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<b>reconsider </b><font color="Maroon">c<sub>2</sub></font> =  <a href="metric_1.html#G1">MetrStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> #) as   <a href="metric_1.html#NM1">MetrSpace</a> <b>by </b><i><a class="txt" href="topmetr.html#E12"><i><font color="Green">Lemma6</font></i></a></i>;<br/>
<a NAME="E2:14_1_1"/>
( the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>2</sub></font> <a href="tarski.html#R1">c=</a> the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font> &amp; ( for <font color="Olive">b<sub>1</sub></font>, <font color="Olive">b<sub>2</sub></font> being  <a href="pre_topc.html#NM2">Point</a> of <font color="Maroon">c<sub>2</sub></font> holds the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>2</sub></font> <a href="metric_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> <a href="hidden.html#R1">=</a> the <a href="metric_1.html#U1">distance</a> of <font color="Maroon">c<sub>1</sub></font> <a href="binop_1.html#K1">.</a> <font color="Olive">b<sub>1</sub></font>,<font color="Olive">b<sub>2</sub></font> ) )
 
;<br/>
<a NAME="E3:14_1_1"/><b>then </b>
<font color="Maroon">c<sub>2</sub></font> is    <a href="topmetr.html#M1" target="_self">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font>
 
<b>by </b><i><a class="ref" href="topmetr.html#D1" target="_self">Def1</a></i>;<br/>
<b>hence </b><a NAME="E4:14_1_1"/>
ex <font color="Olive">b<sub>1</sub></font> being   <a href="topmetr.html#M1" target="_self">SubSpace</a> of <font color="Maroon">c<sub>1</sub></font> st <br/>( <font color="Olive">b<sub>1</sub></font> is <a href="metric_1.html#V1">strict</a> &amp; not <font color="Olive">b<sub>1</sub></font> is <a href="struct_0.html#V3">empty</a> )
 ;<br/>


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