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<div><a class="txt" onclick="hs2(this)" href="javascript:()" title="14_1_1_1"><span class="kw">now </span></a><div class="add"><span class="kw">let </span><font color="Maroon" title="c2">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="cc0sp1.html#K3" title="CC0SP1:func.3">C_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font></span>)</span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font></span><br/><span class="kw">reconsider </span><font color="Maroon" title="c3">v1</font> = <font color="Maroon" title="c2">v</font> as   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <span class="p1">(<span class="default"><a href="cfuncdom.html#K8" title="CFUNCDOM:func.8">CAlgebra</a> <font color="Maroon" title="c1">X</font></span>)</span> <span class="kw">by</span> <span class="lab"><a class="ref" href="tarski.html#D3" title="TARSKI:def.3">TARSKI:def 3</a></span>;<br/><a NAME="E2:14_1_1_1"/>
 <a href="cc0sp1.html#K3" title="CC0SP1:func.3">C_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font> is    <a href="cc0sp1.html#M1" title="CC0SP1:mode.1">ComplexSubAlgebra</a> of  <a href="cfuncdom.html#K8" title="CFUNCDOM:func.8">CAlgebra</a> <font color="Maroon" title="c1">X</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cc0sp1.html#T2" target="_self" title="CC0SP1:th.2">Th2</a></span>;<br/><a NAME="E3:14_1_1_1"/><span class="kw">then </span>
<a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c3">v1</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cc0sp1.html#T3" target="_self" title="CC0SP1:th.3">Th4</a></span>;<br/><span class="kw">hence </span><a NAME="E4:14_1_1_1"/>
<a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c2">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c2">v</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="cfuncdom.html#T12" title="CFUNCDOM:th.12">CFUNCDOM:12</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/></div><span class="kw">end;</span></div>
<span class="kw">hence </span><a NAME="E2:14_1_1"/>
(  <a href="cc0sp1.html#K3" title="CC0SP1:func.3">C_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font> is  <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>  &amp;  <a href="cc0sp1.html#K3" title="CC0SP1:func.3">C_Algebra_of_BoundedFunctions</a> <font color="Maroon" title="c1">X</font> is  <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D5" title="CLVECT_1:def.5">CLVECT_1:def 5</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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