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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   non  <a href="struct_0.html#V2" title="STRUCT_0:attr.2">empty</a>   <a href="rlvect_1.html#V2" title="RLVECT_1:attr.2">Abelian</a>   <a href="rlvect_1.html#V3" title="RLVECT_1:attr.3">add-associative</a>   <a href="clvect_1.html#V2" title="CLVECT_1:attr.2">vector-distributive</a>   <a href="clvect_1.html#V3" title="CLVECT_1:attr.3">scalar-distributive</a>   <a href="clvect_1.html#V4" title="CLVECT_1:attr.4">scalar-associative</a>   <a href="clvect_1.html#V5" title="CLVECT_1:attr.5">scalar-unital</a>   <a href="clvect_1.html#L1" title="CLVECT_1:struct.1">CLSStruct</a> ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">M1</font>, <font color="Olive" title="b2">M2</font> being   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font><br/>  for <font color="Olive" title="b3">z1</font>, <font color="Olive" title="b4">z2</font> being   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>  st <font color="Olive" title="b1">M1</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  &amp; <font color="Olive" title="b2">M2</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b3">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Olive" title="b1">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b4">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Olive" title="b2">M2</font></span>)</span> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c2">M1</font>, <font color="Maroon" title="c3">M2</font> be   <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">z1</font>, <font color="Olive" title="b2">z2</font> being   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>  st <font color="Maroon" title="c2">M1</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  &amp; <font color="Maroon" title="c3">M2</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Olive" title="b2">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a> </span><br/><span class="kw">let </span><font color="Maroon" title="c4">z1</font>, <font color="Maroon" title="c5">z2</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">M1</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  &amp; <font color="Maroon" title="c3">M2</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  implies <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a>  )</span><br/>





<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:92"/><span class="lab"><font color="Green" title="E53">A1</font></span>: 
<font color="Maroon" title="c2">M1</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a> 
 <span class="kw">and </span><br/><a NAME="E2:92"/><span class="lab"><font color="Green" title="E54">A2</font></span>: 
<font color="Maroon" title="c3">M2</font> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> is  <a href="convex4.html#V2" title="CONVEX4:attr.2">convex</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c6">u</font>, <font color="Maroon" title="c7">v</font> be   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="convex4.html#D23" target="_self" title="CONVEX4:def.23">CONVEX4:def 23</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">z</font> being   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>  st  ex <font color="Olive" title="b2">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b2">r</font> &amp;  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b2">r</font> &amp; <font color="Olive" title="b2">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 ) &amp; <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> &amp; <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> holds <br/><span class="p1">(<span class="default"><font color="Olive" title="b1">z</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Olive" title="b1">z</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">v</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span></span><br/><span class="kw">let </span><font color="Maroon" title="c8">s</font> be   <a href="cfunct_1.html#NM1" title="CFUNCT_1:NM.1">Complex</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  ex <font color="Olive" title="b1">r</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">r</font> &amp;  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">r</font> &amp; <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 ) &amp; <font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> &amp; <font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> implies <span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">v</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span> )</span><br/>



<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E3:92"/><span class="lab"><font color="Green" title="E55">A3</font></span>: 
 ex <font color="Olive" title="b1">p</font> being   <a href="real_1.html#NM1" title="REAL_1:NM.1">Real</a> st <br/>( <font color="Maroon" title="c8">s</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Olive" title="b1">p</font> &amp;  <a href="card_1.html#NK1" title="CARD_1:NK.1">0</a>  <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> <font color="Olive" title="b1">p</font> &amp; <font color="Olive" title="b1">p</font> <a href="xxreal_0.html#NR3" title="XXREAL_0:NR.3">&lt;</a> 1 )
 <span class="kw">and </span><br/><a NAME="E4:92"/><span class="lab"><font color="Green" title="E56">A4</font></span>: 
<font color="Maroon" title="c6">u</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span>
 <span class="kw">and </span><br/><a NAME="E5:92"/><span class="lab"><font color="Green" title="E57">A5</font></span>: 
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">v</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span></span><br/>

