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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<div><b>hereby </b>
<div class="add"><b>assume </b><a NAME="E1:62_1"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a> holds  <a href="waybel11.html#K5">sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 ;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/><a NAME="E2:62_1"/>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p2"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p2"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span></span>)</span> #) <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>by </b><i><a class="txt" href="waybel29.html#E1:62_1"><i><font color="Green">E35</font></i></a>, <a class="ref" href="waybel29.html#T35" target="_self">Th35</a></i>;<br/><a NAME="E3:62_1"/><b>then </b>
 <a href="waybel25.html#K1">Omega</a> <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p2"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span></span>)</span> <a href="hidden.html#R1">=</a>  <a href="waybel25.html#K1">Omega</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>by </b><i><a class="ref" href="waybel25.html#T13">WAYBEL25:13</a></i>;<br/><b>hence </b><a NAME="E4:62_1"/>
 <a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="waybel25.html#K1">Omega</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>by </b><i><a class="ref" href="waybel25.html#T15">WAYBEL25:15</a></i>;<br/></div>
<b>end;</b></div>

<b>assume </b><a NAME="E2:62"/><i><font color="Green">E35</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a> holds  <a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Olive">b<sub>1</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="waybel25.html#K1">Omega</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Olive">b<sub>1</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 ;<br/>

<b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="lattice3.html#V3">complete</a> <a href="waybel_0.html#NM8">LATTICE</a>;<br/>

<a NAME="E3:62"/>
 <a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a>  <a href="waybel25.html#K1">Omega</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 
<b>by </b><i><a class="txt" href="waybel29.html#E2:62"><i><font color="Green">E35</font></i></a></i>;<br/>
<a NAME="E4:62"/><b>then </b>
 <a href="pre_topc.html#G1">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p2"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span></span>)</span>,the <a href="pre_topc.html#U1">topology</a> of <span class="p1">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <span class="p2"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span></span>)</span> #) <a href="hidden.html#R1">=</a> <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 
<b>by </b><i><a class="ref" href="waybel25.html#D2">WAYBEL25:def 2</a></i>;<br/>
<b>hence </b><a NAME="E5:62"/>
 <a href="waybel11.html#K5">sigma</a> <span class="p1"><a href="yellow_3.html#K3">[:</a><span class="default"><font color="Maroon">c<sub>2</sub></font>,<font color="Maroon">c<sub>1</sub></font></span><a href="yellow_3.html#K3">:]</a></span> <a href="hidden.html#R1">=</a> the <a href="pre_topc.html#U1">topology</a> of <span class="p1"><a href="borsuk_1.html#K5">[:</a><span class="default"><span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>2</sub></font></span>)</span>,<span class="p2">(<span class="default"><a href="waybel29.html#K1" target="_self">Sigma</a> <font color="Maroon">c<sub>1</sub></font></span>)</span></span><a href="borsuk_1.html#K5">:]</a></span>
 <b>by </b><i><a class="ref" href="yellow_9.html#T51">YELLOW_9:51</a></i>;<br/>


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