIN_1:func.1">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</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="orders_2.html#D9" title="ORDERS_2:def.9">ORDERS_2:def 9</a></span>;<br/><a NAME="E7:26_1"/><span class="lab"><font color="Green" title="E23">A11</font></span>: 
<font color="Maroon" title="c6">x9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c6">x9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></span>;<br/><a NAME="E8:26_1"/>
<font color="Maroon" title="c7">y9</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c7">y9</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E3:26"><span class="lab"><font color="Green" title="E19">A3</font></span></a>, <a class="ref" href="funct_1.html#T35" title="FUNCT_1:th.35">FUNCT_1:35</a></span>;<br/><span class="kw">hence </span><a NAME="E9:26_1"/>
<span class="p1"><a href="tarski.html#K4" title="TARSKI:func.4">[</a><span class="default"><font color="Maroon" title="c4">x</font>,<font color="Maroon" title="c5">y</font></span><a href="tarski.html#K4" title="TARSKI:func.4">]</a></span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 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 class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="txt" href="#E2:26_1"><span class="lab"><font color="Green" title="E21">A9</font></span></a>, <a class="txt" href="#E6:26_1"><span class="lab"><font color="Green" title="E22">A10</font></span></a>, <a class="txt" href="#E7:26_1"><span class="lab"><font color="Green" title="E23">A11</font></span></a>, <a class="ref" href="xboole_0.html#D4" title="XBOOLE_0:def.4">XBOOLE_0:def 4</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">hence </span><a NAME="E6:26"/>
 <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="waybel11.html#K3" title="WAYBEL11:func.3">Net-Str</a> <font color="Maroon" title="c2">D</font>,<span class="p1">(<span class="default"><span class="p2">(<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="nattra_1.html#K1" title="NATTRA_1:func.1">|</a> <font color="Maroon" title="c2">D</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:26"><span class="lab"><font color="Green" title="E17">A1</font></span></a>, <a class="txt" href="#E2:26"><span class="lab"><font color="Green" title="E18">A2</font></span></a>, <a class="ref" href="relat_1.html#D2" title="RELAT_1:def.2">RELAT_1:def 2</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>