<span class="kw">consider </span><font color="Maroon" title="c9">v1</font>, <font color="Maroon" title="c10">v2</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E7:92"/><span class="lab"><font color="Green" title="E58">A6</font></span>: 
<font color="Maroon" title="c7">v</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c9">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c10">v2</font>
 <span class="kw">and </span><br/><a NAME="E8:92"/><span class="lab"><font color="Green" title="E59">A7</font></span>: 
<font color="Maroon" title="c9">v1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font>
 <span class="kw">and </span><br/><a NAME="E9:92"/><span class="lab"><font color="Green" title="E60">A8</font></span>: 
<font color="Maroon" title="c10">v2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E5:92"><span class="lab"><font color="Green" title="E57">A5</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c11">u1</font>, <font color="Maroon" title="c12">u2</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E11:92"/><span class="lab"><font color="Green" title="E61">A9</font></span>: 
<font color="Maroon" title="c6">u</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c11">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c12">u2</font>
 <span class="kw">and </span><br/><a NAME="E12:92"/><span class="lab"><font color="Green" title="E62">A10</font></span>: 
<font color="Maroon" title="c11">u1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font>
 <span class="kw">and </span><br/><a NAME="E13:92"/><span class="lab"><font color="Green" title="E63">A11</font></span>: 
<font color="Maroon" title="c12">u2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E4:92"><span class="lab"><font color="Green" title="E56">A4</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c13">y1</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E15:92"/><span class="lab"><font color="Green" title="E64">A12</font></span>: 
<font color="Maroon" title="c9">v1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c13">y1</font>
 <span class="kw">and </span><br/><a NAME="E16:92"/><span class="lab"><font color="Green" title="E65">A13</font></span>: 
<font color="Maroon" title="c13">y1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E8:92"><span class="lab"><font color="Green" title="E59">A7</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c14">x1</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E18:92"/><span class="lab"><font color="Green" title="E66">A14</font></span>: 
<font color="Maroon" title="c11">u1</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c14">x1</font>
 <span class="kw">and </span><br/><a NAME="E19:92"/><span class="lab"><font color="Green" title="E67">A15</font></span>: 
<font color="Maroon" title="c14">x1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M1</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E12:92"><span class="lab"><font color="Green" title="E62">A10</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E68">A16</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c14">x1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c13">y1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E18:92"><span class="lab"><font color="Green" title="E66">A14</font></span></a>, <a class="txt" href="#E15:92"><span class="lab"><font color="Green" title="E64">A12</font></span></a>, <a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c14">x1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c13">y1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c14">x1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c13">y1</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c14">x1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c13">y1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<font color="Maroon" title="c4">z1</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c14">x1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c13">y1</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></span>
;<br/>
<span class="kw">consider </span><font color="Maroon" title="c15">y2</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E22:92"/><span class="lab"><font color="Green" title="E69">A17</font></span>: 
<font color="Maroon" title="c10">v2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c15">y2</font>
 <span class="kw">and </span><br/><a NAME="E23:92"/><span class="lab"><font color="Green" title="E70">A18</font></span>: 
<font color="Maroon" title="c15">y2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E9:92"><span class="lab"><font color="Green" title="E60">A8</font></span></a></span>;<br/>
<span class="kw">consider </span><font color="Maroon" title="c16">x2</font> being   <a href="clvect_1.html#NM1" title="CLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font><span class="kw"> such that </span><br/><a NAME="E25:92"/><span class="lab"><font color="Green" title="E71">A19</font></span>: 
<font color="Maroon" title="c12">u2</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c16">x2</font>
 <span class="kw">and </span><br/><a NAME="E26:92"/><span class="lab"><font color="Green" title="E72">A20</font></span>: 
<font color="Maroon" title="c16">x2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M2</font>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E13:92"><span class="lab"><font color="Green" title="E63">A11</font></span></a></span>;<br/>
