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<b>let </b><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">L</font> be  non <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>  <a href="robbins1.html#L1" title="ROBBINS1:struct.1">ComplStr</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></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">K</font><br/> for <font color="Olive" title="b2">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>  st the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">K</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">L</font> &amp; <font color="Olive" title="b1">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> holds <br/><font color="Olive" title="b1">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/><b>let </b><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">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">y</font> being  <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>  st the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">K</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> holds <br/><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/><b>let </b><font color="Maroon" title="c4">y</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c2">L</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">K</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> implies <font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  )</span><br/>





<b>assume </b><a NAME="E1:46"/>
( the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c1">K</font> <a href="funct_2.html#R1" title="FUNCT_2:pred.1">=</a> the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">L</font> &amp; <font color="Maroon" title="c3">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> )
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> </span><br/>

<b>then </b><font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  = 
the <a href="robbins1.html#U1" title="ROBBINS1:sel.1">Compl</a> of <font color="Maroon" title="c2">L</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">y</font>
<b>by </b><i><a class="ref" href="robbins1.html#D3" title="ROBBINS1:def.3">ROBBINS1:def 3</a></i>
<br/>.= 
<font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
<b>by </b><i><a class="ref" href="robbins1.html#D3" title="ROBBINS1:def.3">ROBBINS1:def 3</a></i>
;<br/>
<b>hence </b><a NAME="E3:46"/>
<font color="Maroon" title="c3">x</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">y</font> <a href="robbins1.html#K3" title="ROBBINS1:func.3">`</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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