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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="pre_topc.html#NM1">TopSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>2</sub></font>;<br/>





<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="17_1"><b>now </b></a><div class="add"><b>let </b><font color="Maroon">c<sub>4</sub></font> be   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font>;<br/><b>assume </b><a NAME="E1:17_1"/><i><font color="Green">E14</font></i>: 
<font color="Maroon">c<sub>4</sub></font> <a href="hidden.html#R1">=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>
 ;<br/><b>then reconsider </b><font color="Maroon">c<sub>5</sub></font> = <font color="Maroon">c<sub>4</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> <b>by </b><i><a class="ref" href="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/><a NAME="E3:17_1"/>
<font color="Maroon">c<sub>5</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="tsep_1.html#E1:17_1"><i><font color="Green">E14</font></i></a>, <a class="ref" href="borsuk_1.html#D14">BORSUK_1:def 14</a></i>;<br/><a NAME="E4:17_1"/><b>then </b><i><font color="Green">E15</font></i>: 
ex <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="pre_topc.html#V4">closed</a> &amp; <font color="Olive">b<sub>1</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font></span>)</span> <a href="hidden.html#R1">=</a> <font color="Maroon">c<sub>5</sub></font> )
 <b>by </b><i><a class="ref" href="pre_topc.html#T43">PRE_TOPC:43</a></i>;<br/><b>reconsider </b><font color="Maroon">c<sub>6</sub></font> =  <a href="pre_topc.html#K2">[#]</a> <font color="Maroon">c<sub>2</sub></font> as   <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>1</sub></font> <b>by </b><i><a class="ref" href="borsuk_1.html#T35">BORSUK_1:35</a></i>;<br/><a NAME="E6:17_1"/>
<font color="Maroon">c<sub>6</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="ref" href="borsuk_1.html#D14">BORSUK_1:def 14</a></i>;<br/><b>hence </b><a NAME="E7:17_1"/>
<font color="Maroon">c<sub>4</sub></font> is <a href="pre_topc.html#V4">closed</a>
 <b>by </b><i><a class="txt" href="tsep_1.html#E4:17_1"><i><font color="Green">E15</font></i></a>, <a class="ref" href="tops_1.html#T35">TOPS_1:35</a></i>;<br/></div><b>end;</b></div>
<b>hence </b><a NAME="E2:17"/>
<font color="Maroon">c<sub>3</sub></font> is  <a href="borsuk_1.html#V1">closed</a>  <a href="pre_topc.html#M1">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>
 <b>by </b><i><a class="ref" href="tsep_1.html#T7" target="_self">Th7</a>, <a class="ref" href="borsuk_1.html#D14">BORSUK_1:def 14</a></i>;<br/>


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