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<b>let </b><font color="Maroon">c<sub>1</sub></font> be   <a href="rlvect_1.html#NM2">RealLinearSpace</a>;<br/><b>let </b><font color="Maroon">c<sub>2</sub></font> be   <a href="rlvect_1.html#NM1">VECTOR</a> of <font color="Maroon">c<sub>1</sub></font>; <i><font color="Red">:: according to </font></i><a class="ref" href="circled1.html#D1" target="_self">CIRCLED1:def 1</a><br/><b>let </b><font color="Maroon">c<sub>3</sub></font> be   <a href="real_1.html#NM1">Real</a>;<br/>





<a NAME="E1:9"/>
 <a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="rlvect_1.html#G2">RLSStruct</a>(# the <a href="struct_0.html#U1">carrier</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="struct_0.html#U2">Zero</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U1">add</a> of <font color="Maroon">c<sub>1</sub></font>,the <a href="rlvect_1.html#U2">Mult</a> of <font color="Maroon">c<sub>1</sub></font> #)
 
<b>by </b><i><a class="ref" href="rlsub_1.html#D4">RLSUB_1:def 4</a></i>;<br/>
<a NAME="E2:9"/><b>then </b>
<font color="Maroon">c<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a> the <a href="struct_0.html#U1">carrier</a> of <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span>
 
;<br/>
<b>hence </b><a NAME="E3:9"/>
(  <a href="complex1.html#K18">abs</a> <font color="Maroon">c<sub>3</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 1 &amp; <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="rusub_4.html#K3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> implies <font color="Maroon">c<sub>3</sub></font> <a href="rlvect_1.html#K3">*</a> <font color="Maroon">c<sub>2</sub></font> <a href="hidden.html#R2">in</a>  <a href="rusub_4.html#K3">Up</a> <span class="p1">(<span class="default"><a href="rlsub_1.html#K2">(Omega).</a> <font color="Maroon">c<sub>1</sub></font></span>)</span> )
 <b>by </b><i><a class="ref" href="rusub_4.html#D6">RUSUB_4:def 6</a></i>;<br/>


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