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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="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">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">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b2">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Olive" title="b1">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <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">x</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font> holds  <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">x</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</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"> <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span><br/>





<span class="kw">set </span><font color="Maroon" title="c4">n</font> = the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c2">N</font>;<br/>
<span class="lab"><font color="Green" title="E25">A1</font></span>:  <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 <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c2">N</font></span>)</span>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c2">N</font></span>)</span> #) = 
 <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="c2">N</font>,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="waybel_9.html#D8" target="_self" title="WAYBEL_9:def.8">Def8</a></span>
<br/>.= 
 <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 <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</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="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span> #)
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_2.html#D3" title="WAYBEL_2:def.3">WAYBEL_2:def 3</a></span>
;<br/>
<a NAME="E2:61"/><span class="lab"><font color="Green" title="E26">A2</font></span>: 
 <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="c2">N</font>,the <a href="orders_2.html#U1" title="ORDERS_2:sel.1">InternalRel</a> of <font color="Maroon" title="c2">N</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 <span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</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="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span> #)
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_2.html#D3" title="WAYBEL_2:def.3">WAYBEL_2:def 3</a></span>;<br/>
<span class="kw">then </span><span class="kw">reconsider </span><font color="Maroon" title="c5">f2</font> = 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="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span> as   <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" title="c2">N</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">L</font> ;<br/>
<a NAME="E4:61"/><span class="lab"><font color="Green" title="E27">A3</font></span>: 
for <font color="Olive" title="b1">c</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">N</font> holds  <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c2">N</font></span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Olive" title="b1">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Olive" title="b1">c</font>
 
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="61_2"><span class="kw">proof </span></a><div class="add">

<span class="kw">let </span><font color="Maroon" title="c6">c</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"> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c2">N</font></span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">f2</font> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">c</font></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c7">y</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">L</font><span class="kw"> such that </span><br/><a NAME="E2:61_2"/><span class="lab"><font color="Green" title="E28">A4</font></span>: 
<font color="Maroon" title="c7">y</font> <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="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">c</font>
 <span class="kw">and </span><br/><a NAME="E3:61_2"/><span class="lab"><font color="Green" title="E29">A5</font></span>: 
<font color="Maroon" title="c5">f2</font> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">c</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="lattice3.html#K11" title="LATTICE3:func.11">"/\"</a> <font color="Maroon" title="c7">y</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61"><span class="lab"><font color="Green" title="E26">A2</font></span></a>, <a class="ref" href="waybel_2.html#D3" title="WAYBEL_2:def.3">WAYBEL_2:def 3</a></span>;<br/>
<span class="kw">thus </span><span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c2">N</font></span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">c</font> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c7">y</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:61_2"><span class="lab"><font color="Green" title="E28">A4</font></span></a>, <a class="ref" href="funct_2.html#T21" title="FUNCT_2:th.21">FUNCT_2:21</a></span>
<br/>.= 
<font color="Maroon" title="c5">f2</font> <a href="yellow_6.html#K2" title="YELLOW_6:func.2">.</a> <font color="Maroon" title="c6">c</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E3:61_2"><span class="lab"><font color="Green" title="E29">A5</font></span></a>, <a class="ref" href="waybel_1.html#D18" title="WAYBEL_1:def.18">WAYBEL_1:def 18</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>
the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c2">N</font></span>)</span> = 
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="partfun1.html#K1" title="PARTFUN1:func.1">*</a> the <a href="waybel_0.html#U1" title="WAYBEL_0:sel.1">mapping</a> of <font color="Maroon" title="c2">N</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="waybel_9.html#D8" target="_self" title="WAYBEL_9:def.8">Def8</a></span>
<br/>.= 
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="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:61"><span class="lab"><font color="Green" title="E27">A3</font></span></a>, <a class="ref" href="funct_2.html#T113" title="FUNCT_2:th.113">FUNCT_2:113</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E6:61"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c3">x</font> <a href="waybel_1.html#K4" title="WAYBEL_1:func.4">"/\"</a> </span>)</span> <a href="waybel_9.html#K7" title="WAYBEL_9:func.7">*</a> <font color="Maroon" title="c2">N</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c3">x</font> <a href="waybel_2.html#K3" title="WAYBEL_2:func.3">"/\"</a> <font color="Maroon" title="c2">N</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:61"><span class="lab"><font color="Green" title="E25">A1</font></span></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>
