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<b>let </b><font color="Maroon" title="c1">S</font>, <font color="Maroon" title="c2">T</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a>  <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/>

<a NAME="E1:56"/><i><font color="Green" title="E32">A1</font></i>: 
( <font color="Maroon" title="c1">S</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a>  <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 <font color="Maroon" title="c1">S</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="relset_1.html#K6" title="RELSET_1:func.6">~</a> </span>)</span> #) &amp; <font color="Maroon" title="c2">T</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a>  <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 <font color="Maroon" title="c2">T</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="c2">T</font> <a href="relset_1.html#K6" title="RELSET_1:func.6">~</a> </span>)</span> #) )
 
;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="56_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon" title="c3">S</font>, <font color="Maroon" title="c4">S1</font>, <font color="Maroon" title="c5">T</font>, <font color="Maroon" title="c6">T1</font> be    <a href="orders_2.html#L1" title="ORDERS_2:struct.1">RelStr</a> ;<br/><b>assume </b><a NAME="E1:56_1"/><i><font color="Green" title="E33">A2</font></i>: 
( the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c3">S</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 <font color="Maroon" title="c4">S1</font> &amp; the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">T</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 <font color="Maroon" title="c6">T1</font> )
 ;<br/><b>let </b><font color="Maroon" title="c7">a</font> be    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c5">T</font>;<br/><b>consider </b><font color="Maroon" title="c8">f</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c3">S</font>,<font color="Maroon" title="c5">T</font>, <font color="Maroon" title="c9">g</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c5">T</font>,<font color="Maroon" title="c3">S</font><b> such that </b><br/><a NAME="E3:56_1"/><i><font color="Green" title="E34">A3</font></i>: 
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c8">f</font>,<font color="Maroon" title="c9">g</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span>
 <b>by </b><i><a class="ref" href="waybel_1.html#D9" title="WAYBEL_1:def.9">WAYBEL_1:def 9</a></i>;<br/><b>reconsider </b><font color="Maroon" title="c10">f</font> = <font color="Maroon" title="c8">f</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c4">S1</font>,<font color="Maroon" title="c6">T1</font> <b>by </b><i><a class="txt" href="yellow_7.html#E1:56_1"><i><font color="Green" title="E33">A2</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon" title="c11">g</font> = <font color="Maroon" title="c9">g</font> as   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c6">T1</font>,<font color="Maroon" title="c4">S1</font> <b>by </b><i><a class="txt" href="yellow_7.html#E1:56_1"><i><font color="Green" title="E33">A2</font></i></a></i>;<br/><a NAME="E6:56_1"/>
<font color="Maroon" title="c7">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1"><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">[</a><span class="default"><font color="Maroon" title="c10">f</font>,<font color="Maroon" title="c11">g</font></span><a href="waybel_1.html#K1" title="WAYBEL_1:func.1">]</a></span>
 <b>by </b><i><a class="txt" href="yellow_7.html#E3:56_1"><i><font color="Green" title="E34">A3</font></i></a></i>;<br/><b>hence </b><a NAME="E7:56_1"/>
<font color="Maroon" title="c7">a</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c4">S1</font>,<font color="Maroon" title="c6">T1</font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:56"/>
for <font color="Olive" title="b1">f</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  holds <br/> ( ( <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> implies <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a> ,<font color="Maroon" title="c2">T</font> ) &amp; ( <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a> ,<font color="Maroon" title="c2">T</font> implies <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> ) &amp; ( <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> implies <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a>  ) &amp; ( <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a>  implies <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> ) &amp; ( <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> implies <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a> ,<font color="Maroon" title="c2">T</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a>  ) &amp; ( <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a> ,<font color="Maroon" title="c2">T</font> <a href="lattice3.html#K7" title="LATTICE3:func.7">~</a>  implies <font color="Olive" title="b1">f</font> is    <a href="waybel_1.html#M1" title="WAYBEL_1:mode.1">Connection</a> of <font color="Maroon" title="c1">S</font>,<font color="Maroon" title="c2">T</font> ) )
 <b>by </b><i><a class="txt" href="yellow_7.html#E1:56"><i><font color="Green" title="E32">A1</font></i></a></i>;<br/>


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