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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="yellow_0.html#V1">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a>  <a href="orders_2.html#L1">RelStr</a> ;<br/>



<b>assume </b><b>that </b><br/><a NAME="E1:5"/><i><font color="Green">E6</font></i>: 
 <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>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>1</sub></font> #) <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>,the <a href="orders_2.html#U1">InternalRel</a> of <font color="Maroon">c<sub>2</sub></font> #)
 <b>and </b><br/><a NAME="E2:5"/><i><font color="Green">E7</font></i>: 
<font color="Maroon">c<sub>1</sub></font> is <a href="waybel_0.html#V24">up-complete</a>
 ;<br/>

<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>assume </b><a NAME="E1:5_1"/><i><font color="Green">E8</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="txt" href="waybel13.html#E1:5"><i><font color="Green">E6</font></i></a></i>;<br/><a NAME="E4:5_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="waybel_3.html#V1">compact</a>
 <b>by </b><i><a class="txt" href="waybel13.html#E1:5_1"><i><font color="Green">E8</font></i></a>, <a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/><a NAME="E5:5_1"/><b>then </b>
<font color="Maroon">c<sub>5</sub></font> is <a href="waybel_3.html#V1">compact</a>
 <b>by </b><i><a class="txt" href="waybel13.html#E1:5"><i><font color="Green">E6</font></i></a>, <a class="txt" href="waybel13.html#E2:5"><i><font color="Green">E7</font></i></a>, <a class="ref" href="waybel_8.html#T9">WAYBEL_8:9</a></i>;<br/><b>hence </b><a NAME="E6:5_1"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E4:5"/><b>then </b><i><font color="Green">E8</font></i>: 
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="5_2"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>3</sub></font> be    <a href="hidden.html#M1">set</a> ;<br/><b>reconsider </b><font color="Maroon">c<sub>4</sub></font> = <font color="Maroon">c<sub>2</sub></font> as  non <a href="struct_0.html#V3">empty</a> <a href="orders_2.html#V2">reflexive</a> <a href="orders_2.html#V4">antisymmetric</a> <a href="yellow_0.html#V1">lower-bounded</a>  <a href="orders_2.html#L1">RelStr</a>  <b>by </b><i><a class="txt" href="waybel13.html#E1:5"><i><font color="Green">E6</font></i></a>, <a class="ref" href="yellow_0.html#T13">YELLOW_0:13</a></i>;<br/><b>assume </b><a NAME="E2:5_2"/><i><font color="Green">E9</font></i>: 
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 ;<br/><a NAME="E3:5_2"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> is   <a href="struct_0.html#NM1">Element</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>4</sub></font></span>)</span>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>3</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="yellow_0.html#T59">YELLOW_0:59</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> = <font color="Maroon">c<sub>5</sub></font> as   <a href="struct_0.html#NM1">Element</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="txt" href="waybel13.html#E1:5"><i><font color="Green">E6</font></i></a></i>;<br/><a NAME="E6:5_2"/><i><font color="Green">E10</font></i>: 
<font color="Maroon">c<sub>2</sub></font> is <a href="waybel_0.html#V24">up-complete</a>
 <b>by </b><i><a class="txt" href="waybel13.html#E1:5"><i><font color="Green">E6</font></i></a>, <a class="txt" href="waybel13.html#E2:5"><i><font color="Green">E7</font></i></a>, <a class="ref" href="waybel_8.html#T15">WAYBEL_8:15</a></i>;<br/><a NAME="E7:5_2"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="waybel_3.html#V1">compact</a>
 <b>by </b><i><a class="txt" href="waybel13.html#E2:5_2"><i><font color="Green">E9</font></i></a>, <a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/><a NAME="E8:5_2"/><b>then </b>
<font color="Maroon">c<sub>6</sub></font> is <a href="waybel_3.html#V1">compact</a>
 <b>by </b><i><a class="txt" href="waybel13.html#E1:5"><i><font color="Green">E6</font></i></a>, <a class="txt" href="waybel13.html#E6:5_2"><i><font color="Green">E10</font></i></a>, <a class="ref" href="waybel_8.html#T9">WAYBEL_8:9</a></i>;<br/><b>hence </b><a NAME="E9:5_2"/>
<font color="Maroon">c<sub>3</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 <b>by </b><i><a class="ref" href="waybel_8.html#D1">WAYBEL_8:def 1</a></i>;<br/></div><b>end;</b></div>
<a NAME="E6:5"/><b>then </b>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
<b>by </b><i><a class="ref" href="tarski.html#D3">TARSKI:def 3</a></i>;<br/>
<b>hence </b><a NAME="E7:5"/>
the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel_8.html#K1">CompactSublatt</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>
 <b>by </b><i><a class="txt" href="waybel13.html#E4:5"><i><font color="Green">E8</font></i></a>, <a class="ref" href="xboole_0.html#D10">XBOOLE_0:def 10</a></i>;<br/>


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