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<b>let </b><font color="Maroon" title="c1">V</font> be   <a href="rlvect_1.html#NM2" title="RLVECT_1:NM.2">RealLinearSpace</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> for <font color="Olive" title="b1">w1</font>, <font color="Olive" title="b2">w2</font>, <font color="Olive" title="b3">w3</font> being  <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font> holds <br/> ( <font color="Olive" title="b1">w1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b1">w1</font>,<font color="Olive" title="b2">w2</font>,<font color="Olive" title="b3">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Olive" title="b2">w2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b1">w1</font>,<font color="Olive" title="b2">w2</font>,<font color="Olive" title="b3">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Olive" title="b3">w3</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Olive" title="b1">w1</font>,<font color="Olive" title="b2">w2</font>,<font color="Olive" title="b3">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> )</span><br/><b>let </b><font color="Maroon" title="c2">w1</font>, <font color="Maroon" title="c3">w2</font>, <font color="Maroon" title="c4">w3</font> be   <a href="rlvect_1.html#NM1" title="RLVECT_1:NM.1">VECTOR</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">w1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c3">w2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c4">w3</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> )</span><br/>







<a NAME="E1:19"/>
( <font color="Maroon" title="c2">w1</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c3">w2</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c4">w3</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> )
 
<b>by </b><i><a class="ref" href="enumset1.html#D1" title="ENUMSET1:def.1">ENUMSET1:def 1</a></i>;<br/>
<b>hence </b><a NAME="E2:19"/>
( <font color="Maroon" title="c2">w1</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c3">w2</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> &amp; <font color="Maroon" title="c4">w3</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a>  <a href="rlvect_3.html#K1" title="RLVECT_3:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K8" title="DOMAIN_1:func.8">{</a><span class="default"><font color="Maroon" title="c2">w1</font>,<font color="Maroon" title="c3">w2</font>,<font color="Maroon" title="c4">w3</font></span><a href="domain_1.html#K8" title="DOMAIN_1:func.8">}</a></span> )
 <b>by </b><i><a class="ref" href="rlvect_3.html#T18" title="RLVECT_3:th.18">RLVECT_3:18</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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