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<span class="kw">let </span><font color="Maroon" title="c1">K</font>, <font color="Maroon" title="c2">L</font> be   <a href="vectsp_1.html#NM3" title="VECTSP_1:NM.3">Ring</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">  for <font color="Olive" title="b1">J</font> being   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">L</font><br/>  for <font color="Olive" title="b2">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b3">W</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c2">L</font> holds   <a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">W</font>) is    <a href="mod_4.html#M1" title="MOD_4:mode.1">Homomorphism</a> of <font color="Olive" title="b1">J</font>,<font color="Olive" title="b2">V</font>,<font color="Olive" title="b3">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c3">J</font> be   <a href="struct_0.html#NM6" title="STRUCT_0:NM.6">Function</a> of <font color="Maroon" title="c1">K</font>,<font color="Maroon" title="c2">L</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">V</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c1">K</font><br/>  for <font color="Olive" title="b2">W</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c2">L</font> holds   <a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font>) is    <a href="mod_4.html#M1" title="MOD_4:mode.1">Homomorphism</a> of <font color="Maroon" title="c3">J</font>,<font color="Olive" title="b1">V</font>,<font color="Olive" title="b2">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c4">V</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c1">K</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">W</font> being   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c2">L</font> holds   <a href="grcat_1.html#K6" title="GRCAT_1:func.6">ZeroMap</a> (<font color="Maroon" title="c4">V</font>,<font color="Olive" title="b1">W</font>) is    <a href="mod_4.html#M1" title="MOD_4:mode.1">Homomorphism</a> of <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">V</font>,<font color="Olive" title="b1">W</font></span><br/><span class="kw">let </span><font color="Maroon" title="c5">W</font> be   <a href="vectsp_2.html#NM5" title="VECTSP_2:NM.5">LeftMod</a> of <font color="Maroon" title="c2">L</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">  <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>) is    <a href="mod_4.html#M1" title="MOD_4:mode.1">Homomorphism</a> of <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">W</font></span><br/>









<span class="kw">set </span><font color="Maroon" title="c6">z</font> =  <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>);<br/>
<a NAME="E1:74"/>
( (  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>;<br/>
<span class="kw">hence </span><a NAME="E2:74"/>
 <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>) is    <a href="mod_4.html#M1" title="MOD_4:mode.1">Homomorphism</a> of <font color="Maroon" title="c3">J</font>,<font color="Maroon" title="c4">V</font>,<font color="Maroon" title="c5">W</font>
 <span class="kw">by</span> <span class="lab"><a class="ref" href="mod_4.html#D17" target="_self" onmouseover="rs('mod_4/D17')" onmouseout="rh()">Def17</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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