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<span class="kw">take </span>
 <a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">W</font>)
; <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"> ( (  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c4">V</font> holds  <span class="p1">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">W</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">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="Olive" title="b1">x</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="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">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="Olive" title="b2">y</font></span>)</span> ) &amp; (  for <font color="Olive" title="b1">a</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">x</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c4">V</font> holds  <span class="p1">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">W</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">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="Olive" title="b2">x</font></span>)</span> ) )</span><br/>

<span class="kw">thus </span><a NAME="E1:73_1_1"/>
( (  for <font color="Olive" title="b1">x</font>, <font color="Olive" title="b2">y</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c4">V</font> holds  <span class="p1">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">W</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">x</font> <a href="rlvect_1.html#K3" title="RLVECT_1:func.3">+</a> <font color="Olive" title="b2">y</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">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="Olive" title="b1">x</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="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">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="Olive" title="b2">y</font></span>)</span> ) &amp; (  for <font color="Olive" title="b1">a</font> being   <a href="vectsp_1.html#NM6" title="VECTSP_1:NM.6">Scalar</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">x</font> being   <a href="vectsp_1.html#NM8" title="VECTSP_1:NM.8">Vector</a> of <font color="Maroon" title="c4">V</font> holds  <span class="p1">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">W</font>)</span>)</span> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">a</font> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <font color="Olive" title="b2">x</font></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c3">J</font> <a href="funct_2.html#K3" title="FUNCT_2:func.3">.</a> <font color="Olive" title="b1">a</font></span>)</span> <a href="vectsp_1.html#K3" title="VECTSP_1:func.3">*</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default"><a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">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="Olive" title="b2">x</font></span>)</span> ) )
 <span class="kw">by</span> <span class="lab"><a class="txt" href="mod_4.html#E72"><span class="lab"><font color="Green" title="E35">Lm16</font></span></a>, <a class="txt" href="mod_4.html#E73"><span class="lab"><font color="Green" title="E36">Lm17</font></span></a></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"> verum</span><br/>


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