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<b>let </b><font color="Maroon">c<sub>1</sub></font>, <font color="Maroon">c<sub>2</sub></font>, <font color="Maroon">c<sub>3</sub></font>, <font color="Maroon">c<sub>4</sub></font> be    <a href="pre_topc.html#L1" target="_self">TopStruct</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:32"/><i><font color="Green">E13</font></i>: 
 <a href="pre_topc.html#G1" target="_self">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1" target="_self">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font>,the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>2</sub></font> #)
 <b>and </b><br/><a NAME="E2:32"/><i><font color="Green">E14</font></i>: 
 <a href="pre_topc.html#G1" target="_self">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>3</sub></font>,the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>3</sub></font> #) <a href="hidden.html#R1">=</a>  <a href="pre_topc.html#G1" target="_self">TopStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>4</sub></font>,the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>4</sub></font> #)
 ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E3:32"/><i><font color="Green">E15</font></i>: 
 <a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>3</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E4:32"/><i><font color="Green">E16</font></i>: 
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>3</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>3</sub></font> iff ex <font color="Olive">b<sub>2</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>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>1</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>3</sub></font></span>)</span> ) )
 ; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_topc.html#D9" target="_self">PRE_TOPC:def 9</a><br/>

<b>thus </b><a NAME="E5:32"/>
 <a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>4</sub></font> <a href="tarski.html#R1">c=</a>  <a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>2</sub></font>
 <b>by </b><i><a class="txt" href="pre_topc.html#E1:32"><i><font color="Green">E13</font></i></a>, <a class="txt" href="pre_topc.html#E2:32"><i><font color="Green">E14</font></i></a>, <a class="txt" href="pre_topc.html#E3:32"><i><font color="Green">E15</font></i></a></i>; <i><font color="Red">:: according to </font></i><a class="ref" href="pre_topc.html#D9" target="_self">PRE_TOPC:def 9</a><br/>

<b>thus </b><a NAME="E6:32"/>
for <font color="Olive">b<sub>1</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>4</sub></font> holds <br/>( <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>4</sub></font> iff ex <font color="Olive">b<sub>2</sub></font> being  <a href="struct_0.html#NM2">Subset</a> of <font color="Maroon">c<sub>2</sub></font> st <br/>( <font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="pre_topc.html#U1" target="_self">topology</a> of <font color="Maroon">c<sub>2</sub></font> &amp; <font color="Olive">b<sub>1</sub></font> <a href="hidden.html#R1">=</a> <font color="Olive">b<sub>2</sub></font> <a href="subset_1.html#K9">/\</a> <span class="p1">(<span class="default"><a href="pre_topc.html#K2" target="_self">[#]</a> <font color="Maroon">c<sub>4</sub></font></span>)</span> ) )
 <b>by </b><i><a class="txt" href="pre_topc.html#E1:32"><i><font color="Green">E13</font></i></a>, <a class="txt" href="pre_topc.html#E2:32"><i><font color="Green">E14</font></i></a>, <a class="txt" href="pre_topc.html#E4:32"><i><font color="Green">E16</font></i></a></i>;<br/>


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