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<span class="kw">let </span><font color="Maroon" title="c3">a</font> be    <a href="hidden.html#M1" title="HIDDEN:mode.1">object</a> ; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="valued_0.html#D12" onmouseover="rs('valued_0/D12')" onmouseout="rh()">VALUED_0:def 12</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> (  not <font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK1" title="RELAT_1:NK.1">dom</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Maroon" title="c2">x</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span> or <span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Maroon" title="c2">x</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a>  )</span><br/>

<span class="kw">assume </span><a NAME="E1:12_1_1"/><span class="lab"><font color="Green" title="E3">A1</font></span>: 
<font color="Maroon" title="c3">a</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Maroon" title="c2">x</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span>
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Maroon" title="c2">x</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> </span><br/>

<a NAME="E2:12_1_1"/>
( <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="hilbasis.html#K2" title="HILBASIS:func.2">UnitBag</a> <font color="Maroon" title="c2">x</font> or <font color="Maroon" title="c3">a</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="hilbasis.html#K2" title="HILBASIS:func.2">UnitBag</a> <font color="Maroon" title="c2">x</font> )
 
;<br/>
<a NAME="E3:12_1_1"/><span class="kw">then </span>
( <span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Maroon" title="c2">x</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="group_1.html#K1" title="GROUP_1:func.1">1_</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> or <span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Maroon" title="c2">x</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K4" title="STRUCT_0:func.4">0.</a> <a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a> )
 
<span class="kw">by</span> <span class="lab"><a class="txt" href="#E1:12_1_1"><span class="lab"><font color="Green" title="E3">A1</font></span></a>, <a class="ref" href="hilbasis.html#T12" onmouseover="rs('hilbasis/T12')" onmouseout="rh()">HILBASIS:12</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:12_1_1"/>
<span class="p1">(<span class="default"><a href="hilbasis.html#K3" title="HILBASIS:func.3">1_1</a> (<font color="Maroon" title="c2">x</font>,<a href="vectsp_1.html#K2" title="VECTSP_1:func.2">F_Real</a>)</span>)</span> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Maroon" title="c3">a</font> is  <a href="ordinal1.html#V7" title="ORDINAL1:attr.7">natural</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" 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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