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<span class="kw">let </span><font color="Maroon" title="c1">K</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Field</a>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">V</font> being non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font><br/> for <font color="Olive" title="b2">v</font>, <font color="Olive" title="b3">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Olive" title="b1">V</font><br/> for <font color="Olive" title="b4">W</font> being   <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b2">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>  st <font color="Olive" title="b2">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Olive" title="b1">V</font> &amp; <font color="Olive" title="b3">w</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b4">W</font> holds <br/><span class="p1">(<span class="default"><a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Olive" title="b2">v</font>,<font color="Olive" title="b4">W</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b3">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">V</font> be  non  <a href="struct_0.html#V7" title="STRUCT_0:attr.7">trivial</a>  <a href="vectsp_1.html#NM7" title="VECTSP_1:NM.7">VectSp</a> of <font color="Maroon" title="c1">K</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">v</font>, <font color="Olive" title="b2">w</font> being  <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font><br/> for <font color="Olive" title="b3">W</font> being   <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Olive" title="b1">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>  st <font color="Olive" title="b1">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> &amp; <font color="Olive" title="b2">w</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b3">W</font> holds <br/><span class="p1">(<span class="default"><a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Olive" title="b1">v</font>,<font color="Olive" title="b3">W</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b2">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">v</font>, <font color="Maroon" title="c4">w</font> be   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c2">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">W</font> being   <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>  st <font color="Maroon" title="c3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> &amp; <font color="Maroon" title="c4">w</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Olive" title="b1">W</font> holds <br/><span class="p1">(<span class="default"><a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Maroon" title="c3">v</font>,<font color="Olive" title="b1">W</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">W</font> be    <a href="vectsp_5.html#M1" title="VECTSP_5:mode.1">Linear_Compl</a> of  <a href="vectsp_7.html#K1" title="VECTSP_7:func.1">Lin</a> <span class="p1"><a href="domain_1.html#K6" title="DOMAIN_1:func.6">{</a><span class="default"><font color="Maroon" title="c3">v</font></span><a href="domain_1.html#K6" title="DOMAIN_1:func.6">}</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font> &amp; <font color="Maroon" title="c4">w</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font> implies <span class="p1">(<span class="default"><a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c5">W</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font> )</span><br/>







<span class="kw">assume </span><span class="kw">that </span><br/><a NAME="E1:58"/><span class="lab"><font color="Green" title="E32">A1</font></span>: 
<font color="Maroon" title="c3">v</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c2">V</font>
 <span class="kw">and </span><br/><a NAME="E2:58"/><span class="lab"><font color="Green" title="E33">A2</font></span>: 
<font color="Maroon" title="c4">w</font> <a href="struct_0.html#R1" title="STRUCT_0:pred.1">in</a> <font color="Maroon" title="c5">W</font>
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c5">W</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">w</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font></span><br/>

<span class="kw">set </span><font color="Maroon" title="c6">cf</font> =  <a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c5">W</font>;<br/>
<span class="kw">set </span><font color="Maroon" title="c7">cw</font> = the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">W</font>;<br/>
<span class="kw">reconsider </span><font color="Maroon" title="c8">s</font> = <font color="Maroon" title="c4">w</font> as   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Vector</a> of <font color="Maroon" title="c5">W</font> <span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
<a NAME="E4:58"/>
<font color="Maroon" title="c4">w</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">W</font>
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E2:58"><span class="lab"><font color="Green" title="E33">A2</font></span></a>, <a class="ref" href="struct_0.html#D5" title="STRUCT_0:def.5">STRUCT_0:def 5</a></span>;<br/>
<span class="kw">hence </span><span class="p1">(<span class="default"><a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c5">W</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c4">w</font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="vectsp10.html#K7" title="VECTSP10:func.7">coeffFunctional</a> <font color="Maroon" title="c3">v</font>,<font color="Maroon" title="c5">W</font></span>)</span> <a href="relset_1.html#K5" title="RELSET_1:func.5">|</a> the <a href="struct_0.html#U1" title="STRUCT_0:sel.1">carrier</a> of <font color="Maroon" title="c5">W</font></span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c4">w</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="funct_1.html#T72" title="FUNCT_1:th.72">FUNCT_1:72</a></span>
<br/>.= 
<span class="p1">(<span class="default"><a href="hahnban1.html#K7" title="HAHNBAN1:func.7">0Functional</a> <font color="Maroon" title="c5">W</font></span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Maroon" title="c8">s</font>
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:58"><span class="lab"><font color="Green" title="E32">A1</font></span></a>, <a class="ref" href="vectsp10.html#D8" target="_self" title="VECTSP10:def.8">Def8</a></span>
<br/>.= 
 <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <font color="Maroon" title="c1">K</font>
<span class="kw">by</span> <span class="lab"><a class="ref" href="hahnban1.html#T22" title="HAHNBAN1:th.22">HAHNBAN1:22</a></span>
;<br/> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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