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<b>let </b><font color="Maroon" title="c1">PT</font> be  non <a href="struct_0.html#V3" title="STRUCT_0:attr.3">empty</a> <a href="pre_topc.html#NM1" title="PRE_TOPC:NM.1">TopSpace</a>;<br/><b>let </b><font color="Maroon" title="c2">PM</font> be   <a href="metric_1.html#NM1" title="METRIC_1:NM.1">MetrSpace</a>;<br/><b>let </b><font color="Maroon" title="c3">f</font> be   <a href="funct_2.html#NM1" title="FUNCT_2:NM.1">Function</a> of <span class="p1"><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">[:</a><span class="default">the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PT</font>,the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PT</font></span><a href="zfmisc_1.html#K2" title="ZFMISC_1:func.2">:]</a></span>, <a href="numbers.html#K1" title="NUMBERS:func.1">REAL</a> ;<br/>





<b>assume </b><a NAME="E1:8"/><i><font color="Green" title="E4">A1</font></i>: 
<font color="Maroon" title="c3">f</font> <a href="pcomps_1.html#R1" title="PCOMPS_1:pred.1">is_metric_of</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PT</font>
 ;<br/>

<b>assume </b><a NAME="E2:8"/>
<font color="Maroon" title="c2">PM</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="pcomps_1.html#K5" title="PCOMPS_1:func.5">SpaceMetr</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PT</font>,<font color="Maroon" title="c3">f</font>
 ;<br/>

<a NAME="E3:8"/><b>then </b>
<font color="Maroon" title="c2">PM</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="metric_1.html#G1" title="METRIC_1:aggr.1">MetrStruct</a>(# the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PT</font>,<font color="Maroon" title="c3">f</font> #)
 
<b>by </b><i><a class="txt" href="pcomps_2.html#E1:8"><i><font color="Green" title="E4">A1</font></i></a>, <a class="ref" href="pcomps_1.html#D8" title="PCOMPS_1:def.8">PCOMPS_1:def 8</a></i>;<br/>
<b>hence </b><a NAME="E4:8"/>
the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c2">PM</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c1">PT</font>
 ;<br/>


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