<span class="lab"><font color="Green" title="E73">A21</font></span>: <span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c12">u2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v2</font></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c16">x2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c15">y2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E25:92"><span class="lab"><font color="Green" title="E71">A19</font></span></a>, <a class="txt" href="#E22:92"><span class="lab"><font color="Green" title="E69">A17</font></span></a>, <a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c16">x2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c15">y2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c16">x2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="complex1.html#K9" title="COMPLEX1:func.9">*</a> <span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c15">y2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c16">x2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c15">y2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D4" title="CLVECT_1:def.4">CLVECT_1:def 4</a></span>
<br/>.= 
<font color="Maroon" title="c5">z2</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c16">x2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c15">y2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></span>
;<br/>
<a NAME="E28:92"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c16">x2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c15">y2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c3">M2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:92"><span class="lab"><font color="Green" title="E54">A2</font></span></a>, <a class="txt" href="#E3:92"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E26:92"><span class="lab"><font color="Green" title="E72">A20</font></span></a>, <a class="txt" href="#E23:92"><span class="lab"><font color="Green" title="E70">A18</font></span></a>, <a class="ref" href="convex4.html#D23" target="_self" title="CONVEX4:def.23">Def23</a></span>;<br/>
<a NAME="E29:92"/><span class="kw">then </span><span class="lab"><font color="Green" title="E74">A22</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c12">u2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v2</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E27:92"><span class="lab"><font color="Green" title="E73">A21</font></span></a></span>;<br/>
<a NAME="E30:92"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c14">x1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c13">y1</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c2">M1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:92"><span class="lab"><font color="Green" title="E53">A1</font></span></a>, <a class="txt" href="#E3:92"><span class="lab"><font color="Green" title="E55">A3</font></span></a>, <a class="txt" href="#E19:92"><span class="lab"><font color="Green" title="E67">A15</font></span></a>, <a class="txt" href="#E16:92"><span class="lab"><font color="Green" title="E65">A13</font></span></a>, <a class="ref" href="convex4.html#D23" target="_self" title="CONVEX4:def.23">Def23</a></span>;<br/>
<a NAME="E31:92"/><span class="kw">then </span><span class="lab"><font color="Green" title="E75">A23</font></span>: 
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E20:92"><span class="lab"><font color="Green" title="E68">A16</font></span></a></span>;<br/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c11">u1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c12">u2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c10">v2</font></span>)</span></span>)</span> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c12">u2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <span class="p2">(<span class="default"><font color="Maroon" title="c9">v1</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Maroon" title="c10">v2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c12">u2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="clvect_1.html#D2" title="CLVECT_1:def.2">CLVECT_1:def 2</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c12">u2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p3">(<span class="default"><span class="p4">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c12">u2</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v2</font></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c11">u1</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c9">v1</font></span>)</span></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c12">u2</font></span>)</span> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c10">v2</font></span>)</span></span>)</span>
<span class="kw">by</span> <span class="lab"><a class="ref" href="rlvect_1.html#D3" title="RLVECT_1:def.3">RLVECT_1:def 3</a></span>
;<br/>
<span class="kw">hence </span><a NAME="E33:92"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c8">s</font> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c6">u</font></span>)</span> <a href="algstr_0.html#K1" title="ALGSTR_0:func.1">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="complex1.html#K6" title="COMPLEX1:func.6">1r</a> <a href="complex1.html#K11" title="COMPLEX1:func.11">-</a> <font color="Maroon" title="c8">s</font></span>)</span> <a href="clvect_1.html#K1" title="CLVECT_1:func.1">*</a> <font color="Maroon" title="c7">v</font></span>)</span> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1">(<span class="default"><font color="Maroon" title="c4">z1</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c2">M1</font></span>)</span> <a href="rusub_4.html#K7" title="RUSUB_4:func.7">+</a> <span class="p1">(<span class="default"><font color="Maroon" title="c5">z2</font> <a href="convex4.html#K19" title="CONVEX4:func.19">*</a> <font color="Maroon" title="c3">M2</font></span>)</span>
 <span class="kw">by</span> <span class="lab"><a class="txt" href="#E11:92"><span class="lab"><font color="Green" title="E61">A9</font></span></a>, <a class="txt" href="#E7:92"><span class="lab"><font color="Green" title="E58">A6</font></span></a>, <a class="txt" href="#E31:92"><span class="lab"><font color="Green" title="E75">A23</font></span></a>, <a class="txt" href="#E29:92"><span class="lab"><font color="Green" title="E74">A22</font></span></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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