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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>

<a NAME="E1:56"/><i><font color="Green">E32</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7">~</a>  <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> <a href="relset_1.html#K6">~</a> </span>)</span> #) &amp; <font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K7">~</a>  <a href="hidden.html#R1">=</a>  <a href="orders_2.html#G1">RelStr</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,<span class="p1">(<span class="default">the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> <a href="relset_1.html#K6">~</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">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font>, <font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>6</sub></font> be    <a href="orders_2.html#L1">RelStr</a> ;<br/><b>assume </b><a NAME="E1:56_1"/><i><font color="Green">E33</font></i>: 
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font> &amp; the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>5</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>6</sub></font> )
 ;<br/><b>let </b><font color="Maroon">c<sub>7</sub></font> be    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>;<br/><b>consider </b><font color="Maroon">c<sub>8</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>3</sub></font>,<font color="Maroon">c<sub>5</sub></font>, <font color="Maroon">c<sub>9</sub></font> being   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>5</sub></font>,<font color="Maroon">c<sub>3</sub></font><b> such that </b><br/><a NAME="E3:56_1"/><i><font color="Green">E34</font></i>: 
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>8</sub></font>,<font color="Maroon">c<sub>9</sub></font></span><a href="waybel_1.html#K1">]</a></span>
 <b>by </b><i><a class="ref" href="waybel_1.html#D9">WAYBEL_1:def 9</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>10</sub></font> = <font color="Maroon">c<sub>8</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font> <b>by </b><i><a class="txt" href="yellow_7.html#E1:56_1"><i><font color="Green">E33</font></i></a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>11</sub></font> = <font color="Maroon">c<sub>9</sub></font> as   <a href="struct_0.html#NM7">Function</a> of <font color="Maroon">c<sub>6</sub></font>,<font color="Maroon">c<sub>4</sub></font> <b>by </b><i><a class="txt" href="yellow_7.html#E1:56_1"><i><font color="Green">E33</font></i></a></i>;<br/><a NAME="E6:56_1"/>
<font color="Maroon">c<sub>7</sub></font> <a href="hidden.html#R1">=</a> <span class="p1"><a href="waybel_1.html#K1">[</a><span class="default"><font color="Maroon">c<sub>10</sub></font>,<font color="Maroon">c<sub>11</sub></font></span><a href="waybel_1.html#K1">]</a></span>
 <b>by </b><i><a class="txt" href="yellow_7.html#E3:56_1"><i><font color="Green">E34</font></i></a></i>;<br/><b>hence </b><a NAME="E7:56_1"/>
<font color="Maroon">c<sub>7</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>4</sub></font>,<font color="Maroon">c<sub>6</sub></font>
 ;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E3:56"/>
for <font color="Olive">b<sub>1</sub></font> being   <a href="hidden.html#M1">set</a>  holds <br/>( ( <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> implies <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7">~</a> ,<font color="Maroon">c<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7">~</a> ,<font color="Maroon">c<sub>2</sub></font> implies <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> implies <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K7">~</a>  ) &amp; ( <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K7">~</a>  implies <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> ) &amp; ( <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> implies <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7">~</a> ,<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K7">~</a>  ) &amp; ( <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font> <a href="lattice3.html#K7">~</a> ,<font color="Maroon">c<sub>2</sub></font> <a href="lattice3.html#K7">~</a>  implies <font color="Olive">b<sub>1</sub></font> is    <a href="waybel_1.html#M1">Connection</a> of <font color="Maroon">c<sub>1</sub></font>,<font color="Maroon">c<sub>2</sub></font> ) )
 <b>by </b><i><a class="txt" href="yellow_7.html#E1:56"><i><font color="Green">E32</font></i></a></i>;<br/>


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